Infinity

Infinity, also written $\infty$, is the name for a group of ideas about things which never end. The term is from a Latin word meaning "without end". Infinity goes on forever, so sometimes space, numbers, and other things are said to be 'infinite', because they never come to a stop.

Infinity is really not an ordinary number, but it is sometimes used as one.

There are two kinds of infinity: potential infinity and actual infinity. Potential infinity is a process that never stops. For example, adding 10 to a number. No matter how many times 10 is added, 10 more can still be added. Actual infinity is a more abstract idea. For example, there are infinitely many numbers as it is impossible to write them all down.

Infinity has various properties that are not normally found in numbers:

• Infinity added to any number is infinity.
• Infinity times any positive number is infinity.
• Infinity times any negative number is negative infinity.

Infinity in Mathematics

Mathematicians use different kinds of infinity. For example, uncountable sets are bigger than countable sets. Both kinds of set are infinitely big.

Other pages

• Hilbert's paradox of the Grand Hotel
• Countable set
• Uncountable set

Other websites

• A Crash Course in the Mathematics of Infinite Sets, by Peter Suber. From the St. John's Review, XLIV, 2 (1998) 1-59. The stand-alone appendix to Infinite Reflections, below. A concise introduction to Cantor's mathematics of infinite sets.
• Infinite Reflections, by Peter Suber. How Cantor's mathematics of the infinite solves a handful of ancient philosophical problems of the infinite. From the St. John's Review, XLIV, 2 (1998) 1-59.
• Infinity, Principia Cybernetica
• Hotel Infinity
• The concepts of finiteness and infinity in philosophy