Re: .99999....=1

On Oct 24, 1:54 pm, "tman_gl" <u38544@uwe> wrote:
I heard that it is mathmatically posible to prove that .9999.....=1

i find it completely irational but im interested at the same time

any answers would be much apreciated

And here we go again with one of the most popular topics on
this newsgroup, namely the number 0.999....

In the standard, Archimedean complete ordered field R, it is
inevitable that 0.999... = 1.

In a nonstandard set of reals, the numbers may be distinct. We
may have that 0.999... = 1 minus an infinitesimal. In the Cantor
threads, various so-called "cranks" have come up with different
infinitesimals with names such as "iota" and "Lil'Un."

It is also possible to use hyperreals with a Transfer Principle. In
the hyperreals every sequence of reals corresponds to a
hyperreal, so why not consider the sequence:

{0.9, 0.99, 0.999, 0.9999, ...}

If we let N be the hyperreal {1, 2, 3, 4, ...}, then we conclude:

0.999... = 1 - 10^N.

.