# Finite Sets

### Some articles on set, finite sets, sets, finite:

Grothendieck Universes and Inaccessible Cardinals
... two simple examples of Grothendieck universes The empty set, and The set of all hereditarily finite sets ... following two axioms are equivalent (U) For each set x, there exists a Grothendieck universe U such that x ∈ U ... strong limit cardinal because the power set of any element of U is an element of U and every element of U is a subset of U ...
Boolean Algebras Canonically Defined - Other Definitions of Boolean Algebra
... Stone (1936) A Boolean algebra is the set of all clopen sets of a topological space ... two Boolean algebras formed as the clopen sets of two Stone spaces are isomorphic, so are the Stone spaces themselves, which is not the case for arbitrary topological spaces ... Johnstone (1982) A Boolean algebra is a filtered colimit of finite Boolean algebras ...
Segal Conjecture - The Burnside Ring
... The Burnside ring of a finite group G is constructed from the category of finite G-sets as a Grothendieck group ... let M(G) be the commutative monoid of isomorphism classes of finite G-sets, with addition the disjoint union of G-sets and identity element the empty set (which is a G-set ... It is in fact a free abelian group with basis elements represented by the G-sets G/H, where H varies over the subgroups of G ...
Enumeration in Set Theory - Enumeration in Countable Vs. Uncountable Context
... The most common use of enumeration in set theory occurs in the context where infinite sets are separated into those that are countable and those that are not ... This definition is especially suitable to questions of computability and elementary set theory ... define it differently when working with finite sets ...
Combinatorial Species - Definition of Species
... Any structure — an instance of a particular species — is associated with some set, and there are often many possible structures for the same set ... graphs whose node labels are drawn from the same given set ... At the same time, any set could be used to build the structures ...

### Famous quotes containing the words sets and/or finite:

It provokes the desire but it takes away the performance. Therefore much drink may be said to be an equivocator with lechery: it makes him and it mars him; it sets him on and it takes him off.
William Shakespeare (1564–1616)

Are not all finite beings better pleased with motions relative than absolute?
Henry David Thoreau (1817–1862)