Re: .999~ = 1?
.999 (repeating) IS equal to 1.
A repeating nine has an infinite height.
For two numbers to be different from one another, there must be a number that can fit between them.
Examples:
a) 1 and 2. 1.5 fits in between
b) 1.5 and 2. 1.7 fits in between
c) 1.0000000000001 and 1.00000000000011 ... even that has a number that fits in between. In fact, it has INFINITE numbers that fit in between.
There is absolutely no number that can fit between .9 repeating and 1.
Another way to look at it:
.9 repeating is the high end of the spectrum, being another term for "1". On the other end of the spectrum is .0 repeating. It's equal to zero, which most everyone should instantaneously agree to. However, there's a small number that would like to argue that since the zeros would progress into infinite, there could be an incomprehensable unit that would be similar to ".000(repeated)001" on paper, the 1 holding place for infinite.
Realize, folks, that infinite is not a number, but a term. As I said before, I hate infinite, but I do understand it.
And to those of you who said .99(repeated) is the largest number below 1, then .00(repeated) would have the be the smallest number above 0. Both of which are not true on a mathematical sense... which is the only sense for such a number O_o.
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