Cardinalities of Infinity

Welcome to the Cardinalities of Infinity Blog! This blog is dedicated to exploring infinite sums and the underlying mathematics and philosophical interpretation thereof.

Before diving into the more abstract facets of infinity, we need to understand what it is and is not.

Infinity, in its broad application, is defined by www.dictionary.com as:


1. the quality or state of being infinite.
2. something that is infinite.
3. infinite space, time, or quantity.
4. an infinite extent, amount, or number.
5. an indefinitely great amount or number.
6. Mathematics.
a. the assumed limit of a sequence, series, etc., that increases without bound.
b. infinite distance or an infinitely distant part of space.
7. Photography.
a. a distance between a subject and the camera so great that rays of light reflected from the subject may be regarded as parallel.
b. a distance setting of the camera lens beyond which everything is in focus.

A more useful definition for the purpose of this blog is provided by The Free Online Dictionary of Computing:

1. The size of something infinite.Using the word in the context of sets is sloppy, since different infinite sets aren't necessarily the same size cardinality as each other.

In the next blog, we will discuss some of the basic principles and misnomers surrounding infinity.

References:

infinity. (n.d.). Dictionary.com Unabridged (v 1.0.1). Retrieved November 15, 2006, from Dictionary.com website: http://dictionary.reference.com/browse/infinity

infinity. (n.d.). The Free On-line Dictionary of Computing. Retrieved November 15, 2006, from Dictionary.com website: http://dictionary.reference.com/browse/infinity