Set Algebra

[BaalChatzaf]

Excerpted from Wiki: http://en.wikipedia.org/wiki/Set_algebra

In mathematics a field of sets is a pair \langle X, \mathcal{F} \rangle where X is a set and \mathcal{F} is an algebra over X i.e., a non-empty subset of the power set of X closed under the intersection and union of pairs of sets and under complements of individual sets. In other words \mathcal{F} forms a subalgebra of the power set Boolean algebra of X. (Many authors refer to \mathcal{F} itself as a field of sets.) Elements of X are called points and those of \mathcal{F} are called complexes.

Fields of sets play an essential role in the representation theory of Boolean algebras. Every Boolean algebra can be represented as a field of sets.

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A set algebra requires a maximal or universal set X along with a field of sets F a subset of the Power Set of X. So the complement of the empty set in a set algebra is not Everything, it is the maximal (or universal set ) X. Post #1 of the thread "The Opposite of Nothing Is/Isn't Everything" is rife with error. It is a thread written by an amateur who thinks the right book to read on mathematics is ITOE.

Bob Kolker

Edited May 28, 2009 by BaalChatzaf

[tjohnson]

This must be serious, you have signed your real name to it.

[BaalChatzaf]

This must be serious, you have signed your real name to it.

Ooops. But I am serious.

Ba'al Chatzaf