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Prove if $A$ is infinite and $B$ is finite, then card($A \cup B$) = card($A$).

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Orders of subgroups of Infinite Profinite Groups

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How can I prove that $|A| + |B| = |A\cup B| + |A\cap B|$?

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Operations with cardinals in transcendence base proof

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How to prove that every infinite cardinal $Z$ is equal the countable sum of sets of size $Z$?

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If $A$ is a set, then $\mathrm{card}(P(A)) = 2^{\mathrm{card} A}$.

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stationary subset of $cf(\kappa)$

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Axiom of choice , Hartogs ordinals, well-ordering principle

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A question on the power set

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Differences in worlds with and without $\aleph_0<|S|<2^{\aleph_0}$

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List Question

A question on almost disjoint collection

How to explain that $\Bbb{R}$ is not countable to a non-mathematician

Existence of a sequence that has every element of $\mathbb N$ infinite number of times

Prove if $A$ is infinite and $B$ is finite, then card($A \cup B$) = card($A$).

Orders of subgroups of Infinite Profinite Groups

How can I prove that $|A| + |B| = |A\cup B| + |A\cap B|$?

Operations with cardinals in transcendence base proof

How to prove that every infinite cardinal $Z$ is equal the countable sum of sets of size $Z$?

Two Questions on "Set Theory"

If $A$ is a set, then $\mathrm{card}(P(A)) = 2^{\mathrm{card} A}$.

stationary subset of $cf(\kappa)$

Axiom of choice , Hartogs ordinals, well-ordering principle

A question on the power set

Differences in worlds with and without $\aleph_0<|S|<2^{\aleph_0}$

Countable or uncountable

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