Infinity

Infinity is about things which never end. Sometimes, it is also written [math]\infty[/math]. Infinity means many different things, depending on when it is used. The word is from a Latin word, which means "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 not really an ordinary number, but it is sometimes used as one. Infinity often says how many there is of something, instead of how big something is. For example, there are infinitely many whole numbers (called integers), but there is no integer which is infinitely big. But different kinds of math have different kinds of infinity. So its meaning often changes.

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 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