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Let S be a nonempty set, then a filter on S is a nonempty collection F of subsets of S having the following properties: 1. emptyset not in F, 2. If A,B in F, then A ...

The q-series identity product_(n=1)^(infty)((1-q^(2n))(1-q^(3n))(1-q^(8n))(1-q^(12n)))/((1-q^n)(1-q^(24n))) = ...

An extension field F subset= K is called finite if the dimension of K as a vector space over F (the so-called degree of K over F) is finite. A finite field extension is ...

The group C_2×C_2×C_2 is one of the three Abelian groups of order 8 (the other two groups are non-Abelian). An example is the modulo multiplication group M_(24) (which is the ...

C_2×C_4 is one of the three Abelian groups of group order 8 (the other two being non-Abelian). Examples include the modulo multiplication groups M_(15), M_(16), M_(20), and ...

The finite group T is one of the three non-Abelian groups of order 12 (out of a total of fives groups of order 12), the other two being the alternating group A_4 and the ...

Let X be a set and S a collection of subsets of X. A set function mu:S->[0,infty] is said to possess finite monotonicity provided that, whenever a set E in S is covered by a ...

A set function mu is said to possess finite subadditivity if, given any finite disjoint collection of sets {E_k}_(k=1)^n on which mu is defined, mu( union ...

The finite volume method is a numerical method for solving partial differential equations that calculates the values of the conserved variables averaged across the volume. ...

A finitely presented group is a group with a finite number of generators and relations. A mathematical joke involving finitely presented groups is given by Renteln and Dundes ...