Prove that if $x$ is a set, then $x$ is not an element of itself.
62208
If $A$ is a non-empty set, then $A \notin A$
17510
Proving a set is an abelian group.
14496
Is there any example of a non-measurable set whose proof of existence doesn't appeal to the Axiom of choice?
100399
A doubt with a part of a certain proof.
36281
A set is infinite iff it is equivalent to a proper subset of itself
20706
Non-existence of a Surjective Function from a Set to Its Subsets (Cantor's theorem)
37183
Show that the set of all $x$ such that $x \in P$ and $x \notin Q$ exists
71922
Prove Uncountable set minus a countable set is uncountable
59275
If $X$ is an infinite set, then $X$ with the discrete topology is not compact
23764
Proving that $A+A \not\subset 2A $ using a particular definition for sum of sets
139841
Proving $A\setminus(B\setminus C)$ is not equal to $(A\setminus B)\setminus C$
66948
Proving question on sets
25834
Proof a set cannot contain its own powerset - Russell's Paradox
126633
Is a contradiction enough to prove a set equality to $\varnothing$?
56637
In naive set theory ∅ = {∅} = {{∅}}?
16056
Is empty set element of every set if it is subset of every set?
40232
What do we mean when we say "Let $x$ be an element of the set $\mathbb{R}$"?