Question

Proof verification : $X_n \to X$ in distribution, $Y_n \to 0$ in probability $\implies$ $X_nY_n \to 0$ in probability

score 855 · Answer 1 · 2026-03-26 09:18:14

855

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Proof verification : $X_n \to X$ in distribution, $Y_n \to 0$ in probability $\implies$ $X_nY_n \to 0$ in probability

Published on 26 Mar 2026 - 9:18

score 155 · Answer 2 · 2026-03-25 12:50:47

155

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How many solutions are to $x_1+x_2+x_3+x_4+x_5+x_6=30$ if $x_1=6$ then $x_2\neq 4$, $x_3=6$ then $x_4\neq 4$, $x_5=6$ then $x_6\neq 4$?

Published on 25 Mar 2026 - 12:50

score 79 · Answer 3 · 2018-06-27 12:55:59

79

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If $T$ Self Adjoint So T+iI is 1-1

Published on 27 Jun 2018 - 12:55

score 78 · Answer 4 · 2018-06-27 13:11:01

In how many ways can $7$ people take elevator to $5$th floor such that at the last floor all remaining people exit (at least one remains)?

score 143 · Answer 5 · 2018-06-27 14:11:57

143

Views

Is there an "easy" way to prove the general version Hall's Marriage Theorem?

Published on 27 Jun 2018 - 14:11

score 487 · Answer 6 · 2026-03-25 16:03:59

487

Views

Prove that $f(x) = x - {\lfloor}x{\rfloor}$ is periodic.

Published on 25 Mar 2026 - 16:03

score 39 · Answer 7 · 2018-06-27 19:11:59

39

Views

If $M_A(x)=x^3-x$ So $M_{A^2}(x)=x^2-x$

Published on 27 Jun 2018 - 19:11

score 101 · Answer 8 · 2018-06-27 19:16:49

101

Views

Q: Proof with Integers, Multiplicity and Perfect Squares

Published on 27 Jun 2018 - 19:16

score 91 · Answer 9 · 2026-03-26 09:21:46

91

Views

$ \int^1_0 \max\{f_1(x), . . . , f_n(x)\} \, dx \leq C $, $f_n \geq 0$ and $f_n \to 0$, then $f_n \to 0$ in $L^1(0,1)$

Published on 26 Mar 2026 - 9:21

score 463 · Answer 10 · 2018-06-27 22:22:59

463

Views

Proving that $\mathbb{S}^n$ is the one-point-compactification of $\mathbb{S}^n \setminus \{p\}$

Published on 27 Jun 2018 - 22:22

score 49 · Answer 11 · 2026-03-27 20:12:09

49

Views

Invertibility in $\mathbb{Z}_m$.

Published on 27 Mar 2026 - 20:12

score 360 · Answer 12 · 2018-06-28 05:03:59

360

Views

Sine of a finite sum of angles

Published on 28 Jun 2018 - 5:03

score 62 · Answer 13 · 2018-06-28 05:22:03

62

Views

Show set of solutions is linear subspace

Published on 28 Jun 2018 - 5:22

score 49 · Answer 14 · 2018-06-28 07:36:25

What is vertex degree if each vertex represents a string of $\{0,1,2\}$ and there's edge between vertices iff the strings have one digit in common?

score 257 · Answer 15 · 2026-03-25 07:44:35

257

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$ \operatorname{dist}(w,A) \ge \operatorname{dist}(w, \partial A)?$ What is the mistake in this proof?

Published on 25 Mar 2026 - 7:44

List Question

Proof verification : $X_n \to X$ in distribution, $Y_n \to 0$ in probability $\implies$ $X_nY_n \to 0$ in probability

How many solutions are to $x_1+x_2+x_3+x_4+x_5+x_6=30$ if $x_1=6$ then $x_2\neq 4$, $x_3=6$ then $x_4\neq 4$, $x_5=6$ then $x_6\neq 4$?

If $T$ Self Adjoint So T+iI is 1-1

In how many ways can $7$ people take elevator to $5$th floor such that at the last floor all remaining people exit (at least one remains)?

Is there an "easy" way to prove the general version Hall's Marriage Theorem?

Prove that $f(x) = x - {\lfloor}x{\rfloor}$ is periodic.

If $M_A(x)=x^3-x$ So $M_{A^2}(x)=x^2-x$

Q: Proof with Integers, Multiplicity and Perfect Squares

$ \int^1_0 \max\{f_1(x), . . . , f_n(x)\} \, dx \leq C $, $f_n \geq 0$ and $f_n \to 0$, then $f_n \to 0$ in $L^1(0,1)$

Proving that $\mathbb{S}^n$ is the one-point-compactification of $\mathbb{S}^n \setminus \{p\}$

Invertibility in $\mathbb{Z}_m$.

Sine of a finite sum of angles

Show set of solutions is linear subspace

What is vertex degree if each vertex represents a string of $\{0,1,2\}$ and there's edge between vertices iff the strings have one digit in common?

$ \operatorname{dist}(w,A) \ge \operatorname{dist}(w, \partial A)?$ What is the mistake in this proof?

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