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Proof: $n < \aleph_0$

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#elementary-set-theory #cardinals
45
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What is the cardianlity of Z[x], the set of all polynomials with integer coefficients?

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#discrete-mathematics #polynomials #cardinals
94
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Help understanding countable and uncountable infinities

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#limits #cardinals #infinity #ordinals
95
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A question about sets and $ 2^{\aleph_0}$.

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#real-analysis #set-theory #cardinals
78
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Mathematical implications of an infinite cosmos - distance between two arbitrary points?

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#soft-question #cardinals #infinity
74
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What are the practical applications of $\aleph_2$? Does there exist a set with such cardinality that is ordered?

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#elementary-set-theory #cardinals
48
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How to prove that the following object is not a set?

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#elementary-set-theory #cardinals #ordinals
282
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What is wrong with this cardinality-based proof of the Cantor–Schröder–Bernstein theorem?

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#functions #elementary-set-theory #cardinals #fake-proofs
160
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Flaw in my proof that $\mathbb Q$ is countable?

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#elementary-set-theory #cardinals #rational-numbers #fake-proofs
30
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a cardinal notation

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#set-theory #cardinals
156
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Does $2a = 2b$ imply $a = b$ in ZF?

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#set-theory #cardinals #axiom-of-choice
61
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Jech exercise 5.24

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#set-theory #cardinals
61
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How to prove $2^{\aleph_0} = \operatorname{card}(P(\mathbb N))$

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#elementary-set-theory #cardinals
82
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When we assume every set is well-orderable under choice, are we fixing a particular well-order for each set?

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#set-theory #cardinals #ordinals
111
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Various proofs of Cantor's theorem.

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#set-theory #cardinals

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