Thread: Does 0.9 repeated = 1?

This is what Calculus is for. Take a limit of some function, at infinity. That's what it is at infinity, in this case 1. And the limit is just what the function continuously approaches, but never reaches.

There's a reason when you take a Calc exam these types of questions ask "what is the limit of f(x) as n->∞?" and not "what is f(x) at n=∞?"

I believe I see a problem with this paradox. There are 2 rectangles, let's suppose 2 units high each. You argue that the sides are touching, there is continuity, yet there still exists a space between them. The height is 4 here. Basically you're saying that the height of the first box is from 0 to 2, while the second box would have to be 2.0...1 to 4.0...1, to distinguish the border. Your circumstances claim the height is 4.0...1.p\

I like this one, but I believe you can just say the borders have a width "dx" or "dy" - infinitesimally thin.

There's no paradox here in my opinion. The only paradox I see here is everyone is trying to use simple things like fractions/decimals and whole numbers to explain infinities.