Question

Show that for a finite set $A$ of cardinality $n$, the cardinality of $P(A)$ is $2^n$.

score 1.4k · Answer 1 · 2026-03-25 08:13:41

1.4k

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Show that for a finite set $A$ of cardinality $n$, the cardinality of $P(A)$ is $2^n$.

Published on 25 Mar 2026 - 8:13

score 124 · Answer 2 · 2026-03-28 04:52:19

124

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Continuous function, not on reals: each value twice?

Published on 28 Mar 2026 - 4:52

score 444 · Answer 3 · 2026-03-25 21:46:21

444

Views

An integral inequality from AMM

Published on 25 Mar 2026 - 21:46

score 56 · Answer 4 · 2026-04-04 09:16:35

56

Views

Exercise on first and second order derivative in sense of distributions.

Published on 04 Apr 2026 - 9:16

score 251 · Answer 5 · 2026-03-26 07:33:19

251

Views

Let $(X,d_{disc})$. Show that $E\subset X$ is disconnected

Published on 26 Mar 2026 - 7:33

score 53 · Answer 6 · 2026-03-25 21:45:52

53

Views

dot product and norm "one"

Published on 25 Mar 2026 - 21:45

score 35 · Answer 7 · 2018-02-07 21:47:29

35

Views

Polynomial Root Neighbourhood

Published on 07 Feb 2018 - 21:47

score 32 · Answer 8 · 2018-02-07 22:24:04

32

Views

Consider for any positive number $a$, how to show that $\sqrt{x} + \sqrt{x} \sqrt{\ln{x}} \leq 2 + 2x$?

Published on 07 Feb 2018 - 22:24

score 36 · Answer 9 · 2026-03-24 22:09:40

36

Views

Condition on $\nu$ which makes the inclusion map from $C(X)$ to $L^{\infty}(X)$ injective

Published on 24 Mar 2026 - 22:09

score 1.7k · Answer 10 · 2026-04-01 09:03:47

1.7k

Views

Understanding Compact and Connected Sets

Published on 01 Apr 2026 - 9:03

score 240 · Answer 11 · 2026-04-01 04:19:48

240

Views

Self Study standards for Real Analysis.

Published on 01 Apr 2026 - 4:19

score 1.5k · Answer 12 · 2026-03-25 10:25:33

1.5k

Views

$s + \frac{1}{n}$ is an upper bound for $A$ and $s - \frac{1}{n}$ is not an upper bound for $A$. Show $s = \sup A.$

Published on 25 Mar 2026 - 10:25

score 5.1k · Answer 13 · 2026-04-06 21:43:48

5.1k

Views

Showing that a totally bounded set is relatively compact (closure is compact)

Published on 06 Apr 2026 - 21:43

score 670 · Answer 14 · 2026-04-04 07:19:39

670

Views

Pointwise and Uniform Convergence. Showing unique limit.

Published on 04 Apr 2026 - 7:19

score 136 · Answer 15 · 2018-02-08 10:33:11

136

Views

Finding converging majorant for $\sum_{n=1}^\infty\left(\frac{n^2}{n^2+1}\right)^{n^3}$

Published on 08 Feb 2018 - 10:33

List Question

Show that for a finite set $A$ of cardinality $n$, the cardinality of $P(A)$ is $2^n$.

Continuous function, not on reals: each value twice?

An integral inequality from AMM

Exercise on first and second order derivative in sense of distributions.

Let $(X,d_{disc})$. Show that $E\subset X$ is disconnected

dot product and norm "one"

Polynomial Root Neighbourhood

Consider for any positive number $a$, how to show that $\sqrt{x} + \sqrt{x} \sqrt{\ln{x}} \leq 2 + 2x$?

Condition on $\nu$ which makes the inclusion map from $C(X)$ to $L^{\infty}(X)$ injective

Understanding Compact and Connected Sets

Self Study standards for Real Analysis.

$s + \frac{1}{n}$ is an upper bound for $A$ and $s - \frac{1}{n}$ is not an upper bound for $A$. Show $s = \sup A.$

Showing that a totally bounded set is relatively compact (closure is compact)

Pointwise and Uniform Convergence. Showing unique limit.

Finding converging majorant for $\sum_{n=1}^\infty\left(\frac{n^2}{n^2+1}\right)^{n^3}$

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