Does 0.9999 repeating 9 equal 1?

[mjah]

There is a place for opinion in mathematics. This is not one of them. This area of mathematics is well understood and agreed upon by mathematical minds of significance (a group that certainly doesn't include me). It's also provable. You might as well be arguing that "1 = 1" is a matter of opinion because you don't agree with the definition.

Holding out for an incredibly unlikely future event that proves everyone wrong is only a good idea if you can bring something to the argument that others can't refute. Particularly since the proof has been presented here multiple times.

Short of bringing some new evidence to the table, arguing against a proven tenet of mathematics is just pissing in the wind.

[Kosher Ham]

^^^ Confirmed. Thanks.

[LaxBuddy21]

So 1 + 1 = 2 is an opinion?

I consider it a fact.

If you think 1 + 1 = 3, then you can say that's your opinion, if you'd like. But I know that 1 + 1 = 2, and I know it's a fact. And I know 1 + 1 = 3 is not a fact.

You can call them opinions if you'd like, but these exist as opinions only in your mind.

There's no magic discovery that's going to cause human kind to suddenly conclude that .999... equals something other than exactly one.

I think its pretty magical that you think one number equals another number when they are clearly two different numbers. And 1 + 1 = 2 is a fact because it has been agreed upon so readily. It is math in its simplest form and is pretty near impossible (if not impossible) to refute. The issue is as you get more complicated with math, the uncertainty grows. You can say 1 + 1 = 2 with absolute certainty but can you tell me the derivative of 4x^3y^2-3x+2y-3 with as much certainty? How about the moment generating function of a gamma distribution? Continuous numbers are much more complex than discrete numbers which is why we tend to use discrete values to approximate them for simplicity.

[Kosher Ham]

Why would the color Green be called Green ? Most of the world does not say green is green.

And who is to say that it is not blue ?

[boofMcboof]

IMO, doesn't the original question have to be philosophical since it's based on our understanding of infinity? It's been noted that infinity is not a number and for the most part doesn’t behave like a number. So how can a proof be derived from the original problem? The only thing we can state about infinity is that it doesn't exist as a complete something, it exists as a process that can never be completed. If it can't be completed how can we state for certain mathematically .9999 repeating is one?

From what I've read:

Modern mathematics is totally dependent upon the assumed existence of actual infinities but the existence of these can neither be proven nor disproven outside of mathematics. This leaves modern mathematicians in the position of defending their belief in the existence of actual infinities and discrediting any opposing ideas, but the real question is - do actual infinites exist?

All the evidence (no one can even define it, let alone observed it) seems to suggest that they only exist within the context of modern mathematics, which would seem to suggest that modern mathematics should return to its axioms and see where the problem arises.

[Mark The Homer]

I think its pretty magical that you think one number equals another number when they are clearly two different numbers. ...

This is only "clear" to you and a handful of others in this thread.

The math and science world know you are wrong. And that's not just their opinion.

[Fergasun]

I'm sorry; but the number I proposed, "blah" does in fact exist. You cannot travel between any two numbers, x and y without passing through "blah", in fact there are an infinite amount of "blah" between those two numbers.

It doesn't matter that "blah" simplifies down to zero for all intents and purposes... it is non-zero.

[Mark The Homer]

IMO, doesn't the original question have to be philosophical since it's based on our understanding of infinity?

No. Because we're not dealing with infinity as a value, we're dealing with a finite expression using infinite trailing numbers to express it.

Those are two different things.

.333... is a finite value. It's one-third. The trailing threes go on forever but it's still exactly one-third. There is nothing to philosophize about.

Well... except perhaps as to why one cannot comprehend and accept this after thirty-six proofs have been presented.

Or why one cannot accept this when evidence shows it's been embraced in whole by the mathematics and science community.

I like mjah's post above. Some of you should read it.

[Mark The Homer]

I'm sorry; but the number I proposed, "blah" does in fact exist. You cannot travel between any two numbers, x and y without passing through "blah", in fact there are an infinite amount of "blah" between those two numbers.

It doesn't matter that "blah" simplifies down to zero for all intents and purposes... it is non-zero.

Blah only exists if you are correct and .999 and 1 are two different distinct values. It's already been proven they are one and the same.

You need to put up a better argument.

Actually, you need to accept the truth. It's time.

[DjTj]

I'm sorry; but the number I proposed, "blah" does in fact exist. You cannot travel between any two numbers, x and y without passing through "blah", in fact there are an infinite amount of "blah" between those two numbers.

It doesn't matter that "blah" simplifies down to zero for all intents and purposes... it is non-zero.

If x=y, there is no "blah."

[HailinginSeattle]

1=1 and only 1=1... period.

[DjTj]

Why would the color Green be called Green ? Most of the world does not say green is green.

And who is to say that it is not blue ?

You can call it uno, un, один, 一, एक, or whatever you want, but 0.999 repeating is still going to be equal to it.

[greenspandan]

does the integer 9999999999 repeating 9 equal infinity?

[December90]

If x=y, there is no "blah."

Your inability to measure it does not mean it doesn't exist.

for proof of this concept look up "Redskins Offense - 2008:)

[Thinking Skins]

Convergence is not equality, it means it approaches equality as the limit is approached. It is used for approximation. Most things in life converge to a standard normal distribution as n goes to infinity, that does not mean they are exactly normally distributed. It means, because of this convergence, we can approximate parameters as n becomes larger. The larger the n, the smaller the error in these approximations but the error never goes away.

The definition of convergence for an infinite series is that we say that we can write in tems of equality.

If you don't agree with that, then you're just disputing notation.

The fact that you agree that 1 is the limit means that whether you admit it or not, you're accepting that 1 = .9999etc.

[Thinking Skins]

This is math. Math is not about opinions.

which is why I love math.

[Thinking Skins]

Ah but it is. This is why math goes from theorem to law. There are many many theorems out there but nowhere near the amount of laws because as more is discovered, those theorems can change. We still do not have ultimate knowledge when it comes to math and it will continue to change (although at slower rates) over time as more is learned. If there were no opinions, why do mathematical scholars disagree ever? It should always be obvious to them!

Wrong. A theorem is a proven mathematical fact.

check the wiki on this.

http://en.wikipedia.org/wiki/Theorem

"In mathematics, a theorem is a statement proved on the basis of previously accepted or established statements such as axioms."

I think you're confusing theorem with theory. Theories can be wrong, theorems cannot. Theorems are the same as laws. Theories are the same as conjectures, and can be right or wrong.

Your 'theory' that 1 is not equal to .999etc is a theory, an incorrect theory, but a theory nontheless.

[boofMcboof]

I don't see how infinity can have a value in the first place. 'Infinity' is simply a noun and 'infinite' is an adjective. The same tenets apply to both words. If mathematics cannot prove the existence of actual infinity or an infinite set of numbers, how can it define its operations?

[SonOfWashington]

So...does 1.9 repeating equal 2?

[PokerPacker]

So...does 1.9 repeating equal 2?

if you were to assume .9 repeating is 1, then yes as it is just 1+.9 repeating.

[Fergasun]

Mark The Homer,

If my number; "blah" which is 1 - .999... doesn't exist, then .999... also doesn't exist. Since we know that 1 exists, it must be .999... that is breaking the math.

I'd have to say that many years ago when those on our fence relented it was agreeable to say .999... is equal to 1 they all assumed everyone would remember it is a simplification. "blah" breaks math; and the only way to make math work is to assume it is equal to zero, or else you can never reach the next number on the number line...if that makes sense.

[PeterMP]

Wrong. A theorem is a proven mathematical fact.

check the wiki on this.

http://en.wikipedia.org/wiki/Theorem

"In mathematics, a theorem is a statement proved on the basis of previously accepted or established statements such as axioms."

I think you're confusing theorem with theory. Theories can be wrong, theorems cannot. Theorems are the same as laws. Theories are the same as conjectures, and can be right or wrong.

Your 'theory' that 1 is not equal to .999etc is a theory, an incorrect theory, but a theory nontheless.

Not to harp, but you are now you are misrepresenting a theory:

"The term is often used colloquially to refer to any explanatory thought, even fanciful or speculative ones, but in scholarly use it is reserved for ideas which meet baseline requirements about the kinds of observations made, the methods of classification used, and the consistency of the theory in its application among members of that class. These requirements vary across different fields of knowledge, but in general theories are expected to be functional and parsimonious: i.e. a theory should be the simplest possible tool that can be used to effectively address the given class of phenomena."

Note the use of the word colloquially, which really should be incorrect.

[Mark The Homer]

Mark The Homer,

If my number; "blah" which is 1 - .999... doesn't exist, then .999... also doesn't exist. Since we know that 1 exists, it must be .999... that is breaking the math.

I'd have to say that many years ago when those on our fence relented it was agreeable to say .999... is equal to 1 they all assumed everyone would remember it is a simplification. "blah" breaks math; and the only way to make math work is to assume it is equal to zero, or else you can never reach the next number on the number line...if that makes sense.

I can't believe this thread is still active.

If you mean to say "blah" is zero, then I would agree "blah" exists.

Ferg, you're confused. The decimal equivalent of a whole as .999... was never a simplification in the real world. It's only a simplification within your calculator. And it always will be, forever.

And if we were living within the box which is your calculator, I would agree with you. But we're not.

You need to get out of that box. There's a whole big beautiful undiscovered world out there!

[SonOfWashington]

Who would've guessed this thread would go on for 30 pages (in 15 post format)?

[Spec138]

Let it die Mark, LET IT DIE!!!!!

I wouldn't suspect anyone is going to change their view if they haven't yet. Just be happy you are enlightened.