If $A$ is a non-empty set, then $A \notin A$
20140
Example of set which contains itself
17461
Show that a set is dense in $[-1,1]$
7733
If A is infinite, does there have to exist a subset of A that is equivalent to A?
130418
Is ${\{\emptyset,\{\emptyset\},\{\{\emptyset\}\},\{\{\{\emptyset\}\}\},...\}} $ a set?
32929
Questions about proving $\lnot \lnot a = a$
80827
Let $A$ be a nonempty subset of $\mathbb{R}$. Prove...
36485
$H_n(X,A) \not \approx \tilde{H}_n(X/A)$
74860
Why is the empty set a subset of every set?
58594
Is the empty set a subset of itself?
138055
If $A$ has a positive Lebesgue measure then there exist subsets which are not measurable
83714
$A \in B$ vs. $A \subset B$ for proofs
110957
No non-trivial clopen sets in $\mathbb{R}$? How to give a direct proof?
5230
Why can a 1 element set be a member of another set but not a subset of it?
126633
Is a contradiction enough to prove a set equality to $\varnothing$?
82315
is an empty set an element of {empty set}
77286
Proving set theory question
73336
If $A$ is a nowhere dense subset of a topological space $X$, then $X\setminus A$ is dense in $X$.