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injection from $\mathbb{N^ {N}}$ to $\mathbb{R}$?

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#real-analysis #elementary-set-theory #cardinals
95
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Is $\mathcal P(\Bbb R)\sim$ the set of all real functions defined on $\Bbb R$ with values in $\{0,1\}$?

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#real-analysis #analysis #cardinals #characteristic-functions
70
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Countability of the preimages of a real valued function

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#elementary-set-theory #cardinals
39
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A slightly different definition of successors.

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#cardinals #ordinals
249
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Suppose GCH, then Aleph function and Beth function are isomorphic?

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#set-theory #cardinals
78
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Vector space isomorphism and cardinalities

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#linear-algebra #elementary-set-theory #vector-spaces #cardinals
679
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How to define infinite lists?

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#logic #set-theory #cardinals #ordinals
86
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Show that $(0,1)\cup S$ is equinumerous with $\mathbb R$.

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#elementary-set-theory #cardinals
45
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Cadinality of real sets using bijection

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#cardinals
229
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What's the strongest theory weaker than ZF without uncountable sets?

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#elementary-number-theory #set-theory #cardinals #infinity #axiom-of-choice
110
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Why is the Rado–Milner paradox considered a paradox, anyway?

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#cardinals #ordinals
321
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Can such a Dedekind cardinal exist?

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#set-theory #cardinals #axiom-of-choice
59
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If $f:\mathbb{R}\to\mathbb{R}$ then $|f(\mathbb{N})|\leq\aleph_0$

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#elementary-set-theory #cardinals
128
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How do you find the enumeration of $\mathbb N^3$

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#cardinals
112
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Proof in ZF set theory involving surjection and cardinality

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#set-theory #cardinals

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