Words containing zermel
Maybe these words will be useful:
- zermelo's axiom — axiom of choice.
- zermelo fränkel set theory — (mathematics) A set theory with the axioms of Zermelo set theory (Extensionality, Union, Pair-set, Foundation, Restriction, Infinity, Power-set) plus the Replacement axiom schema: If F(x,y) is a formula such that for any x, there is a unique y making F true, and X is a set, then {F x : x in X} is a set. In other words, if you do something to each element of a set, the result is a set. An important but controversial axiom which is NOT part of ZF theory is the Axiom of Choice.
- zermelo set theory — (mathematics) A set theory with the following set of axioms: Extensionality: two sets are equal if and only if they have the same elements. Union: If U is a set, so is the union of all its elements. Pair-set: If a and b are sets, so is {a, b}. Foundation: Every set contains a set disjoint from itself. Comprehension (or Restriction): If P is a formula with one free variable and X a set then {x: x is in X and P(x)}. is a set. Infinity: There exists an infinite set. Power-set: If X is a set, so is its power set. Zermelo set theory avoids Russell's paradox by excluding sets of elements with arbitrary properties - the Comprehension axiom only allows a property to be used to select elements of an existing set.