## 1=.999999...?

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### Re: 1=.999999...?

Wonderer wrote:
Sidhe wrote:
Wonderer wrote:and it doesn't mean it is.

I am more than satisfied with my understanding of math.

maybe you're getting me wrong and think I'm saying that .333 cannot or should not be used as being equal to 1/3. Pragmatically .333 bar does equal 1/3, it's just an error in logic to look at the pattern and say it equals one. looking at the pattern it's obvious beyond argument that the number approaches 1/3 but never reaches one third. this means that with infinite 3's it will simply be infinitely close to 1/3, making it pragmatically equal to 1/3.

people simply need to make that extra bit of effort to think the problem out

You mean mathematicians need to accept that there axioms are wrong and yours are right because you say so. You can try convincing them but I don't think you'll get anywhere, set theory and thus all maths depends on them. Without them you might as well bin it and start with something you like that doesn't apply to any number system we know. Your choice, I sincerely hope that it works for you, and have no problem with you saying that. Just don't study maths at degree level you'll be lost.

It takes no effort for me to say I cannot conceive of infinity.

look I'm not trying to dictate "axioms". i'm just pointing out an inconsequential logical inconsistency.

what I'm saying is that an infinite amount of digits after a decimal place does not allow us to "round up" the number without losing some theoretical precision, even if it is infinitesimally small.

i don't know how i can say this in terms i havn't already. Imagine chopping down a tree. let's say with each chop you take down half of what is left on the tree.

how many chops will it take to get rid of the tree? infinite?

with such a chopping strategy there will always be a remainder, regardless of infinity or not.

the idea is to make the remainder so small it doesn't matter.

I know what you are trying to do it is not illogical at all to say .999...=1. No offence but try there. If they don't bin the thread through having seen it turn up to often to care to prove set/number theory to you. You might get somewhere. I'm out though. I genuinely without sarcasm think you should ask this, because it'll give you a greater understanding of what maths is, and what infinities mean. So don't take my ennui as being churlish. i appreciate that but i won't be needing any other opinions. i have been told the same thing about 50 000 times.

you see my head as being screwy, i see all you guys as being unable to see the logical error.

In that case maths is not for you. No offence or slight intended.

You have to realise that maths is a self contained number system, that is not reflective absolutely of reality. There are no numbers in reality only numbers of things. Thus you can define them to preserve the application when it comes to number of things without any need to say it is illogical. It might be axiomatic but it works and without it maths is trashed and useless.
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### Re: 1=.999999...?

as i said before my comprehension is more than adequate.

i have spoken to many mathematicians on many forums and in real life. in real life everyone seems to agree with me but there are many people who do not on these forums.

they tell me it comes down to a matter of acceptance. the way i see it looking past a trivial error like the .999bar = 1 proof isn't hard, what is hard is understanding it as an issue in the first place.

I don't believe i need to be shown any proofs, i just want someone to address the logical inconsistency i am pointing out.

call it gravy for the sake of math perhaps?
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### Re: 1=.999999...?

Wonderer wrote:as i said before my comprehension is more than adequate.

i have spoken to many mathematicians on many forums and in real life. in real life everyone seems to agree with me but there are many people who do not on these forums.

they tell me it comes down to a matter of acceptance. the way i see it looking past a trivial error like the .999bar = 1 proof isn't hard, what is hard is understanding it as an issue in the first place.

I don't believe i need to be shown any proofs, i just want someone to address the logical inconsistency i am pointing out.

call it gravy for the same of math perhaps?

Yes when applied to reality there are no actual infinities. The Greeks realised this ~2400 years ago. It's only illogical if you want to make maths something it isn't. That's of course up to you.

Everything about pure maths is conceptual not real. Sets don't exist, nor do infinities, nor a cardinality of infinities they are just useful axioms in the closed system that is maths.

I don't think it's a matter of acceptance it's a matter of not caring about useless trivialities that have no application. I suppose that's where we differ. I understand what you mean, I just don't see the need to define things in terms of it, to point out that maths isn't ultimately reality. All mathematicians know this, but have moved beyond the trivial truth. If maths was ultimately truth there would be no need for science or philosophy.
Last edited by Sidhe on Mon May 04, 2009 9:09 pm, edited 2 times in total.
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### Re: 1=.999999...?

just useful?

sacrificing logic for function is foolish if you aren't aware of the sacrifice.

math is just quantitative logic. sometimes we mar theory to make it fit reality better, i'm just pointing this out.

i just want people to realize that an infinite sequence of 9's after a decimal does not actually equal 1 in reality or theory. (in reality it might as well)
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### Re: 1=.999999...?

Wonderer wrote:just useful?

sacrificing logic for function is foolish if you aren't aware of the sacrifice.

math is just quantitative logic. sometimes we mar theory to make it fit reality better, i'm just pointing this out.

Fair enough then we are agreed. It is quantitative logic not literally real. I think modal logic and language are capable substitutes for our lack of comprehension of a concept we could never conceive of. You can spend a life time analysing something that you will never comprehend. There just seems not point or use for such a venture. We don't sacrifice logic for function, we sacrifice it for general all encompassing utility in mathematical theory and application.

Maths has limits and logical limitations, understood, thus logic can transcend maths. "Only two things are infinite, the universe and human stupidity, and I'm not sure about the former. –- Albert Einstein

"The notion of infinity is our greatest friend; it is also the greatest enemy of our peace of mind." -- James Pierpont

"The infinite! No other question has ever moved so profoundly the spirit of man." -- David Hilbert

"[Paradoxes of the infinite arise] only when we attempt, with our finite minds, to discuss the infinite, assigning to it those properties which we give to the finite and limited;" -- Galileo Galilei

"The infinite in mathematics is always unruly unless it is properly treated." -- Edward Kasner and James Newman

"God created infinity, and man, unable to understand infinity, had to invent finite sets." -- Gian Carlo Rota
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### Re: 1=.999999...?

imagine if you wrote the test to become God, it has an infinite amount of questions.

pretend for a second you answered them all, and you only got 1 wrong.

did you get 100%?

did you get .999[bar]?

if you cut an orange into 3 perfect pieces, one piece can be considered .333[bar]/1 of a whole orange.

so when you add the three pieces together, do you have .999[bar]/1 of a whole orange?

where did that little piece go?

here is how i understand the problem, and here is where i blame the loss of precision.

dividing one into three leaves you carrying the 3 forever. it's an impossible action. There literally is no number for 1/3 other than a presumed infinitely long series of .3's. 1/3 simply cannot be expressed as a single digit. the time bound physical world guarantees this.

what this means is when you calculate something with .3[bar] involved you are going to lose whatever precision depending on how many digits of precision you used (it's inevitable that you lose precision when using the [bar] form because you can never use infinite digits)

to show this we look at the equations from the opening post.

we get 9.999[bar], but we have already lost some precision

when we multiplied the number .999[bar] by ten, we simply moved the decimal place up one. because we calculate with imprecision (meaning there is a last 9 in our calculations), we actually added an extra 9 into our calculations.

The decimal stays where it's at, and we move the whole sequence of numbers one spot to the left, to make it ten times greater. what happens when we do this is that at the imaginary end of the sequence, another 9 pops into where a zero should go.

so when you subtract a regular .999[bar] from a 10(.999[bar]) = 9.999[bar] - .999[bar] you actually get less than 9, which is exactly how the proof from the op steps out of logic and produces the trivial loophole on which this thread is based.

I hope this is comprehensible.
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### Re: 1=.999999...?

Wonderer wrote:imagine if you wrote the test to become God, it has an infinite amount of questions.

pretend for a second you answered them all, and you only got 1 wrong.

did you get 100%?

did you get .999[bar]?

Was I that petty that I decided that even though it was almost infinitely accurate and that I could actually by definition never finish the test. I gave myself 99.999 and almost infinite .99 instead of 100% so I missed out on the A* and got A. Would I be a God or an arsehole.

if you cut an orange into 3 perfect pieces, one piece can be considered .333[bar]/1 of a whole orange.

so when you add the three pieces together, do you have .999[bar]/1 of a whole orange?

where did that little piece go?

Nowhere your making petty dilineations on integrals, if you don't even understand integration then maths is definitely beyond you at University. try a tailor series of the number 1/3. .333... is decimal shorthand for a third. By definition you can't cut an orange into .333 to infinity -1 anyway, it doesn't exist. If you cut it into 3 pieces all precisely the same size to the planck scale then it is 1/3 or ~0.33333333333333333333333333333333333333333333333333333333333333333333333333 which is close enough.

History

The Greek philosopher Zeno considered the problem of summing an infinite series to achieve a finite result, but rejected it as an impossibility: the result was Zeno's paradox. Later, Aristotle proposed a philosophical resolution of the paradox, but the mathematical content was apparently unresolved until taken up by Democritus and then Archimedes. It was through Archimedes's method of exhaustion that an infinite number of progressive subdivisions could be performed to achieve a finite result. Liu Hui independently employed a similar method a few centuries later.

In the 14th century, the earliest examples of the use of Taylor series and closely-related methods were given by Madhava of Sangamagrama. Though no record of his work survives, writings of later Indian mathematicians suggest that he found a number of special cases of the Taylor series, including those for the trigonometric functions of sine, cosine, tangent, and arctangent. The Kerala school of astronomy and mathematics further expanded his works with various series expansions and rational approximations until the 16th century.

In the 17th century, James Gregory also worked in this area and published several Maclaurin series. It was not until 1715 however that a general method for constructing these series for all functions for which they exist was finally provided by Brook Taylor, after whom the series are now named.

The Maclaurin series was named after Colin Maclaurin, a professor in Edinburgh, who published the special case of the Taylor result in the 18th century.

Let's put this simply you said perfect pieces right so by definition they are exactly 1/3 to the limit of infinity. You've just defined why .333...=1/3 beautifully, well done.

here is how i understand the problem, and here is where i blame the loss of precision.

Do you really think the best minds in maths care to know that there axioms are not infinitely correct, because infinities are paradoxical and can't exist in reality?

dividing one into three leaves you carrying the 3 forever. it's an impossible action. There literally is no number for 1/3 other than a presumed infinitely long series of .3's. 1/3 simply cannot be expressed as a single digit. the time bound physical world guarantees this.

Brilliant so? We all know this, it's like your saying something that to a maths idiot would be a revelation, but sounds to me like a platitude.

what this means is when you calculate something with .3[bar] involved you are going to lose whatever precision depending on how many digits of precision you used (it's inevitable that you lose precision when using the [bar] form because you can never use infinite digits)

No you are. If something had 10000000000000000000000 decimals, then nothing in the Universe would be inaccurate until we reach the level beyond the planck scale where nothing actually exists as such as a definite particle.

to show this we look at the equations from the opening post.

we get 9.999[bar], but we have already lost some precision

No we haven't you just can't understand that that means 1/10th or.999... of an orange in decimal shorthand because your obsessed with something that is paradoxical.

when we multiplied the number .999[bar] by ten, we simply moved the decimal place up one. because we calculate with imprecision (meaning there is a last 9 in our calculations), we actually added an extra 9 into our calculations.

The decimal stays where it's at, and we move the whole sequence of numbers one spot to the left, to make it ten times greater. what happens when we do this is that at the imaginary end of the sequence, another 9 pops into where a zero should go.

so when you subtract a regular .999[bar] from a 10(.999[bar]) = 9.999[bar] - .999[bar] you actually get less than 9, which is exactly how the proof from the op steps out of logic and produces the trivial loophole on which this thread is based.

I hope this is comprehensible.

It is but it's pointlessly pedantic. You can't move the decimal to the left or right of a number that never ends anyway. So you're essentially being monumentally anal about something that doesn't exist except as a concept? Why bother? It's just pointless.

Prove x^2/x = infinity.

Why would I say oh wait infinity can't exist so it's undefined? Am I a moron or do I accept that x^2 increases arbitrarily faster than x and at the limit of the infinite will = infinity? Or do I just throw the concept in the bin and fundamentally agree that all maths is shit and worthless.

Having OCD over infinity is pointless. You need to get over yourself and accept that infinity is a paradox that has no physical reality. Once you accept that then the whole of maths in number theory becomes 100% accurate anyway, like it always was before you decided to make an issue of nothing literally. Or the difference between .999... and 1 at lim---->infinity.

Why is 0/infinity=0. But infinity/0 undefined? Why does 0^0=1? and 1^0=1? isn't 1 larger than 0? Answer that and you have number theory and a glimpse at what the concept means, if not the number, infinity isn't a numerically expressible number. It is the limit of everything to which everything asymptotically approaches but never reaches.

This is why the universe is of finite size and also infinite. That's probably the only example of infinity that isn't paradoxical.

The Isha Upanishad of the Yajurveda (c. 4th to 3rd century BC) states that "if you remove a part from infinity or add a part to infinity, still what remains is infinity".

Pūrṇāt pūrṇam udacyate
Pūrṇasya pūrṇam ādāya
Pūrṇam evāvasiṣyate.

That is whole, this is whole
From the whole, the whole arises
When the whole is taken from the whole
The whole still will remain — Isha Upanishad.

The Indian mathematical text Surya Prajnapti (c. 400 BC) classifies all numbers into three sets: enumerable, innumerable, and infinite. Each of these was further subdivided into three orders:

* Enumerable: lowest, intermediate and highest
* Innumerable: nearly innumerable, truly innumerable and innumerably innumerable
* Infinite: nearly infinite, truly infinite, infinitely infinite
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### Re: 1=.999999...?

Sidhe...Fractions are not numbers... That is the question here, whether in multiplying a fraction so that it should be one, whether it is the same as one... So; are the parts equal to the whole??? Can we even represent fractions as numbers... To me, units are units because they cannot be divided... If you ever do divide a unit you get equalities, and they can not be shown to be equal... Math is just an abstraction of reality, and it suffers as all abstractions from the fact that it cannot be examined as are objects, as realities in their own right...When math says something that is contrary to logic, there is no way to disprove it with math...Identity is essential to logic...Is it possible for math to contradict its most basic premise??? The whole thing should fold like a house of cards...
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### Re: 1=.999999...?

Wonderer wrote:just useful?

sacrificing logic for function is foolish if you aren't aware of the sacrifice.

math is just quantitative logic. sometimes we mar theory to make it fit reality better, i'm just pointing this out.

i just want people to realize that an infinite sequence of 9's after a decimal does not actually equal 1 in reality or theory. (in reality it might as well)

That, one is one is the identity upon which all the logic of math is based... Do you think it is possible in theory for the logic of math to actually contradict the identity upon which it is based??? If you come by .9999.... by multiplying .333..by three..... then everyone knows the answer must be one, and not some fraction, or decimal representation of one... Math says one thing, and the mind says another...What then, is correct??? We know units are units because they cannot be divided...If it were possible to divide one so that, recombined it could be one, the one would not be a true unit... A dollar is not a unit because it can be divided into pennies... A penny is a unit...Try to divide that...
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### Re: 1=.999999...?

Anyone that's denying the equation's preicions clearly has not actually taken any math courses and has no understanding of it. The problem can alternatively be solved by proving 1/x=0 as x->infinity using l'hopital's rule (which you can easily find and hopefully understand if you just look it up on wolfram mathworld). This entire thread is one giant retarded example of a pseudoanalytical approach to a numerical problem. Holy fuck. Ing shit. the weak man wishes to die nobly for...the strong man wishes to live humbly for... oh yeah he died bravely
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### Re: 1=.999999...?

Juggernaut wrote:Sidhe...Fractions are not numbers... That is the question here, whether in multiplying a fraction so that it should be one, whether it is the same as one... So; are the parts equal to the whole??? Can we even represent fractions as numbers... To me, units are units because they cannot be divided... If you ever do divide a unit you get equalities, and they can not be shown to be equal... Math is just an abstraction of reality, and it suffers as all abstractions from the fact that it cannot be examined as are objects, as realities in their own right...When math says something that is contrary to logic, there is no way to disprove it with math...Identity is essential to logic...Is it possible for math to contradict its most basic premise??? The whole thing should fold like a house of cards...

Why are you talking to me, quick go out and by a calculus book... Of course if I slice an orange into three exactly equal parts, it's a fraction 1/3 and .333...

Say I take a sphere 1kg uniform mass and divide it into 2 equal parts.

What's the integral of x dx? Now what is it for limits 0 and 1? Now 0-2? Now infinity? is it exactly 1/2kg? or 0.5kg What

So integral x dx=1/2x^2.

Or the general integral = 1/n+1x^(n+1).

Where x = x^1 or itself.

Say I take a sphere of xkg uniform mass and divide it into 3 equal parts what do I get? I get as an integral of that?

1/6x^2.kg what does it equal 0-1? 0-100? infinity?

Now do 4 and then all the fractions up to 100? What do you find as any fraction approaches infinity? If you have a maths program like mine that can do very large integers or numbers of decimal places (dps), you notice that eventually the program throws out a fraction, when the limits get large enough say 1^10x1000000000000000000000 instead of a decimal approximation to x sig fig. It's not doing this arbitrarily though even when I still have say 2000 or 20,000 dps to go it still throws out a fraction for many sums. Can we assume it's true for both 1/2,1/3,1/4,1/5,1/6,1/7,1/8,1/9,1/10,1,11...x/infinity? I'd say that was perfectly logical.

Integration is taking the whole and dividing it into exactly equal parts to the limit of infinity, the more parts you have the more accurate it is. This shows that any decimal= any fraciton lim x-----> infinity.

Ahhhhhhhhhhhhhhhh, wonders away with cane blindly tapping the path ahead.

This is the problem with people who like logic but have no grasp whatsoever of limits or infinity or number theory.

Infinity is indivisible but we can as a concept divide it, you cannot subtract or add anything to it in reality, but it's useful as an assymptote or limit to which anything approaches but is never equal to.

If number theory real did contradict it's most basic tenet do you think anyone would use it? Christ on a unicycle.  Here's something for you.

The infinity of all decimals and the infinity of all fractions are the same, ie they are 1 to 1 and add up to the same "number"?!?! But how!!. Put that in your pipe and smoke it. In the cardinality of infinities aleph 0 the N whole numbers = aleph 1 the fractions = aleph 2 the decimals and so on. We can prove this as for every fraction 1/1,1/2,1/3 and so on there is exactly one whole real number. Vis a vis maths works.

Now is there 1 decimal for every fraction? Yes there is you've won a prize! Therefore .333=1/3 at the limit of infinity, ta da!

Any chance of any comprehension at all?   ref: Maths for dummies. pg x-x^2

These simple but axiomatic tenets use infinity but nothing in maths precisely equates it numerically with the paradox that is all there is, because that is impossible.
Last edited by Sidhe on Tue May 05, 2009 3:33 pm, edited 23 times in total.
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### Re: 1=.999999...?

Rouzbeh wrote:Anyone that's denying the equation's preicions clearly has not actually taken any math courses and has no understanding of it. The problem can alternatively be solved by proving 1/x=0 as x->infinity using l'hopital's rule (which you can easily find and hopefully understand if you just look it up on wolfram mathworld). This entire thread is one giant retarded example of a pseudoanalytical approach to a numerical problem. Holy fuck. Ing shit. Precisely.

Either that and they have and they are just not very good at maths. Either way you're either ignorant or just not cut out to be a mathematician. Perhaps this might help:

Reception of the argument

At the start, Cantor's Theory was controversial among mathematicians and (later) philosophers. As Leopold Kronecker claimed: "I don't know what predominates in Cantor's theory - philosophy or theology, but I am sure that there is no mathematics there." Many mathematicians agreed with Kronecker that the completed infinite may be part of philosophy or theology, but that it has no proper place in mathematics.

Before Cantor, the notion of infinity was often taken as a useful abstraction which helped mathematicians reason about the finite world, for example the use of infinite limit cases in calculus. The infinite was deemed to have at most a potential existence, rather than an actual existence. "Actual infinity does not exist. What we call infinite is only the endless possibility of creating new objects no matter how many exist already" (Poincaré quoted from Kline 1982). Gauss's views on the subject can be paraphrased as: 'Infinity is nothing more than a figure of speech which helps us talk about limits. The notion of a completed infinity doesn't belong in mathematics'. In other words, the only access we have to the infinite is through the notion of limits, and hence, we must not treat infinite sets as if they have an existence exactly comparable to the existence of finite sets.

Cantor's ideas ultimately were largely accepted, strongly supported by David Hilbert, amongst others. Although constructivists and the intuitionists developed their schools of mathematics as a reaction to Cantor's infinitary ideas, most mathematicians do not have qualms about Cantor's Theory. It would appear that Hilbert's prediction has proved mostly accurate: "No one will drive us from the paradise which Cantor created for us" (Hilbert, 1926). To which Wittgenstein replied "if one person can see it as a paradise of mathematicians, why should not another see it as a joke?" (RFM V. 7)...

...Objection to the axiom of infinity
Further information: Finitism

A common objection to Cantor's theory of infinite number involves the axiom of infinity. It is generally recognised view by all logicians that this axiom is not a logical truth. Indeed, as Mark Sainsbury (1979, p.305) has argued "there is room for doubt about whether it is a contingent truth, since it is an open question whether the universe is finite or infinite". Bertrand Russell for many years tried to establish a foundation for mathematics that did not rely on this axiom. Mayberry (2000, p.10) has noted that "The set-theoretical axioms that sustain modern mathematics are self-evident in differing degrees. One of them – indeed, the most important of them, namely Cantor's axiom, the so-called axiom of infinity – has scarcely any claim to self-evidence at all".

Another objection is that the use of infinite sets is not adequately justified by analogy to finite sets. Hermann Weyl wrote:
“ … classical logic was abstracted from the mathematics of finite sets and their subsets …. Forgetful of this limited origin, one afterwards mistook that logic for something above and prior to all mathematics, and finally applied it, without justification, to the mathematics of infinite sets. This is the Fall and original sin of [Cantor's] set theory …."
(Weyl, 1946) ”

Richard Arthur, philosopher and expert on Leibniz, has argued that Cantor's appeal to the idea of an actual infinite (formally captured by the axiom of infinity) is philosophically unjustified. Arthur argues that Leibniz' idea of a "syncategorematic" but actual infinity is philosophically more appealing. (See external link below for one of his papers).

The difficulty with finitism is to develop foundations of mathematics using finitist assumptions, that incorporates what everyone would reasonably regard as mathematics (for example, that includes real analysis).

http://en.wikipedia.org/wiki/Controvers ... 27s_theory
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### Re: 1=.999999...?

Sidhe....I/3 is not an answer, but an unresoved question...If it were possible to cut an orange into three equal parts, it would not be possible to make one orange out of three equal parts... So you say, 3 times 1/3 equals 1...In math only.... Units can not be divided... No whole cow can be made from any number of half cows...If a pound of rice can be divided it is because the unit, a pound, is not a true unit...And I do not need to buy a calculus book to tell me that all of math is based upon a single identity, of one, the unit, which is how we conceive of self and our universe...All numbers are made of one number... Does .999... equal one... As much as that is the question, the answer is: does it add to the utility or the comprehensibility of math... If math is not more simple than reality it is useless as a form....
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### Re: 1=.999999...?

Juggernaut wrote:Sidhe....I/3 is not an answer, but an unresoved question...If it were possible to cut an orange into three equal parts, it would not be possible to make one orange out of three equal parts... So you say, 3 times 1/3 equals 1...In math only.... Units can not be divided... No whole cow can be made from any number of half cows...If a pound of rice can be divided it is because the unit, a pound, is not a true unit...And I do not need to buy a calculus book to tell me that all of math is based upon a single identity, of one, the unit, which is how we conceive of self and our universe...All numbers are made of one number... Does .999... equal one... As much as that is the question, the answer is: does it add to the utility or the comprehensibility of math... If math is not more simple than reality it is useless as a form....

So you are saying if I throw a cup on the floor and it breaks I can't put it back together as it was, is a reason all maths is wrong? I disagree.

I think it's possible to reassemble matter the way it was by running time backwards. And since almost all matter seems CPT (Charge Parity Time) invariant there is no reason that we couldn't cut an atom and then reassemble it using the exact reverse process. Maths is only useless if you don't understand what it is or how it is applied if you ask me. E=mc^2.

UUD Quark.

Is a proton, I could take energy and make a proton, I could smash two protons together and make the exact amount of energy in 2 U and U and Down quarks, that hold the protons together. Or likewise I could make a proton or two given the right amount of energy.

1/3 maybe conceptual but it has applications.

If I took an anti proton and a proton and smashed them together the resultant energy would be exactly 2UUD Quarks in eV plus the momentum energy or 2(1/3Px3)+2a=2+c. I could also from that amount of energy observe the formation of two protons in theory. In fact in experiment too.

Where P=the energy/mass equivalence of a proton.

I also doubt you really understand calculus at all but that's beside the point.
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### Re: 1=.999999...?

Sidhe wrote:
Wonderer wrote:imagine if you wrote the test to become God, it has an infinite amount of questions.

pretend for a second you answered them all, and you only got 1 wrong.

did you get 100%?

did you get .999[bar]?

Was I that petty that I decided that even though it was almost infinitely accurate and that I could actually by definition never finish the test. I gave myself 99.999 and almost infinite .99 instead of 100% so I missed out on the A* and got A. Would I be a God or an arsehole.
so the same logic that tells me .333 cannot work tells you that you cannot finish the test?

this leads into an objection. pretend you did finish the test. if you got them all right, it would be 100%, obviously. And if you got one wrong we have no real idea how to calculate.

intuition tells me 99.9[bar] percent, but then imagine you get two wrong...

you still got 99.9[bar]. this highlights our inability to work with the infinitesimally small differences.

1, 10 or 1 million questions wrong all yield a 99.9% theoretically.

the more 9's we add after the decimal the gap between .999 and 1 closes. the operation continues indefinitely. We assume that an imaginary infinite 9's, like completing an imaginary test of infinite questions, will solve the problem, but infinite 9's or 3's are inadequate. this unworkable infinitesimal is the difference between 1 and the actual limit of .999[bar]. The pattern does not approach 1, it approaches an infinitely precise number which is just under one. and i do mean, just under.

when it comes down to it it's a matter of forgiving a loss of precision, and then picking it up elsewhere later on because the meaning is obvious.

The reason the proof works is because those incalculable differences are lost and then found. lost when the [bar] is used in simple arithmetic and found when
according to calculations

x=.999

.999 X 10 = 9.990

9.990 - .999 = 8.991

doing the operation with the [bar] form creates imprecision. 1 does not equal .999[bar].

.999bar could be said to approach 1 if you define a limit as something that it will never or can never reach.

in this case the limit is still less than 1.

.999[bar] will never reach infinite 9's,
Sidhe wrote:
if you cut an orange into 3 perfect pieces, one piece can be considered .333[bar]/1 of a whole orange.

so when you add the three pieces together, do you have .999[bar]/1 of a whole orange?

where did that little piece go?

Nowhere your making petty dilineations on integrals, if you don't even understand integration then maths is definitely beyond you at University. try a tailor series of the number 1/3. .333... is decimal shorthand for a third. By definition you can't cut an orange into .333 to infinity -1 anyway, it doesn't exist. If you cut it into 3 pieces all precisely the same size to the planck scale then it is 1/3 or ~0.33333333333333333333333333333333333333333333333333333333333333333333333333 which is close enough.
by definition you cannot divide 1 into 3. i agree. we can either call it 1/3, or use .333... which is close enough... Sidhe wrote:
History

The Greek philosopher Zeno considered the problem of summing an infinite series to achieve a finite result, but rejected it as an impossibility: the result was Zeno's paradox. Later, Aristotle proposed a philosophical resolution of the paradox, but the mathematical content was apparently unresolved until taken up by Democritus and then Archimedes. It was through Archimedes's method of exhaustion that an infinite number of progressive subdivisions could be performed to achieve a finite result. Liu Hui independently employed a similar method a few centuries later.

In the 14th century, the earliest examples of the use of Taylor series and closely-related methods were given by Madhava of Sangamagrama. Though no record of his work survives, writings of later Indian mathematicians suggest that he found a number of special cases of the Taylor series, including those for the trigonometric functions of sine, cosine, tangent, and arctangent. The Kerala school of astronomy and mathematics further expanded his works with various series expansions and rational approximations until the 16th century.

In the 17th century, James Gregory also worked in this area and published several Maclaurin series. It was not until 1715 however that a general method for constructing these series for all functions for which they exist was finally provided by Brook Taylor, after whom the series are now named.

The Maclaurin series was named after Colin Maclaurin, a professor in Edinburgh, who published the special case of the Taylor result in the 18th century.

Let's put this simply you said perfect pieces right so by definition they are exactly 1/3 to the limit of infinity. You've just defined why .333...=1/3 beautifully, well done.

well a string of infinite 3's would not really yield a true 1/3, it would be a number indefinably close to 1/3.
Sidhe wrote:
here is how i understand the problem, and here is where i blame the loss of precision.

Do you really think the best minds in maths care to know that there axioms are not infinitely correct, because infinities are paradoxical and can't exist in reality?
you sought me out...

i am not trying to "stick it" to "the best minds in maths".

i don't know about you but i enjoy understanding exceptions, no matter how trivial. but i guess that's just me.

Sidhe wrote:
dividing one into three leaves you carrying the 3 forever. it's an impossible action. There literally is no number for 1/3 other than a presumed infinitely long series of .3's. 1/3 simply cannot be expressed as a single digit. the time bound physical world guarantees this.

Brilliant so? We all know this, it's like your saying something that to a maths idiot would be a revelation, but sounds to me like a platitude.

i would suggest replying to my sentences in bulk, because my sentence begins with "what this means is...". replying to things like this tends to make for dry responses.
Sidhe wrote:
what this means is when you calculate something with .3[bar] involved you are going to lose whatever precision depending on how many digits of precision you used (it's inevitable that you lose precision when using the [bar] form because you can never use infinite digits)

No you are. If something had 10000000000000000000000 decimals, then nothing in the Universe would be inaccurate until we reach the level beyond the planck scale where nothing actually exists as such as a definite particle.
i've came out and said already that this "thing" i have been pointing out makes no difference. that said i fail to see what the planck scale has to do with theoretical numbers (the planck scale is the size of matter that is affected by gravity, and thus, "matters"? perhaps?)
Sidhe wrote:

to show this we look at the equations from the opening post.

we get 9.999[bar], but we have already lost some precision

No we haven't you just can't understand that that means 1/10th or.999... of an orange in decimal shorthand because your obsessed with something that is paradoxical.
i don;t really consider myself obsessed. stubborn perhaps, but more so, correct.

anyway, these numerous replies are getting dry huh? Sidhe wrote:
when we multiplied the number .999[bar] by ten, we simply moved the decimal place up one. because we calculate with imprecision (meaning there is a last 9 in our calculations), we actually added an extra 9 into our calculations.

The decimal stays where it's at, and we move the whole sequence of numbers one spot to the left, to make it ten times greater. what happens when we do this is that at the imaginary end of the sequence, another 9 pops into where a zero should go.

so when you subtract a regular .999[bar] from a 10(.999[bar]) = 9.999[bar] - .999[bar] you actually get less than 9, which is exactly how the proof from the op steps out of logic and produces the trivial loophole on which this thread is based.

I hope this is comprehensible.

It is but it's pointlessly pedantic. You can't move the decimal to the left or right of a number that never ends anyway. So you're essentially being monumentally anal about something that doesn't exist except as a concept? Why bother? It's just pointless.

Prove x^2/x = infinity.

Why would I say oh wait infinity can't exist so it's undefined? Am I a moron or do I accept that x^2 increases arbitrarily faster than x and at the limit of the infinite will = infinity? Or do I just throw the concept in the bin and fundamentally agree that all maths is shit and worthless.
if you cannot "move the decimal" in a number that never ends, how can you multiply it by ten?

and once again, i never said math is shit or worthless. i have admitted many times that the problems this may cause are trivial at best.

now you're making a big deal out of things, and not in a respectable way

Sidhe wrote:
Having OCD over infinity is pointless. You need to get over yourself and accept that infinity is a paradox that has no physical reality. Once you accept that then the whole of maths in number theory becomes 100% accurate anyway, like it always was before you decided to make an issue of nothing literally. Or the difference between .999... and 1 at lim---->infinity.

Why is 0/infinity=0. But infinity/0 undefined?

why is 1/0 undefined?

0 divided by anything is zero. zero divided by zero is conceivably undefined however.
Sidhe wrote:Why does 0^0=1? and 1^0=1? isn't 1 larger than 0? Answer that and you have number theory and a glimpse at what the concept means, if not the number, infinity isn't a numerically expressible number.

It is the limit of everything to which everything asymptotically approaches but never reaches

This is why the universe is of finite size and also infinite. That's probably the only example of infinity that isn't paradoxical.
tell me, why is anything to the power of zero, 1?

Sidhe wrote:
The Isha Upanishad of the Yajurveda (c. 4th to 3rd century BC) states that "if you remove a part from infinity or add a part to infinity, still what remains is infinity".

Pūrṇāt pūrṇam udacyate
Pūrṇasya pūrṇam ādāya
Pūrṇam evāvasiṣyate.

That is whole, this is whole
From the whole, the whole arises
When the whole is taken from the whole
The whole still will remain — Isha Upanishad.

The Indian mathematical text Surya Prajnapti (c. 400 BC) classifies all numbers into three sets: enumerable, innumerable, and infinite. Each of these was further subdivided into three orders:

* Enumerable: lowest, intermediate and highest
* Innumerable: nearly innumerable, truly innumerable and innumerably innumerable
* Infinite: nearly infinite, truly infinite, infinitely infinite

you can add an infinitesimally small number to an infinitesimally small number, and you still have an infinitesimally small number...
Whatever makes you happy. Wonderer
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### Re: 1=.999999...?

Sidhe wrote:
Juggernaut wrote:Sidhe....I/3 is not an answer, but an unresoved question...If it were possible to cut an orange into three equal parts, it would not be possible to make one orange out of three equal parts... So you say, 3 times 1/3 equals 1...In math only.... Units can not be divided... No whole cow can be made from any number of half cows...If a pound of rice can be divided it is because the unit, a pound, is not a true unit...And I do not need to buy a calculus book to tell me that all of math is based upon a single identity, of one, the unit, which is how we conceive of self and our universe...All numbers are made of one number... Does .999... equal one... As much as that is the question, the answer is: does it add to the utility or the comprehensibility of math... If math is not more simple than reality it is useless as a form....

So you are saying if I throw a cup on the floor and it breaks I can't put it back together as it was, is a reason all maths is wrong? I disagree.

I think it's possible to reassemble matter the way it was by running time backwards. And since almost all matter seems CPT (Charge Parity Time) invariant there is no reason that we couldn't cut an atom and then reassemble it using the exact reverse process. Maths is only useless if you don't understand what it is or how it is applied if you ask me. E=mc^2.

You are a funny one...It think it would be possible if I could do the impossible... Get real...You can't fix broke cups, and I can't fix broke people...
UUD Quark.

Is a proton, I could take energy and make a proton, I could smash two protons together and make the exact amount of energy in 2 U and U and Down quarks, that hold the protons together. Or likewise I could make a proton or two given the right amount of energy.

1/3 maybe conceptual but it has applications.

If I took an anti proton and a proton and smashed them together the resultant energy would be exactly 2UUD Quarks in eV plus the momentum energy or 2(1/3Px3)+2a=2+c. I could also from that amount of energy observe the formation of two protons in theory. In fact in experiment too.

Where P=the energy/mass equivalence of a proton.

I also doubt you really understand calculus at all but that's beside the point.

Yes, I don't understand calculus, and you do not understand reality... Better luck to both of us...
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### Re: 1=.999999...?

Juggernaut wrote:Yes, I don't understand calculus, and you do not understand reality... Better luck to both of us...

You sound like a petulant child to be honest, I don't like the rules because I can't grasp that something that even if something were added to it would be infinite, which is undefined and yet defined, which is eternal and asymptotic is just beyond your comprehension. End of the day you still got grounded, and everyone just went on with out you. You want maths to use a conceptual thing that doesn't really exist, but to use it illogically and say .999... is not equal to 1, so that maths doesn't work, and proofs like x^2/x-----> lim ∞ = ∞ are nonsense. Well good luck with that. I really don't think it's maths that is the problem or logic clearly, it's stubborn refusal to even tacitly affirm a concept. It's stubborn refusal to accept or even understand that infinity is everything and thus nothing can be greater than it, if that wasn't the case then indeed .999... would equal something else, but because it is- and your woeful lack of understanding aside - the concept being unknowably large, forces you to reject it intuitively and logically (I wouldn't worry no one can imagine something endless like ∞ it's paradoxical too).

Reality is reality, but infinity something that is endless and innumerate is a paradox and conceptual only, when something approaches it it means that things become increasingly accurate, like integrals, with an infinite number of pixels on a graph the value is exact. Think of it this way, say you have the best graphics card and the best monitor ever made or that will ever be: complete with Pinsharp Crikeyvision™. No matter how many pixels it has, it is not really real, however with infinite pixels, it is exactly the same image as the real, with smoothness that is beyond the level of the measurably finite (just like the line of a graph a differential that's no longer an approximation of the tangent of rate of change dy/dx, or the area under the graph an integral with 100% precision). Without infinity anything is an approximation for which we use +/-. Or in science error margins, for those things that aren't 100% reliably predictable. When scientists hit an infinite they know there is a problem with the theory, because no such thing can exist in a finite Universe (with huge but finite energy), so they create new maths to deal with it like black hole theories, and singularity mechanics. The Universe is both finite, ie its about 41.7 billion years old and about 150 billion light years wide, that is as close to infinite as we can physically get. Those who can't or wont ever comprehend the rules of the infinite and maths I suggest with no offence meant they get over themselves. You don't like maths fine, no one is forcing you to study it. And patently with your so called "logic" you'll never be able to apply it. Everyone's happy. Honestly you'd think some people were molestered by their maths teacher or something. 1+1=2 not 3, .999...+.999=2 not 1.999, live with it or don't. I doubt many mathematicians are going to lose sleep because they are using a term to establish proofs for finite sets, and not as a synonym for God or whatever other "logic" so called logical people want it to be in their own pointless world where infinite can be encompassed and ends. Its you that doesn't understand that infinity isn't a part of reality (beyond the conceptual, think of it like God, something we can approach but who's level we can never attain, who is all and yet nothing divisible ).

yes .999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999=1 =1 might as well be true because nothing can be measured beyond that precision or ever likely will be (we usually round up to the planck scale), but it is not. .999...=1 is though the .999s never stop thus being less than something that never ends is a pretty illogical statement.

In fact its absurd, but then I'm only concerned with the obvious, not adding or taking 1 from something which you can't. Or moving the decimal place one way or another on something that never ends (which obviously becomes pointless). So long story long, it's you who doesn't understand reality, good luck with that.
"I am God": Dawkins

Logic it's not just for smart people anyone can play! Sidhe
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### Re: 1=.999999...?

Sidhe; Math does not work because of specific equality, but because of gross equality... If you say infinity is conceptual only, then it is nothing, or that is a lie.... Which is to say that nothing is conceptual only... Concepts, forms are always drawn from a certain reality, and thins is true even of the notion of infinity, that it extends this act, or moment forever..It is still false, but no less based upon something...
What you say, about .999... + .999...= 2 is false... I would agree if it were twice .999; because close enough is close enough...But of an infinte we can make no true statement, and while math says this equals that, all math is based upon the value of one as one... And one has a certain ratio to all the other numbers, excepting, of course, zero that has no ratio to anything...The difficulty arises of showing that ratio with one represented as an infinite .999... The object of math is ease...The object of all concepts is ease... If we first build the conceptual house the real house is a breeze... And houses are loaded with math, as is all spacial reality, and that is fine, but to introduce the element of time into a spacial concept is filled with problems, not just the difficulty of showing a ratio when one side is an infinite, but dealing with the reality we all know, that time changes everything, and everything changes all the time... We can show 1 is 1 today... We can't say what it will be tomorrow, and certainly not in infinity...
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### Re: 1=.999999...?

Juggernaut wrote:Sidhe; Math does not work because of specific equality, but because of gross equality... If you say infinity is conceptual only, then it is nothing, or that is a lie.... Which is to say that nothing is conceptual only... Concepts, forms are always drawn from a certain reality, and thins is true even of the notion of infinity, that it extends this act, or moment forever..It is still false, but no less based upon something...
What you say, about .999... + .999...= 2 is false... I would agree if it were twice .999; because close enough is close enough...But of an infinte we can make no true statement, and while math says this equals that, all math is based upon the value of one as one... And one has a certain ratio to all the other numbers, excepting, of course, zero that has no ratio to anything...The difficulty arises of showing that ratio with one represented as an infinite .999... The object of math is ease...The object of all concepts is ease... If we first build the conceptual house the real house is a breeze... And houses are loaded with math, as is all spacial reality, and that is fine, but to introduce the element of time into a spacial concept is filled with problems, not just the difficulty of showing a ratio when one side is an infinite, but dealing with the reality we all know, that time changes everything, and everything changes all the time... We can show 1 is 1 today... We can't say what it will be tomorrow, and certainly not in infinity...

The ratio of 1:.999... is exactly one if infinity = unbounded and non numeric, simply all. That's it. You've got it but you don't accept it. So what. Not my problem though it's yours and your inability to accept that concepts aren't real physical objects. If we define infinity as a number to which number systems approach but cannot ever reach then .999...=1. End of story. End of the maths lesson. Don't accept it, but an axiom doesn't become false because you have a grain of sand in your aural canal.

Spacial concept the Universe is the same mass and had the same dimensions it did was when at the singularity, what changed? Scale, scalar, space itself expanded. Thus the Universe has and always will be infinitely infinite.

We can show 1=1 in infinity and we can show .999...=1 easilly and I have done about 15 times now.

If we take all numbers, all fractions and all decimals they are 1 to 1, ie there are the same number of whole numbers as there are fractions and decimals. That's it, it's really that simple.

I can see you wont accept mathematical logic though so I'll leave you to it. There are none so blind as those who will not see, especially when it is this obvious. Time to unsubscribe methinks.
"I am God": Dawkins

Logic it's not just for smart people anyone can play! Sidhe
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### Re: 1=.999999...?

Sidhe wrote:
Juggernaut wrote:Sidhe; Math does not work because of specific equality, but because of gross equality... If you say infinity is conceptual only, then it is nothing, or that is a lie.... Which is to say that nothing is conceptual only... Concepts, forms are always drawn from a certain reality, and thins is true even of the notion of infinity, that it extends this act, or moment forever..It is still false, but no less based upon something...
What you say, about .999... + .999...= 2 is false... I would agree if it were twice .999; because close enough is close enough...But of an infinte we can make no true statement, and while math says this equals that, all math is based upon the value of one as one... And one has a certain ratio to all the other numbers, excepting, of course, zero that has no ratio to anything...The difficulty arises of showing that ratio with one represented as an infinite .999... The object of math is ease...The object of all concepts is ease... If we first build the conceptual house the real house is a breeze... And houses are loaded with math, as is all spacial reality, and that is fine, but to introduce the element of time into a spacial concept is filled with problems, not just the difficulty of showing a ratio when one side is an infinite, but dealing with the reality we all know, that time changes everything, and everything changes all the time... We can show 1 is 1 today... We can't say what it will be tomorrow, and certainly not in infinity...

The ratio of 1:.999... is exactly one if infinity = unbounded and non numeric, simply all. That's it. You've got it but you don't accept it. So what. Not my problem though it's yours and your inability to accept that concepts aren't real physical objects. If we define infinity as a number to which number systems approach but cannot ever reach then .999...=1. End of story. End of the maths lesson. Don't accept it, but an axiom doesn't become false because you have a grain of sand in your aural canal.

Spacial concept the Universe is the same mass and had the same dimensions it did was when at the singularity, what changed? Scale, scalar, space itself expanded. Thus the Universe has and always will be infinitely infinite.

We can show 1=1 in infinity and we can show .999...=1 easilly and I have done about 15 times now.

If we take all numbers, all fractions and all decimals they are 1 to 1, ie there are the same number of whole numbers as there are fractions and decimals. That's it, it's really that simple.

I can see you wont accept mathematical logic though so I'll leave you to it. There are none so blind as those who will not see, especially when it is this obvious. Time to unsubscribe methinks.

The notion of identity is essential to all reasoning; logic, to you...Your notion contradicts the idea that one is one, which is to say, that no other number is one...Well, if we say that fractions are not a true number, but that, depending upon the operation, if a fraction equals one, it is one, then it is the same as any other operation, and there is an end to it...If 3 times 1/3 equals one, it is one, and that is the end of it...
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### Re: 1=.999999...?

Juggernaut wrote:
Sidhe wrote:
Juggernaut wrote:Sidhe; Math does not work because of specific equality, but because of gross equality... If you say infinity is conceptual only, then it is nothing, or that is a lie.... Which is to say that nothing is conceptual only... Concepts, forms are always drawn from a certain reality, and thins is true even of the notion of infinity, that it extends this act, or moment forever..It is still false, but no less based upon something...
What you say, about .999... + .999...= 2 is false... I would agree if it were twice .999; because close enough is close enough...But of an infinte we can make no true statement, and while math says this equals that, all math is based upon the value of one as one... And one has a certain ratio to all the other numbers, excepting, of course, zero that has no ratio to anything...The difficulty arises of showing that ratio with one represented as an infinite .999... The object of math is ease...The object of all concepts is ease... If we first build the conceptual house the real house is a breeze... And houses are loaded with math, as is all spacial reality, and that is fine, but to introduce the element of time into a spacial concept is filled with problems, not just the difficulty of showing a ratio when one side is an infinite, but dealing with the reality we all know, that time changes everything, and everything changes all the time... We can show 1 is 1 today... We can't say what it will be tomorrow, and certainly not in infinity...

The ratio of 1:.999... is exactly one if infinity = unbounded and non numeric, simply all. That's it. You've got it but you don't accept it. So what. Not my problem though it's yours and your inability to accept that concepts aren't real physical objects. If we define infinity as a number to which number systems approach but cannot ever reach then .999...=1. End of story. End of the maths lesson. Don't accept it, but an axiom doesn't become false because you have a grain of sand in your aural canal.

Spacial concept the Universe is the same mass and had the same dimensions it did was when at the singularity, what changed? Scale, scalar, space itself expanded. Thus the Universe has and always will be infinitely infinite.

We can show 1=1 in infinity and we can show .999...=1 easilly and I have done about 15 times now.

If we take all numbers, all fractions and all decimals they are 1 to 1, ie there are the same number of whole numbers as there are fractions and decimals. That's it, it's really that simple.

I can see you wont accept mathematical logic though so I'll leave you to it. There are none so blind as those who will not see, especially when it is this obvious. Time to unsubscribe methinks.

The notion of identity is essential to all reasoning; logic, to you...Your notion contradicts the idea that one is one, which is to say, that no other number is one...Well, if we say that fractions are not a true number, but that, depending upon the operation, if a fraction equals one, it is one, then it is the same as any other operation, and there is an end to it...If 3 times 1/3 equals one, it is one, and that is the end of it...

Ok I'll answer one more post that's it. You are wrong, you do not understand maths, and you are being illogical. It's really as easy as that and its not my fault you can't grasp infinity of .9s so go away and think about why maths works and what you are suggesting wouldn't and never ever study anything to do with maths, because if your logic here is any indication you will be utterly lost beyond trigonometry and particularly in calculus. That's not meaning to be insulting that's just criticism based on the fact that not everyone has a mind that understands maths or the concept of limits. You are one of them I'm afraid, don't worry though I'm sure whatever you decide to do with your brain will not involve any maths at all.

If maths didn't work for the reasons you suggest which are totally erroneous anyway no one would use it, simple as that.

I'm well aware that equals in maths means numerically equal, as it does in the statement .999...=1 because it just does (limit x----->infinity)

Didn't you say earlier you said there was no such thing as fractions. Which is not true. There is no such thing as .33333333333333333333333333333333333333333333333 of something, but as x approaches infinity there is, it's called a third or 1/3.
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Logic it's not just for smart people anyone can play! Sidhe
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### Re: 1=.999999...?

Juggernaut wrote:The notion of identity is essential to all reasoning; logic, to you...Your notion contradicts the idea that one is one, which is to say, that no other number is one...Well, if we say that fractions are not a true number, but that, depending upon the operation, if a fraction equals one, it is one, then it is the same as any other operation, and there is an end to it...If 3 times 1/3 equals one, it is one, and that is the end of it...

All this proof shows is that writing 0.99999999[bar] is the same thing as writing 1. So it's not another number at all.

Unless you would also disagree that 1/3 = 0.33333333333333[bar], or even that 1/2 = 0.5.

You can write every number in multiple ways. 0.99999[bar] is just one way of writing the number 1. Some other ways of writing the number 1:

2-1
2/2
1.0
X^0 (where X is any non-zero number)
0.5+0.5
4*0.25
cos^2(x)+sin^2(x)

Saying that 1=0.9999[bar] is no different than writing any of the others. It's a simple identity.
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### Re: 1=.999999...?

1.000[bar] is a whole.
0.999[bar] is not.

1.000[bar] = 1
0.999[bar] does not.   Rocket

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### Re: 1=.999999...?

Rocket wrote:1.000[bar] is a whole.
0.999[bar] is not.

1.000[bar] = 1
0.999[bar] does not. What does 1/3 equal in decimals?
"He told you to be free, and you obeyed." Faust, "Miss Fortune" Pnoom

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### Re: 1=.999999...?

Pnoom wrote:
Rocket wrote:1.000[bar] is a whole.
0.999[bar] is not.

1.000[bar] = 1
0.999[bar] does not. What does 1/3 equal in decimals?

0.333[bar] is the accepted way we can represent it in decimal form. The number is derived from 1 divided by 3.  Rocket

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