Statistics

[Tiberius]

No problem.

Incidentally, the reason why mathematics does not break down when dealing with infinitely long decimals (like 0.999999...) is down to the existence of real numbers, and being able to be placed on a number line between two others. That is to say, despite a number having an infinite number of digits after the decimal place, we can always find a number that is both higher and lower than it, without having to look at all the numbers (thus, we never actually need to expand the number to it's infinite length).

---

"In analytic geometry, an asymptote of a curve is a line such that the distance between the curve and the line approaches zero as they tend to infinity."

Not to be a stickler here, but can't an asymptote be a curve that approaches any number but doesn't reach it? For example, there are asymptotes at 1 in f(x) = 1/(x-1).

I think you've read the definition wrong.

It's not saying the asymptote itself is equal to 0, but that the distance between the curve and the line (the asymptote) approaches 0 (which holds true for any convergent number).

In your example, the distance between the curve of the function f(x) and the asymptote approaches 0.