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### Does 1 = 0.999... ?

Posted: Sat Aug 22, 2015 6:43 pm
Does 1 = 0.999... ?

Most if not all mathematicians say that 1 = 0.999...

They are an infinitesimal off.

I demonstrate this below, without the literal introduction of "an infinitesimal".

So, the following statements are correct:

Statement A: x < 1
Statement B: x <= 0.999...

Statement A = Statement B

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Another way of putting this is to create an algorithm to determine whether one number is less than another number. This is done on my website.

### Re: Does 1 = 0.999... ?

Posted: Sun Aug 23, 2015 5:29 am
indigoboy83 wrote:Does 1 = 0.999... ?

Most if not all mathematicians say that 1 = 0.999...

All of them. Those who say otherwise do not understand enough math to be called mathematicians. In particular, not what the string "0.999..." means.
They are an infinitesimal off.

No, they are not. In the standard space of real numbers there are no infinitesimals. Even in non-standard spaces that do contain infintesimals these two expressions are exacly equal.
I demonstrate this below, without the literal introduction of "an infinitesimal".

So, the following statements are correct:

Statement A: x < 1
Statement B: x <= 0.999...

Statement A = Statement B

That does not demonstrate anything.
Another way of putting this is to create an algorithm to determine whether one number is less than another number. This is done on my website.