Search for "Axiom of choice" in article titles:

1. Axiom of choice: In mathematics, the axiom of choice, abbreviated AC or AoC, is an axiom of set theory equivalent to the statement that a Cartesian product of a collection of non-empty sets is non-empty. Informally put, the axiom of choice ... (Axiom of set theory) [100%] 2023-12-17 [Axiom of choice]
2. Axiom of choice: One of the axioms in set theory. It states that for any family $F$ of non-empty sets there exists a function $f$ such that, for any set $S$ from $F$, one has $f(S)\in S$ ($f$ is called ... (Mathematics) [100%] 2023-12-13
3. Axiom of choice: In mathematics, the axiom of choice, AC, or AoC is an axiom of set theory equivalent to the statement that a Cartesian product of a collection of non-empty sets is non-empty. Informally put, the axiom of choice says ... (Axiom of set theory) [100%] 2023-12-23 [Axiom of choice]
4. Axiom of choice: In mathematics, the Axiom of Choice or AC is a fundamental principle in set theory which states that it is possible to choose an element out of each of infinitely many sets simultaneously. The validity of the axiom is not ... [100%] 2023-06-22
5. Axiom of Choice: The Axiom of Choice (AC) in set theory states that "for every set made of nonempty sets there is a function that chooses an element from each set". This function is called a choice function. [100%] 2023-02-15 [Set Theory] [Advanced Mathematics]...
6. Axiom of countable choice: The axiom of countable choice or axiom of denumerable choice, denoted ACω, is an axiom of set theory that states that every countable collection of non-empty sets must have a choice function. That is, given a function A with domain ... [86%] 2022-08-16 [Axiom of choice]
7. Axiom of global choice: In mathematics, specifically in class theories, the axiom of global choice is a stronger variant of the axiom of choice that applies to proper classes of sets as well as sets of sets. Informally it states that one can simultaneously ... [86%] 2022-06-10 [Axioms of set theory] [Axiom of choice]...
8. Axiom of finite choice: In mathematics, the axiom of finite choice is a weak version of the axiom of choice which asserts that if ( S α ) α ∈ A {\displaystyle (S_{\alpha })_{\alpha \in A}} is a family of non-empty finite sets, then If every ... (Axiom in set theory) [86%] 2023-05-20 [Axioms of set theory] [Axiom of choice]...
9. Axiom of dependent choice: In mathematics, the axiom of dependent choice, denoted by \displaystyle{ \mathsf{DC} }[/math], is a weak form of the axiom of choice (\displaystyle{ \mathsf{AC} }[/math]) that is still sufficient to develop most of real analysis. It was introduced by ... [86%] 2023-12-15 [Axiom of choice]
10. The Axiom of Choice: The principle of set theory known as the Axiom of Choice has been hailed as “probably the most interesting and, in spite of its late appearance, the most discussed axiom of mathematics, second only to Euclid’s axiom of parallels ... (Philosophy) [86%] 2021-12-28
11. Axiom of dependent choice: In mathematics, the axiom of dependent choice, denoted by D C {\displaystyle {\mathsf {DC}}} , is a weak form of the axiom of choice ( A C {\displaystyle {\mathsf {AC}}} ) that is still sufficient to develop much of real analysis. It was ... (Weak form of the axiom of choice) [86%] 2023-12-15 [Axiom of choice]
12. Axiom of countable choice: The axiom of countable choice or axiom of denumerable choice, denoted ACω, is an axiom of set theory that states that every countable collection of non-empty sets must have a choice function. That is, given a function A with domain ... [86%] 2024-03-08 [Axiom of choice]
13. Axiom of countable choice: The axiom of countable choice or axiom of denumerable choice, denoted ACω, is an axiom of set theory that states that every countable collection of non-empty sets must have a choice function. That is, given a function A {\displaystyle A ... [86%] 2024-05-20 [Axiom of choice]