Category:Axioms/Axiom of Extension
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This category contains axioms related to Axiom of Extension.
Set Theory
Let $A$ and $B$ be sets.
The Axiom of Extension states that:
- $A$ and $B$ are equal
- they contain the same elements.
That is, if and only if:
and:
This can be formulated as follows:
- $\forall x: \paren {x \in A \iff x \in B} \iff A = B$
Class Theory
The axiom of extension in the context of class theory has the same form:
Let $A$ and $B$ be classes.
Then:
- $\forall x: \paren {x \in A \iff x \in B} \iff A = B$
Pages in category "Axioms/Axiom of Extension"
The following 10 pages are in this category, out of 10 total.
E
- Axiom:Axiom of Extension
- Axiom:Axiom of Extension (Classes)
- Axiom:Axiom of Extension (Sets)
- Axiom:Axiom of Extension/Also known as
- Axiom:Axiom of Extension/Class Theory
- Axiom:Axiom of Extension/Set Theory
- Axiom:Axiom of Extension/Set Theory/Formulation 1
- Axiom:Axiom of Extension/Set Theory/Formulation 2
- Axiom:Axiom of Extensionality
- Axiom:Axiom of Extent