# 1 = 0.999...

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I said I was done, and so I am... after this one last thing to prove that you are confusing infinity with finite.

You divided 9.999... by ten, not nine.

Looks like it, doesn't it?

After all, the claim was that 0.999... * 10 = 9.999..., however, that is either impossible or not true. Using any finite number of nines, this would be true, which is what makes it so easy to trick you.

I'll rewrite it:

0.999... * 10 = (0.999... + 0.999... + 0.999... + 0.999... + 0.999... + 0.999... + 0.999... + 0.999... + 0.999... + 0.999...)

Subtract 0.999...:

0.999... * 9 = (0.999... + 0.999... + 0.999... + 0.999... + 0.999... + 0.999... + 0.999... + 0.999... + 0.999...)

Divide by 9:

0.999... * 1 = (0.999...)

0.999... = 0.999...

Now I'd like to note that the above is not me defending my proofs, I am not debating this any further, even in self-defense, the above was me showing that you are still looking at it from a finite perspective and that is all.

No, the whole crux is the infinite nines, hence there is no number between 0.999... and 1.

Nmenth, just because it is impossible to write 0.999..., does not mean we cannot multiply it. It is also impossible to write out pi, but obviously people use pi in multiplication all the time.

but obviously people use pi in multiplication all the time.

Oblivious statements like that aren't helping your side.

If after reading back what you wrote, you still don't see your mistake, you are not worthy to be debating this.

I gave an example of a number with infinite digits which can be multiplied to another number. What are you insinuating?

All this comes from a lack of understanding of infinity, and this is natural without a formal study of the matter. For example:

Which is bigger, the set of positive whole numbers, or the set of positive whole even numbers? I.e. {1,2,3,...} vs. {2,4,6,...}

Which is bigger, the set of all numbers between 0 and 1, or the set of positive whole numbers?

etc.

All this comes from a lack of understanding of infinity, and this is natural without a formal study of the matter. For example:

Which is bigger, the set of positive whole numbers, or the set of positive whole even numbers? I.e. {1,2,3,...} vs. {2,4,6,...}

Which is bigger, the set of all numbers between 0 and 1, or the set of positive whole numbers?

etc.

Yes I agree. However there is no reason why we cannot multiply a number just because we can't write it, which was my point earlier. We can all agree that 0.999... does not equal infinity. The fact that it has infinite digits does not affect it's value. We know it's value because we have proven it to be 1. No one has yet provided a mathematical statement to contradict it.

What are you insinuating?

Hee hee, alright, I'll explain it to you. There is not one person on this planet that multiplies pi. Pi is not yet defined, and if it is infinite, it never will be. People that multiply pi, do so with it rounded at some point, meaning it is no longer infinite, nor is it truly pi. Since it is an irrational number, there is no repeating pattern to be multiplying, thus, it is impossible to multiply pi and it is never done.

pi * 1/pi = 1. There, I multiplied pi.

pi * 1/pi = 1. There, I multiplied pi.

Funny man...

Pi, as with all infinites, can be multiplied by 0 and 1, but nothing else.

Reduce any infinite to a finite number and it can be multiplied easy.

Not sure how pi is infinite, as it's certainly bounded above by 4.

All these claims that you're making essentially 'break' mathematics, and would imply that the last ~400 years of work in the field has been for nothing, which should tell you immediately that you're probably wrong if for no other reason than the math actually works.

can i have 9.99 apple please?

The definition of pi however is defined with multiplying with inphinity however, which confuses me.

The fact that you multiply with inphinity is the reason nothing can be defined as exactly circular. well you can, but nothing is.

I still see 1 and 0.999... as 2 different numbers. They are visually not the same, and the fact the nines go out in inphinity doesn't make it 1

I'm not sure but if you say 1 = 0.999... then 2 = 2.999... as well since the nines go out in infinity?

So practically you say that all numbers are just rounded up if they end with 999... ?

If so I think you're definitly wrong.

http://qntm.org/?pointnine

I rest my case.

0.999... repeating equals 1. There is no counterproof, and if you have one, it is wrong.

Sorry Doc, but Nmenth is absolutely right, and you are in error. This is simply because the human mind cannot perceive infinite. The universe is infinite. If you were to get into a spaceship and fly away from the Earth, when you are 99.999...% of the way to the end of the universe, would that be the same as actually arriving at the end? Yes, you could turn around , come back, and tell people you made it. Some would believe you, some would dispute you, some would not believe you. What would you show as proof? I'm sorry, but .999... did not, does not, and never will equal 1, any more than flying 99.999...% of the way to the edge of the universe is the same as flying all the way, 100%.

It doesn't matter if we can perceive infinity or not, but infinity is not part of the discussion. 0.999... = 1. There is no mathematical argument to prove otherwise. And note that I said mathematical, not "logical."

Either way, your entire argument is fallacious anyway. The universe doesn't stop anywhere so traveling a percentage of it is... well... frankly impossible. There is no boundary to define the amount.

But, back to the point. 0.999... = 1. Learn it, live it, love it.

And it seems like all of you on the other side seem to forget that in order for numbers to actually be different, there has to be another value in between. There is no other value between 0.999... and 1.

It doesn't matter if we can perceive infinity or not, but infinity is not part of the discussion. 0.999... = 1. There is no mathematical argument to prove otherwise. And note that I said mathematical, not "logical."

Very important point which I tried to make earlier. Nmenth nor anyone else has provided a mathematical counterproof.

Either way, your entire argument is fallacious anyway. The universe doesn't stop anywhere so traveling a percentage of it is... well... frankly impossible. There is no boundary to define the amount.

I lol'd.

But, back to the point. 0.999... = 1. Learn it, live it, love it.

And it seems like all of you on the other side seem to forget that in order for numbers to actually be different, there has to be another value in between. There is no other value between 0.999... and 1.

Indeed, however some people don't believe this apparently.

Agreeing to disagree + lazyness = lack of arguement/debate

And it seems like all of you on the other side seem to forget that in order for numbers to actually be different, there has to be another value in between. There is no other value between 0.999... and 1.

So theoretical you say that the value 0.999... does not exist at all, since you say that it is "1".

So 0.999... is theoretically an impossible value since it's "1".

So are discussing a value/number that does not exist.

Since 0.999... does not exist, we shouldn't debate whether it's "1" or not. (Since the value theoretically doesn't exist).

We should rather discuss whether the value 0.999 exists or not.

It does exist, therefor it isn't 1. It's 2 different numbers with the (theoretically) same "value".

EDIT: Just because it is a value with infinite nines repeating (0.999...) doesn't mean it don't exist.

Just because a value is bounded to infinity doesn't mean it doesn't exist. (Because that would be the same as saying the universe (if it's infinite) doesn't exist either).

Edited by Stevie_K

It doesn't matter if we can perceive infinity or not, but infinity is not part of the discussion. 0.999... = 1. There is no mathematical argument to prove otherwise. And note that I said mathematical, not "logical."

Actually it does matter. You want to take an infinite like .999... and make it finite like 1.0 but when

I do the same thing, like take an infinite universe and make it finite, 100%, you change the rules. (The decimal for 100% is 1.0). In the same way, you cannot multiply an infinite number such as .333... by any finite number such as 3 and conclude that it somehow equals some other infinite like .999... which would be like saying you could fly your spaceship to 33.3...% of the way to the end of universe, then do it again, and then do it a third time. Then you make the same mistake when you multiply .999... times finite 10. For sake of argument, what would you say is the answer to .999... times 2? or 3, or 4, or 5, or 6, or 7, or 8, or 9???

But, back to the point. 0.999... does not = 1. Learn it, live it, love it.

And it seems like all of you on the other side seem to forget that in order for numbers to actually be different, there has to be another value in between. There is no other value between 0.999... and 1.

Another false assumption. If you have an apple in one hand, and a kiwi in the other, and you bring them closer and closer to each other until you can't get another fruit between them, at what point are the the same fruit? If God comes into your heart, He is so close, the Devil can't get between, does that make you a God?

I don't make it a finite 1.0, it's an infinite 1.000... but that's not the real point. The real point is that every argument you have is entirely, 100 percent wrong. You have yet to provide any mathematical proof to contradict that 0.999... = 1. Real proof - you have none. Don't give me any phony arguments using finite quantities or things that don't exist. That's not mathematical and ultimately, irrelevant.

The thing here is that you don't understand infinity. Mathmeticians do. All real numbers have infinitely long values. This is where everyone who tries to use non-mathematical reasoning falls flat.

Read the link I posted earlier. It destroys every argument you have.

I don't make it a finite 1.0, it's an infinite 1.000... but that's not the real point. The real point is that every argument you have is entirely, 100 percent wrong. You have yet to provide any mathematical proof to contradict that 0.999... = 1. Real proof - you have none. Don't give me any phony arguments using finite quantities or things that don't exist. That's not mathematical and ultimately, irrelevant.

From the linked page, the first line:

ALL numbers are infinite decimal expansions.

And this is immediately where it falls flat on its face. This is a huge assumption to make. Because 1.0000... and 0.9999 are infinite decimal expansions if you will... but it is not equal to "1". Because 1 comes from the integer set Z, and 1.000... and 0.999 come from the real set R. You can define 1 to be equal to 1.00000.... but as soon as you get into these numbers, you introduce approximations.

If you only consider the real set (this is a separate argument, the sentence before here is the assumption) with 1.0000... and 0.999.... then indeed, there is no number between these two - yet if you try to write them down, they will fail, as you cannot write them down completely. If someone comes up with an example, you just add a decimal.

But even if there is no number between the two, that does not mean they are equal. With decimal expansions, you introduce rounding errors, and that means that symbolic math no longer exactly applies. So, the whole 0.333 times 3 thing fails, because it doesn't think about these rounding errors.

I'd debunk most of these arguments, but to be honest most don't make a whole lot of sense...

And this is immediately where it falls flat on its face. This is a huge assumption to make. Because 1.0000... and 0.9999 are infinite decimal expansions if you will... but it is not equal to "1". Because 1 comes from the integer set Z, and 1.000... and 0.999 come from the real set R. You can define 1 to be equal to 1.00000.... but as soon as you get into these numbers, you introduce approximations.

No, 0.999... and 1 are shorthand, not approximations.

But even if there is no number between the two, that does not mean they are equal. With decimal expansions, you introduce rounding errors, and that means that symbolic math no longer exactly applies. So, the whole 0.333 times 3 thing fails, because it doesn't think about these rounding errors.

Actually, it does mean just that.

Consider this 1.000... - 0.999... = 0.000...

Hence 0.999... = 1.

I'd debunk most of these arguments, but to be honest most don't make a whole lot of sense...

Well that's unfortunate for you. All of the arguments presented here make sense to me, even DD's short and generic ones. I, of course, don't think some of the arguments are correct, but I understand them all (ok, I didn't get VampireA05, but that's the exception).

I'd like to clarify something for DD though...

You have yet to provide any mathematical proof to contradict that 0.999... = 1.

You misunderstand our purpose here. We are not trying to prove that 1 ≠ 0.999…, but rather are trying to disprove that 1 = 0.999….

I know, it sounds like a contradiction of rephrased words, but it is nevertheless true.

It's like this, your side has given us mathematical equations supposedly proving that 1 = 0.999…, however we don't believe these equations to be correct and are explaining why they are wrong. So, from our side, you have not proven that 1 = 0.999… and from your side, we have not proven that 1 ≠ 0.999…. The presence of equations is not proof, and saying that 1 - 0.999… = 0 does not make it so. It ultimately breaks down to what each individual's concept of which mathematical laws are true.

I.e., I say it is law that infinity cannot be multiplied by anything other than 1 and 0, which your side refuses to acknowledge because you claim that infinity is not comparable to infinite repetition.

Your side says that it is law that if there is no possible other number between two existent numbers, they must be equal, which our side refuses to acknowledge because this is an arbitrary rule that only exists to prove your point (I realize I make your argument sound stupid, but I am not writing unbiased here, you know).

Because we disagree on what laws apply, no matter what 'proofs' are presented, neither side will be persuaded.

So what laws are true? Well, some mathematicians may be so arrogant as to say that the universe conforms to the laws of mathematics. This, however, is false. It is mathematics that conforms to the laws of the universe. The universe is what it is, and math cannot change it. Math is a concept and the universe can change it. Therefore, the laws of mathematics can only be shaped by observations of reality and has no truth in of itself, but is subjected to the universal truths. Because humans are not omniscient and are quite fallible and not one of us has seen infinity, it is hard for us to form the mathematical rules governing it.

I still say my laws are correct and you still say your laws are correct, but I'm afraid there is no answer to be generated here.

"But," some of you might say, "There must be one true law, both can't be right."

Yes, that one true law is determined by the universal truths that we can only observe and speculate. Remember that mathematics is not truth, but only concept. Decimals do not exist in reality, fractions are reality, decimals are numbers created to fit our base 10 numeration system. Our 9 means nothing to the Mayan’s base 20, or Babylonian’s base 60, which are systems unfamiliar to our culture.

So then, are mathematical laws just made up by mankind? No, they are determined by reality, but decimals are not reality, so that makes it difficult.

Since we cannot see infinity, we have to decide what rules apply from our limited perspective. I think my judgment is the one truth, you think your judgment is the one truth. One of us are right, but until we can see infinity, neither of us can say for sure. If you cannot admit that there is any uncertainty, then you are not just stubborn, but simply stupid.

Which means this debate serves no purpose. I should have realized I was opening Pandora’s box before I started this...

I was never good at maths... but I don't understand the concept that different numbers must have a number in between???

Can I have the george-bush-for-president simple answer?

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