Question

Prove that for any integers $x, y$ and $z$ and any integer $k$that if $x \equiv_k y$ and $y \equiv_k z$ then $x \equiv_k z$

score 204 · Answer 1 · 2020-01-04 23:21:10

204

Views

Prove that for any integers $x, y$ and $z$ and any integer $k$that if $x \equiv_k y$ and $y \equiv_k z$ then $x \equiv_k z$

Published on 04 Jan 2020 - 23:21

score 24 · Answer 2 · 2020-01-05 14:36:19

24

Views

Calculate standard deviation of given data

Published on 05 Jan 2020 - 14:36

score 203 · Answer 3 · 2020-01-05 14:44:51

203

Views

Simplify $\frac{m}{n}$ if:$m=2244851485148514627\\n=8118811881188118000$

Published on 05 Jan 2020 - 14:44

score 113 · Answer 4 · 2020-01-05 15:47:01

113

Views

Disjoint Topological Embeddings

Published on 05 Jan 2020 - 15:47

score 242 · Answer 5 · 2020-01-05 18:54:23

242

Views

Is this proof of $\cos(z)=\cos^2\left(\frac z2\right)-\sin^2\left(\frac z2\right)$ correct?

Published on 05 Jan 2020 - 18:54

score 373 · Answer 6 · 2020-01-05 19:59:39

373

Views

If $p$ is a prime satisfying $n<p<2n$ then $\binom{2n}{n}\equiv 0 \pmod p$.

Published on 05 Jan 2020 - 19:59

score 53 · Answer 7 · 2020-01-05 22:33:52

53

Views

Isosceles trapezoid circunference

Published on 05 Jan 2020 - 22:33

score 109 · Answer 8 · 2020-01-06 02:26:38

109

Views

Proof verification: Bolzano-Weierstrass theorem fails in $\ell^2$

Published on 06 Jan 2020 - 2:26

score 72 · Answer 9 · 2026-02-24 00:50:26

72

Views

Prove that $\lim\limits_{n\rightarrow \infty}P_n(A)=P(A)$ implies $\lim\limits_{n\rightarrow \infty} \int f ~dP_n = \int f ~dP$

Published on 24 Feb 2026 - 0:50

score 48 · Answer 10 · 2020-01-06 13:57:49

48

Views

A function $f:(-1,1)\to \mathbb R$ which is differentiable and uniformly continuous but $f'$ is unbounded on the interval.

Published on 06 Jan 2020 - 13:57

score 166 · Answer 11 · 2020-01-06 17:43:50

166

Views

Counting votes: How many possible paths exist on which candidate A is never 2 votes ahead

Published on 06 Jan 2020 - 17:43

score 79 · Answer 12 · 2020-01-06 17:48:50

79

Views

Prove $\lim\limits_{n\rightarrow \infty} \int f_n ~dP_n = \int f ~dP$

Published on 06 Jan 2020 - 17:48

score 34 · Answer 13 · 2020-01-06 18:06:42

34

Views

If $f$ and $\operatorname{sign}(f)\in L^2([0,1])$, is $f\in L^1([0,1])$?

Published on 06 Jan 2020 - 18:06

score 480 · Answer 14 · 2020-01-06 19:00:54

480

Views

Prove $m^3 \leq 2^m$ for $m \geq 10$ with induction

Published on 06 Jan 2020 - 19:00

score 91 · Answer 15 · 2020-01-07 02:37:19

91

Views

proof-check: $\frac{x+a}{x^2+1}$ always has $3$ inflection points

Published on 07 Jan 2020 - 2:37

List Question

Prove that for any integers $x, y$ and $z$ and any integer $k$that if $x \equiv_k y$ and $y \equiv_k z$ then $x \equiv_k z$

Calculate standard deviation of given data

Simplify $\frac{m}{n}$ if:$m=2244851485148514627\\n=8118811881188118000$

Disjoint Topological Embeddings

Is this proof of $\cos(z)=\cos^2\left(\frac z2\right)-\sin^2\left(\frac z2\right)$ correct?

If $p$ is a prime satisfying $n<p<2n$ then $\binom{2n}{n}\equiv 0 \pmod p$.

Isosceles trapezoid circunference

Proof verification: Bolzano-Weierstrass theorem fails in $\ell^2$

Prove that $\lim\limits_{n\rightarrow \infty}P_n(A)=P(A)$ implies $\lim\limits_{n\rightarrow \infty} \int f ~dP_n = \int f ~dP$

A function $f:(-1,1)\to \mathbb R$ which is differentiable and uniformly continuous but $f'$ is unbounded on the interval.

Counting votes: How many possible paths exist on which candidate A is never 2 votes ahead

Prove $\lim\limits_{n\rightarrow \infty} \int f_n ~dP_n = \int f ~dP$

If $f$ and $\operatorname{sign}(f)\in L^2([0,1])$, is $f\in L^1([0,1])$?

Prove $m^3 \leq 2^m$ for $m \geq 10$ with induction

proof-check: $\frac{x+a}{x^2+1}$ always has $3$ inflection points

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