The Boolean algebra of all 32-bit bit vectors is the two-element Boolean algebra raised to the 32nd power, or power set algebra of a 32-element set, denoted 2 32.
12.
To put this in perspective, infinite sets arise as filtered colimits of finite sets, infinite CABAs as filtered limits of finite power set algebras, and infinite Stone spaces as filtered limits of finite sets.
13.
A Boolean algebra is a CABA if and only if it is complete and completely distributive, giving a third definition of CABA . A fourth definition is as any Boolean algebra isomorphic to a power set algebra.
14.
Free CABAs exist for all cardinalities of a set " V " of generators, namely the power set algebra 2 2 " V ", this being the obvious generalization of the finite free Boolean algebras.
15.
The preceding five pairs of laws & mdash; the commutative, associative, distributive, identity and complement laws & mdash; encompass all of set algebra, in the sense that every valid proposition in the algebra of sets can be derived from them.
16.
Under Pritchett, the district saw eight years of steady academic improvement thanks to a number of initiatives, including a partnership with the National Urban Alliance to strengthen literacy and a math / science initiative that set algebra as the eighth-grade gateway math course.
17.
In particular, whereas there can be no countably infinite power set algebras ( the smallest infinite power set algebra is the power set algebra 2 " N " of sets of natural numbers, Cantor to be uncountable ), there exist various countably infinite Boolean algebras.
18.
In particular, whereas there can be no countably infinite power set algebras ( the smallest infinite power set algebra is the power set algebra 2 " N " of sets of natural numbers, Cantor to be uncountable ), there exist various countably infinite Boolean algebras.
19.
In particular, whereas there can be no countably infinite power set algebras ( the smallest infinite power set algebra is the power set algebra 2 " N " of sets of natural numbers, Cantor to be uncountable ), there exist various countably infinite Boolean algebras.
20.
An algebraic view is to see it as an algebra of monotonic functions over a complete lattice, with operators consisting of functional composition plus the least and greatest fixed point operators; from this viewpoint, the modal ?-calculus is over the lattice of a power set algebra.
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