2009-01-08, 08:24 PM
Ben Wrote:Actually...
0.999... = 1, :. 89.999... = 90
Alloy Wrote:10x - x = 9.9999999... - 0.9999999...
THAT is the wrong part. There's a small thing in maths called... infinitesimals.
The MOST small number, consisting in an infinitely small number, thus indefined.
Basically, 0.9999999... is 1 minus an infinitesimal. After multiplying by ten, it goes to...
10(-10 infinitesimals) - 1(+1 infinitesimal)
And taking those out, you get...
9(-9 infinitesimals)
ACTUALLY, by proximity, you get it closer to 8.99999999..., instead of 9.
Alloy Wrote:ok...
An infinitesimal can be defined as:
0.000000...
BUT imagine it has a 1 in the end (after infinity zeros), to put it simple. That'd be the smallest number EVER. So small that can't be defined.
0.999999... Would be 1 minus that number, as you can figure out. If you follow the calculus at the first post, it uses an aproximation when multiplying by ten, and takes off those 9 extra infinitesimals, when it shouldn't.
In my post, you see what happens with them, after adding them in. Granted, the result is practically the same, but not exactly.
There, taken from an obscure thread lost in time long ago... D: