Small Infinity, Big Infinity | Science News

ADVERTISEMENT

SUPPORT SCIENCE NEWS

Science News is a nonprofit.

Help us keep you informed.


Math Trek

Small Infinity, Big Infinity

Infinity can be big or bigger, countable or not

By
5:30pm, January 8, 2008

Infinity is bigger than any number. But saying just how much bigger is not so simple. In fact, infinity comes in infinitely many different sizes—a fact discovered by Georg Cantor in the late 1800s.

Now a mathematician has come up with a new, different proof. Based on a simple game, the proof uses a strategy that might someday shed light on one of the great unsolved questions in mathematics.

The smallest infinity is the one you'd get to if you could count forever. The numbers 1, 2, 3, 4… are called the natural numbers, and they are the most obvious example of this size of infinity. In honor of them, anything that has this size of infinity is called "countable."

Lots of infinite things are countable. For example, suppose you take just the even numbers. They're countable,

This article is only available to Science News subscribers. Already a subscriber? Log in now. Or subscribe today for full access.

Get Science News headlines by e-mail.

More from Science News

From the Nature Index Paid Content