## Uh oh. My math teacher says .999... does not equal 1.

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Unakau
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### Uh oh. My math teacher says .999... does not equal 1.

I'm just making sure that I'm completely right on this one.

He says that the Intermediate Value Theorem (Which says that there are infinitely many values in between any two different numbers) proves that .999..=/=1.

I'm just making sure that I'm right, but in order for that to be true, wouldn't he have to assume that .999... and 1 are two different values in the first place?

I apologize in advance for the .999... and 1 topic, but this has been bugging me.

SimonM
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### Re: Uh oh. My math teacher says .999... does not equal 1.

You right, his initial assumption is the flaw in his logic. And please no more 0.999..=1 topics

And get a new math teacher. Seriously.
mosc wrote:How did you LEARN, exactly, to suck?

ikerous
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### Re: Uh oh. My math teacher says .999... does not equal 1.

If theres an infinite set of numbers between .999r and 1, certainly he can tell you what one of them is.

HenryS
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### Re: Uh oh. My math teacher says .999... does not equal 1.

ikerous wrote:If theres an infinite set of numbers between .999r and 1, certainly he can tell you what one of them is.
That isn't entirely fair. There are sets of real numbers that we know exist by cardinality arguments but that we cannot name a member of.

PaulT
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### Re: Uh oh. My math teacher says .999... does not equal 1.

While there are indeed infinitely many values between any two distinct real numbers, that's only relevant if 0.999... and 1 are distinct numbers, which is what he's trying to show. That's begging the question, fallacy fans!

Also, the Intermediate Value Theorem is something else entirely isn't it?

Unakau
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### Re: Uh oh. My math teacher says .999... does not equal 1.

Thanks, guys. I just wanted to make sure that I was right here.

He's actually a great teacher, I just think that he might be living with a single incorrect assumption (Which is hardly applicable to anything else, anyway).

PaulT, I think that was what he called it. I could be wrong, but the idea is still there.

Also, I apologize again for the .999... versus 1 topic, I was just making sure that I could go about disproving his idea in the right way.

SimonM
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### Re: Uh oh. My math teacher says .999... does not equal 1.

Well, your not disproving him by spotting his error. You can disprove him by having a solid proof of the opposite
mosc wrote:How did you LEARN, exactly, to suck?

aguacate
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### Re: Uh oh. My math teacher says .999... does not equal 1.

Yeah, IVT has to do with functions... what function was even mentioned??

What the teacher is incorrectly trying to apply is the fact that the real numbers are dense. That is, every number in the set of the real numbers is a limit point.

doublez
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### Re: Uh oh. My math teacher says .999... does not equal 1.

erm, wouldn't he be using IVT on f(x)=x?
still fallacious logic though.

jestingrabbit
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### Re: Uh oh. My math teacher says .999... does not equal 1.

doublez wrote:erm, wouldn't he be using IVT on f(x)=x?
still fallacious logic though.

That works, using IVT that way, but it makes a lot more sense to use the Archimedean property, surely.
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