Encyclopedia > Simple theorems in the algebra of sets
Elementary mathematics courses sometimes leave students under an erroneous impression that the subject matter of set theory is the algebra of union, intersection, and complementation of sets. Those topics are treated below. For an account of some elementary topics in set theory, see also set, naive set theory, axiomatic set theory, Cantor-Bernstein-Schroeder theorem, Cantor's diagonal argument, Cantor's first uncountability proof, Cantor's theorem, well-ordering theorem, axiom of choice, Zorn's lemma.
We list without proof several simple properties of the operations of union, intersection, and complementation of sets. These properties can be visualized with Venn diagrams.
Discrete mathematics, also called finite mathematics, is the study of mathematical structures that are fundamentally discrete, in the sense of not supporting or requiring the notion of continuity.
Most, if not all, of the objects studied in finite mathematics are countable sets, such as integers, finite graphs, and formal languages.
Linear algebra - a study of related linear equations.
The peak set of a permutation $\sigma$ is the set $\{i:\sigma(i–1)
A polytope P is the convex hull of a finite set of points in R^d, and its boundary is a collection of lower-dimensional polytopes known as the faces of P.
Then the set of splines (of all degrees) on \hat\Delta is a graded module C^r(\hat\Delta) over the polynomial ring R in d+1 variables, and the dimension of C^r_k(\Delta) is the dimension of C^r(\hat\Delta) in degree exactly k.
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