Prove $\langle P(\omega),\subseteq\rangle $ has chains with same cardinality as $P(\omega)$
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
20085
What's the cardinality of all sequences with coefficients in an infinite set?
98897
Proving that the set of $\nu$ measurable sets $M\subseteq P(X)$ is an algebra
83050
Show that $P[x]+\langle x\rangle $ is a prime ideal of $R[x]$.
128710
Prove that $\langle a^n \rangle \bigcap \langle a^k \rangle = \langle a^{lcm (n,k)} \rangle$
157218
If $E\subseteq X$ is connected, $E\cap A\neq\emptyset$ and $E\cap(X\setminus A)\neq\emptyset$ then $E\cap\partial A\neq\emptyset$
33157
Proof that an infinite subset of $\mathbb{N}$ is countable
120522
Showing any countable, dense, linear ordering is isomorphic to a subset of $\mathbb{Q}$
41783
Cardinality of the Cartesian Product of Two Equinumerous Infinite Sets
59459
Binary sequences and ${2}^{\mathbb{N}}$ have the same cardinality
150385
The use of the Axiom of Choice in this proof of the sequence lemma
48523
Let $A$ be any uncountable set, and let $B$ be a countable subset of $A$. Prove that the cardinality of $A = A - B $
62687
Proving Cardinality of Cosets in Abstract Algebra
98518
Cardinality of equivalence relations on N
38785
Prove previsibility and $E[X_{T \wedge n}] \le E[X_{S \wedge n}]$
53642
Cardinality of Borel sigma algebra