Question

Explicit bijection between $[0,1)$ and $(0,1)$

score 6.8k · Answer 1 · 2015-09-07 15:38:15

6.8k

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Explicit bijection between $[0,1)$ and $(0,1)$

Published on 07 Sep 2015 - 15:38

score 1.8k · Answer 2 · 2015-09-08 18:48:23

1.8k

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Proving Power Set of $\mathbb N$ is Uncountable

Published on 08 Sep 2015 - 18:48

score 570 · Answer 3 · 2015-09-09 10:07:05

570

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If $X$ is finite and $f:X \rightarrow Y$ is a function, then $f(X)$ is a finite set with $|f(X)| \leq |X|$.

Published on 09 Sep 2015 - 10:07

score 326 · Answer 4 · 2015-09-09 16:10:59

326

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Does there exist a bijection between sets $A\setminus B$ and $A$?

Published on 09 Sep 2015 - 16:10

score 146 · Answer 5 · 2015-09-10 14:16:20

146

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Proving $2^{\aleph_0} = {\aleph_0}!$

Published on 10 Sep 2015 - 14:16

score 144 · Answer 6 · 2015-09-11 17:18:49

144

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if $\alpha$ is an ordinal is it true that ${\aleph _{\alpha +1}}^{\aleph _{\alpha}}=\aleph _{\alpha +1}$?

Published on 11 Sep 2015 - 17:18

score 8.1k · Answer 7 · 2015-09-11 18:43:00

8.1k

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Trouble with definition of countable, denumerable

Published on 11 Sep 2015 - 18:43

score 341 · Answer 8 · 2015-09-13 16:15:16

341

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Monotonic "Subfunction"

Published on 13 Sep 2015 - 16:15

score 20.8k · Answer 9 · 2015-09-14 03:23:04

20.8k

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Prove: Any open interval has the same cardinality of $\Bbb R$ (without using trigonometric functions)

Published on 14 Sep 2015 - 3:23

score 885 · Answer 10 · 2015-09-15 19:50:48

885

Views

Give a bijection $f: (c,d) \to \Bbb R$ (f no trigonometric) to prove every open interval has the same cardinality of R

Published on 15 Sep 2015 - 19:50

score 67 · Answer 11 · 2015-09-16 01:27:53

67

Views

Basic Facts About the Cardinality of the Power Set

Published on 16 Sep 2015 - 1:27

score 162 · Answer 12 · 2015-09-17 04:43:25

162

Views

Prove that if $X$ and $Y$ are sets where $\,\left|X\right|=\left|Y\right|,\,$ then $\,\left|P\left(X\right)\right|=\left| P\left(Y\right)\right|$.

Published on 17 Sep 2015 - 4:43

score 142 · Answer 13 · 2015-09-18 00:13:07

142

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Comparability of vector spaces over the same field

Published on 18 Sep 2015 - 0:13

score 97 · Answer 14 · 2015-09-19 11:35:56

97

Views

Infinite Cardinal number power.

Published on 19 Sep 2015 - 11:35

score 64 · Answer 15 · 2015-09-22 08:19:35

64

Views

Question about cardinal arithmetic

Published on 22 Sep 2015 - 8:19

List Question

Explicit bijection between $[0,1)$ and $(0,1)$

Proving Power Set of $\mathbb N$ is Uncountable

If $X$ is finite and $f:X \rightarrow Y$ is a function, then $f(X)$ is a finite set with $|f(X)| \leq |X|$.

Does there exist a bijection between sets $A\setminus B$ and $A$?

Proving $2^{\aleph_0} = {\aleph_0}!$

if $\alpha$ is an ordinal is it true that ${\aleph _{\alpha +1}}^{\aleph _{\alpha}}=\aleph _{\alpha +1}$?

Trouble with definition of countable, denumerable

Monotonic "Subfunction"

Prove: Any open interval has the same cardinality of $\Bbb R$ (without using trigonometric functions)

Give a bijection $f: (c,d) \to \Bbb R$ (f no trigonometric) to prove every open interval has the same cardinality of R

Basic Facts About the Cardinality of the Power Set

Prove that if $X$ and $Y$ are sets where $\,\left|X\right|=\left|Y\right|,\,$ then $\,\left|P\left(X\right)\right|=\left| P\left(Y\right)\right|$.

Comparability of vector spaces over the same field

Infinite Cardinal number power.

Question about cardinal arithmetic

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