How to prove that you can choose an element from a set in ZF?
27025
How do I choose an element from a non-empty set?
158671
Cardinality of a set that consists of all existing cardinalities
43024
Well-ordered sets, properties of an element that is not largest in the set
101453
Existence of a Boolean algebra with a unique ultrafilter in ZF
156252
Are sets constructed using only ZF measurable using ZFC?
32441
How to prove or disprove statements about sets
6291
Proving something is a linearly independent subset
111723
Can it be proven in $\sf ZF^{\neg\infty}$ that the sets $x_n=\{x_{n+1}\}$ do not exist?
142886
Find set with maximal cardinality given constraints
144181
Given an arbitrary set $X$, can one always find an element outside $X$?
77548
Given an arbitrary infinite set $S$, how to construct an injection $\mathbb{N} \to S$ with the Axiom of Choice?
142534
Proof of $k {n\choose k} = n {n-1 \choose k-1}$ using direct proof
83185
How to show countability of $\omega^\omega$ or $\epsilon_0$ in ZF?
71133
prove inequlity about cardinality power sets
31212
The existence of the empty set is an axiom of ZFC or not?
3673
SELECT statement using set Algebra
93771
Prove that for any set $A$ there is some $x \notin A$