Question

If $X= \lim\limits_{n \to \infty} X_n$ and $X_n=Y_n$ everywhere and $Y_n= \lim\limits_{n \to \infty} Y$ then is X=Y a.s

score 47 · Answer 1 · 2026-04-16 07:32:39

47

Views

If $X= \lim\limits_{n \to \infty} X_n$ and $X_n=Y_n$ everywhere and $Y_n= \lim\limits_{n \to \infty} Y$ then is X=Y a.s

Published on 16 Apr 2026 - 7:32

score 39 · Answer 2 · 2026-04-13 18:04:53

39

Views

A non-empty perfect set has a perfect subset with arbitrary small diameter

Published on 13 Apr 2026 - 18:04

score 181 · Answer 3 · 2026-04-14 00:12:45

181

Views

A non-empty perfect subset of $\Bbb R$ has the cardinality of $2^{\aleph_0}$

Published on 14 Apr 2026 - 0:12

score 592 · Answer 4 · 2026-04-15 23:30:16

592

Views

Bounded Sequence in $L^\infty$ and Interpolation in $L^p$

Published on 15 Apr 2026 - 23:30

score 28 · Answer 5 · 2026-04-13 08:10:21

28

Views

Prove convergence rate to zero increases as n increases

Published on 13 Apr 2026 - 8:10

score 4k · Answer 6 · 2026-04-13 23:04:30

4k

Views

A family has two children. Given that one of the children is a boy, what is the probability that both children are boys?

Published on 13 Apr 2026 - 23:04

score 81 · Answer 7 · 2026-04-15 12:47:00

81

Views

How does Hatcher conclude that the set of points where $\tilde f_1$ and $\tilde f_2$ agree is both open and closed?

Published on 15 Apr 2026 - 12:47

score 87 · Answer 8 · 2026-04-16 05:27:25

87

Views

Proof verification: $\int _0 ^{2π} \frac {2e^{it}} {1+(2e^{it})^2}dt=0$

Published on 16 Apr 2026 - 5:27

score 55 · Answer 9 · 2026-04-23 11:28:59

55

Views

g and f : ℝ -> ℝ, $f(x)=x^2; g(x)=x$. Prove that f(x) ≥g(x), for all x≥1

Published on 23 Apr 2026 - 11:28

score 89 · Answer 10 · 2026-04-16 12:11:10

89

Views

Prove that $ \binom{n}{d} \binom{n}{a} \geq \binom{n}{d+a}$

Published on 16 Apr 2026 - 12:11

score 948 · Answer 11 · 2026-04-14 09:32:27

948

Views

Proving $(ab)^{-1} = a^{-1}b^{-1}$, if $a,b\ne 0$

Published on 14 Apr 2026 - 9:32

score 216 · Answer 12 · 2026-04-13 05:10:18

216

Views

Is $8n^3+12n^2-2n-3$ divisible by 5, with $n$ congruent with 1,2,3 mod 5?

Published on 13 Apr 2026 - 5:10

score 41 · Answer 13 · 2026-04-12 00:13:56

41

Views

Measurable set.

Published on 12 Apr 2026 - 0:13

score 260 · Answer 14 · 2026-04-14 18:49:46

260

Views

Assuming Axiom of Choice, every uncountable closed set contains a perfect subset

Published on 14 Apr 2026 - 18:49

score 547 · Answer 15 · 2026-04-15 18:16:50

547

Views

Lebesgue outer measure of image of set is less than or equal to the Lebesgue outer measure of set

Published on 15 Apr 2026 - 18:16

List Question

If $X= \lim\limits_{n \to \infty} X_n$ and $X_n=Y_n$ everywhere and $Y_n= \lim\limits_{n \to \infty} Y$ then is X=Y a.s

A non-empty perfect set has a perfect subset with arbitrary small diameter

A non-empty perfect subset of $\Bbb R$ has the cardinality of $2^{\aleph_0}$

Bounded Sequence in $L^\infty$ and Interpolation in $L^p$

Prove convergence rate to zero increases as n increases

A family has two children. Given that one of the children is a boy, what is the probability that both children are boys?

How does Hatcher conclude that the set of points where $\tilde f_1$ and $\tilde f_2$ agree is both open and closed?

Proof verification: $\int _0 ^{2π} \frac {2e^{it}} {1+(2e^{it})^2}dt=0$

g and f : ℝ -> ℝ, $f(x)=x^2; g(x)=x$. Prove that f(x) ≥g(x), for all x≥1

Prove that $ \binom{n}{d} \binom{n}{a} \geq \binom{n}{d+a}$

Proving $(ab)^{-1} = a^{-1}b^{-1}$, if $a,b\ne 0$

Is $8n^3+12n^2-2n-3$ divisible by 5, with $n$ congruent with 1,2,3 mod 5?

Measurable set.

Assuming Axiom of Choice, every uncountable closed set contains a perfect subset

Lebesgue outer measure of image of set is less than or equal to the Lebesgue outer measure of set

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