Are $\{\}$ and $\{\{\}\}$ equal in set theory?
56637
In naive set theory ∅ = {∅} = {{∅}}?
79734
Is every sub-lattice of $\mathcal P(X)$ isomorphic to a sub-lattice of $\mathcal P(X')$ containing singleton sets?
58285
Is it true that if $X$ is connected, then for every nonempty proper subset $A$ of $X$, we have $\mathbf{Bd} \ne \emptyset$
126633
Is a contradiction enough to prove a set equality to $\varnothing$?
83996
For any two sets $A,B$ , $|A|\leq|B|$ or $|B|\leq|A|$
94741
Are all infinities equal?
96845
Question: Compare the cardinality between the sets $\Bbb R$ and $\Bbb N^{\Bbb N}$
54497
Set Notation - Inclusion and Proper Inclusion
109054
Given an infinite set of cardinality $X$, is there a chain in $\mathcal P(X)$ of the same cardinalty of $\mathcal P(X)$?
91163
Let the set S be infinite, and the set T countably infinite. Show that S and S U T have the same cardinality
89712
For every set $A$, the empty set is a subset of $A$. The empty set is a set. Therefore, the empty set has a cardinality $\geq 1\ldots$
43462
Disprove $\mathcal{P}(A\Delta B) \setminus \{\emptyset\} = \mathcal{P}(A) \Delta\mathcal{P}(B) $. Is my proof good?
77286
Proving set theory question
86154
Why is this true? A set is Dedekind infinite if and only if equipotent to the union with the set containing itself
28223
Prove/Disprove that if two sets have the same power set then they are the same set
142631
Show that A has the same cardinality as $A\setminus\{x,y,z\}$
44160
Set theory: difference between belong/contained and includes/subset?