Prove if A is a set finite and B is infinite then $|A|+|B|=|B|$
127656
How to prove that if $A$ is infinite and $B$ is finite, then $|A\cup B|=|A|$?
91163
Let the set S be infinite, and the set T countably infinite. Show that S and S U T have the same cardinality
151295
Proving $|S \times \mathbb{N}|=|S|$ when $S$ is an infinite set
76049
Prove that if $a|b$ and $a|c$ then $a|(sb+tc)$ for all $s, t \in \mathbb{Z}$
128437
How to prove that a finite set is countable
33157
Proof that an infinite subset of $\mathbb{N}$ is countable
6478
Prove that for any infinite poset there is an infinite subset which is either linearly ordered or antichain.
46240
Show that if $A$ and $B$ are sets, then $(A\cap B) \cup (A\cap \overline{B})=A$.
48797
Proving Two Sets are Equal - Infinite Sets - Example
66301
The cardinality of the set of countably infinite subsets of an infinite set
63535
Prove that if $A – C = B – C$ and $A\cap C = B\cap C$ then $A = B$
123979
Checking proof for: It is possible to find addition assumptions on the sets $A$ and $B$, so $P(A)\cup P(B) = P(A\cup B)$.
83518
Proving Two sets have same cardinality
144360
For any sets $A$ and $B$, show that $(B\smallsetminus A)\cup A=B \iff A\subseteq B$.
152382
Can an infinite set A be larger than an infinite set B but still have the same cardinality?
48278
Inequality about infinite cardinals
144787
Show that the set of all infinite subsets of $\mathbb{N}$ has cardinality greater than $\mathbb{N}$