this doesn't make sense to me, smart people? (infinity)

[CoccoBill]

My logic says 0.999... is infinitesimally close to 1 but not quite there. Smells like something that's just a close enough approximation to be used for practical purposes, not something worthy of a = in my book.

[daviddem]

My logic says 0.999... is infinitesimally close to 1 but not quite there. Smells like something that's just a close enough approximation to be used for practical purposes, not something worthy of a = in my book.

Your logic is flawed because the convention is that 9... represents an infinite number of 9's, not a number of 9's tending to infinity.

If 9... was a number of 9's tending to infinity, then your assertion would be correct.

A number that is infinitesimally close to 1 is equal to 1. A number that tends to be infinitesimally close to 1 is "not quite 1", as you said.

If you wished though, you could adopt for yourself the convention that 9... represents a number of 9's tending to infinity, however this would not generally be recognized by the community of mathematicians at large. Conventionally, the way mathematicians would represent a number smaller than 1 that tends to 1 is:
lim
x->1-
(with x->1- in subscript below the "lim") like here: http://en.wikipedia.org/wiki/One-sided_limit

or in calculus you can write for short
1-dx
where it is conventionally understood that dx is a positive quantity tending to zero.