Re: Proof 0.999... is not equal to one.

On May 31, 1:02 am, chaja...@xxxxxxxx wrote:
On May 31, 12:33 am, William Hughes <wpihug...@xxxxxxxxxxx> wrote:

let a = 0.999... be a real number. We do not need
to give a full definition at this point
a<=1
and
a>(1-(1/10^n) for any natural number n

You have defined 0.999... to be a real number without jusitification.
I can make no such assumption. Each position within 0.999... can be
expressed as a real number, but the totality, the very infinite nature
of it, seems to render it a never ending relation more than a specific
explicit location on the real number line.

Oh, I'm SO glad you said this. I think the same thing! In fact, it
generalizes to other digits besides 9 as well! The case with
0 is particularly interesting. Clearly 0.000... is also a "never
ending relation more than a specific location on the real
number line." I mean, *obviously* it's different from 0. Look
at all those additional digits on the end!


Marshall

PS. Sadly, because this is sci.math, I have to be explicit that
I am speaking ironically.

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