The concept of "infinity" is perhaps best approached through the concept of "the infinite." Intuitively, what is infinite has no end. If the universe is infinite--and you could travel forever in one direction, never reaching the edge of space--then the idea of "forever" requires that time, too, must be infinite.

These intuitions are of little use to physics, however, without some further mathematical precision. Mathematically, the idea of infinity is, in essence, the idea that there is no largest number (integer). For any number n that you advance as the largest number, I can counter with n + 1.

Calculus is built on the idea of infinity. Differential calculus finds the slope of a curve at an infinitely small point; integral calculus finds the area under a curve by adding up infinitely thin slivers (of the space bounded by the curve). In both cases, the properties of the infinitely small...