Definition:The Algebra of Sets
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Let $E$ be a universal set.
The power set $\powerset E$, together with:
- the binary operations union $\cup$ and intersection $\cap$
- the unary operation complement $\complement$
is referred to as the algebra of sets on $E$.
Also defined as
Note that the concept of an algebra of sets is a more specific concept that is applied to a subset of $\powerset E$ that is closed under union, intersection and complement, and also has a unit.
So while the algebra of sets is an algebra of sets, the reverse is not necessarily true.
The concept of an algebra of sets was invented by George Boole, after whom Boolean algebra was named.
- 1965: J.A. Green: Sets and Groups ... (previous) ... (next): $\S 1.5$. The algebra of sets
- 1989: Ephraim J. Borowski and Jonathan M. Borwein: Dictionary of Mathematics ... (previous) ... (next): algebra of sets
- 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): algebra of sets