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15
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Rational numbers - countability

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#cardinals
142
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Proof that $|A-\{x\}| = n-1$ using bijection

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#elementary-set-theory #cardinals
130
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Help showing a composition of functions is surjective

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#functions #elementary-set-theory #cardinals
820
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Prove that the collection of all rational $\epsilon$-neighbourhoods of $\mathbb{R}^n$ centered on $x \in \mathbb{Q}^n$ is countable

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#real-analysis #general-topology #cardinals
4.4k
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Show that it is impossible to list the rational numbers in increasing order

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#elementary-set-theory #order-theory #cardinals #rational-numbers
69
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Showing Rationals are Countable - Confusing Notation

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#real-analysis #cardinals #rational-numbers #decimal-expansion
472
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Calculating the cardinality

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#cardinals
62
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Struggling of a proof of cardinality

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#proof-writing #cardinals #real-numbers
73
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In Riemann rearrangement theorem are there number of rearrangements that converge to a given sum, infinitly countable or uncountable?

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#set-theory #cardinals
44
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Is there such set?

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#cardinals
1.4k
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Prove that for any set $A$, there is no one-one correspondence between $A$ and its power set $P(A)$

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#real-analysis #cardinals
97
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Cardinality of bases in Universal Algebra

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#cardinals #independence #universal-algebra #change-of-basis
385
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Is there such a thing as a "coinfinite" topology?

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#general-topology #elementary-set-theory #cardinals
43
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Can the reals be the union of a countable set and a set of lower cardinality?

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#set-theory #cardinals #axiom-of-choice
885
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Proving the cardinality of set intersections

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#elementary-set-theory #cardinals

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