0.999 recurring does not equal one?

[Endercreeper01]

I don't think 0.999... = 1. If 0.999... = 1, then 1 - 0.999... = 0. But, it does not turn out to be 0. Instead, it turns out to be infinitesimal. If 0.999... = 1, it would be 0.

What do you think? Does 0.999 recurring equal one?

[mathematic]

I don't think 0.999... = 1. If 0.999... = 1, then 1 - 0.999... = 0. But, it does not turn out to be 0. Instead, it turns out to be infinitesimal. If 0.999... = 1, it would be 0.

What do you think? Does 0.999 recurring equal one?

Yes. "Infinitesimal" is not a number.

[Strange]

 

Does 0.999 recurring equal one?

Of course it does:

 

 

But, it does not turn out to be 0. Instead, it turns out to be infinitesimal.

 

How does "infinitesimal" differ from 0?

If you think that 0.999... is not equal to 1, perhaps you could write down the exact value of the difference.

 

0.000... = 0/9

0.111... = 1/9

0.222... = 2/9

0.333... = 3/9 (1/3)

etc.

0.888... = 8/9

0.999... = 9/9 = 1

Edited December 22, 2013 by Strange

[hypervalent_iodine]

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Moderator Note

Endercreeper, I have moved this to Speculations.you are going to need to do a better job of proving your claim here, as well as why the current proofs for why 0.999... = 1 are not correct. Again, this will be closed if you don't comply. You should also be warned that you are wearing our patience very thin with these sorts of threads.

[Endercreeper01]

 

 

How does "infinitesimal" differ from 0?

If you think that 0.999... is not equal to 1, perhaps you could write down the exact value of the difference.

 

0.000... = 0/9

0.111... = 1/9

0.222... = 2/9

0.333... = 3/9 (1/3)

etc.

0.888... = 8/9

0.999... = 9/9 = 1

An infinitesimal differs from 0 because if you have an infinite sum of an infinitesimal (an integral), you don't get 0. Infinitesimals have a value.

I think I might have been wrong on how 0.999... does not equal 1, since 9 * 0.111... = 9 * 1/9 = 1 = 0.999...

[Unity+]

I don't think 0.999... = 1. If 0.999... = 1, then 1 - 0.999... = 0. But, it does not turn out to be 0. Instead, it turns out to be infinitesimal. If 0.999... = 1, it would be 0.

What do you think? Does 0.999 recurring equal one?

Before anything, answer this question.

 

Do you agree that [math]\lim_{n \to \infty }\frac{1}{n}=0[/math]?

[ajb]

Infinitesimals have a value.

Not a value as a real number, other than zero.

Edited December 22, 2013 by ajb

[Strange]

Infinitesimals have a value.

 

Which is?

[John Cuthber]

I don't think 0.999... = 1. If 0.999... = 1, then 1 - 0.999... = 0. But, it does not turn out to be 0. Instead, it turns out to be infinitesimal. If 0.999... = 1, it would be 0.

What do you think? Does 0.999 recurring equal one?

"I don't think 0.999... = 1. "

You are mistaken.

"If 0.999... = 1, then 1 - 0.999... = 0. "

And it is, because

1-0.9999... = zero exactly

" But, it does not turn out to be 0."

Yes it does.

You based that idea on a mistake.

"it turns out to be infinitesimal."

No, it turns out to be zero.

 

". If 0.999... = 1, it would be 0."

And it is, so it is.

 

"Does 0.999 recurring equal one?"

Yes.

 

So, it doesn't matter what an infinitesimal is, nor what value it has because 1-0.999... isn't one.

 

Since this whole thread was based on a mistake, (now corrected "I think I might have been wrong on how 0.999... does not equal 1, since 9 * 0.111... = 9 * 1/9 = 1 = 0.999...") can we close the thread to avoid repetition?

[Strange]

 

can we close the thread to avoid repetition?

 

Seconded.

[Phi for All]

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Moderator Note

Closed, on the authority of the Department of Redundancy Department.