Beyond Every Number

Infinity is not a number. It is a concept meaning "without end." Name any number you like, and infinity is still larger. You cannot reach it by counting, even if you counted forever. That makes infinity unlike anything on the number line.

Here is the twist that broke mathematicians' brains in the 1800s: infinity comes in different sizes. Some infinities are genuinely bigger than others. The mathematician Georg Cantor proved this, and it was so strange that many of his peers dismissed it. The rest of this lesson shows how he was right.