Why are natural numbers defined with union in Zermelo–Fraenkel (ZF) set theory?
70369
Why do we use von Neumann ordinals and not Zermelo ordinals?
44160
Set theory: difference between belong/contained and includes/subset?
153969
The "elements" of a real number
18364
When does the set enter set theory?
154230
In $\mathsf{ZF}$, for each set $A$ exists an ordinal $\alpha$ such that no surjection $A\to \alpha$ exists
52682
Is the power set of the natural numbers countable?
156660
The set of all strictly increasing sequences of natural numbers
52451
Ordered Triples and Set Theory
63276
Is an arbitrary union of a chain of countable sets countable?
126015
Elementary number theory in sets
85398
$\mathsf{ZF}$ is not finitely axiomatizable
77957
How is $\mathbb N$ actually defined?
108957
Cardinality of a totally ordered union
2342
How does equality $\mathfrak{m}^\mathfrak{m} = 2^\mathfrak{m}$ in $\sf{ZF}$ relate to the axiom of choice?
22310
Why not to extend the set of natural numbers to make it closed under division by zero?
149673
Cardinality of an infinite union of finite sets
94620
Which number was removed from the first $n$ naturals?