Because, inherently we accept that (for ie) any number to the power of negative infinity equals to 0. That's probably the first thing a teacher will tell you when he/she introduces limits and such. But we both know that 0 and x^-inf are two different things conceptually.

Just as duality exists in the way scientists accept light, wave or particle, there is duality in this, no more no less. I stand firm on the belief that .9999999 = 1 practically but not conceptually. And the trick with the equation is that you can't always treat irrational numbers like natural numbers.

I looked up the wikepedia link and here is what I copied from it:

"A 19th-century reaction against such liberal summation methods resulted in the definition that still dominates today: the sum of a series is defined to be the

**limit**of the sequence of its partial sums."

So, it is simply agreed that to refer to a function like that one can express it in terms of its limit. And the limit of 0.9999.... is 1 but they are not the same.

Although, after reading the wikepedia page on 0.99999 I retract everything that I have said. It's just mind numbing how deep that rabbit hole goes. People far more able than me have messed with it and other similar, complicated dudu. There is a lot to learn out there. I am not disenchanted though, just humbled.