set of axioms
41Hereditarily countable set — In set theory, a set is called hereditarily countable if and only if it is a countable set of hereditarily countable sets. This inductive definition is in fact well founded and can be expressed in the language of first order set theory. A set is… …
42Naive Set Theory (book) — See also naive set theory for the mathematical topic. Naive Set Theory is a mathematics textbook by Paul Halmos originally published in 1960. This book is an undergraduate introduction to not very naive set theory. It is still considered by many… …
43Field axioms — ▪ Table Field axioms axiom 1 Closure: the combination (hereafter indicated by addition or multiplication) of any two elements in the set produces an element in the set. axiom 2 Addition is commutative: a + b = b + a for any elements in the set.… …
44Continuum (set theory) — In the mathematical field of set theory, the continuum means the real numbers, or the corresponding cardinal number, . The cardinality of the continuum is the size of the real numbers. The continuum hypothesis is sometimes stated by saying that… …
45Morass (set theory) — For the variety of wetland, see marsh. In axiomatic set theory, a mathematical discipline, a morass is an infinite combinatorial structure, used to create large structures from a small number of small approximations. They were invented by Ronald… …
46Power set — In mathematics, given a set S , the power set (or powerset) of S , written mathcal{P}(S), P ( S ), or 2 S , is the set of all subsets of S . In axiomatic set theory (as developed e.g. in the ZFC axioms), the existence of the power set of any set… …
47Uncountable set — Uncountable redirects here. For the linguistic concept, see Uncountable noun. In mathematics, an uncountable set is an infinite set that contains too many elements to be countable. The uncountability of a set is closely related to its cardinal… …
48Union (set theory) — Union of two sets …
49Infinite set — In set theory, an infinite set is a set that is not a finite set. Infinite sets may be countable or uncountable. Some examples are: * the set of all integers, {..., 1, 0, 1, 2, ...}, is a countably infinite set; and * the set of all real numbers… …
50Dedekind-infinite set — In mathematics, a set A is Dedekind infinite if some proper subset B of A is equinumerous to A. Explicitly, this means that there is a bijective function from A onto some proper subset B of A. A set is Dedekind finite if it is not Dedekind… …
