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Mathematics
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Set Theory
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Axiom of regularity (also called the axiom of foundation)
Axiom of regularity (also called the axiom of foundation)
Every non-empty set contains an element that is disjoint from the set itself (prohibits infinite descending membership chains).
📜
The statement of the theorem
∀
A
(
A
≠
∅
⟹
∃
x
∈
A
(
x
∩
A
=
∅
)
)
\forall A (A \neq \emptyset \implies \exists x \in A (x \cap A = \emptyset))
∀
A
(
A
=
∅
⟹
∃
x
∈
A
(
x
∩
A
=
∅
))
.