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🏠
/
Mathematics
/
Set Theory
/
Axiom of infinity
Axiom of infinity
Asserts the existence of an infinite set (typically the set of natural numbers).
📜
The statement of the theorem
∃
I
(
∅
∈
I
∧
∀
x
(
x
∈
I
⟹
x
∪
{
x
}
∈
I
)
)
\exists I (\emptyset \in I \land \forall x (x \in I \implies x \cup \{x\} \in I))
∃
I
(
∅
∈
I
∧
∀
x
(
x
∈
I
⟹
x
∪
{
x
}
∈
I
))
.