Question

Lindelöf and co-countable topology

score 426 · Answer 1 · 2020-06-14 13:45:39

426

Views

Lindelöf and co-countable topology

Published on 14 Jun 2020 - 13:45

score 74 · Answer 2 · 2020-06-14 14:02:47

74

Views

Solving $2\sin(x)= \cot(5x)$ without finding the intersections of the graphs of the two sides

Published on 14 Jun 2020 - 14:02

score 163 · Answer 3 · 2020-06-14 18:52:12

163

Views

basis and Hausdorff space

Published on 14 Jun 2020 - 18:52

score 120 · Answer 4 · 2020-06-15 19:07:00

120

Views

If $A$, $B$ and $C$ are sets, where $A \triangle C = B \triangle C $, then $ A = B $

Published on 15 Jun 2020 - 19:07

score 44 · Answer 5 · 2020-06-16 06:16:04

44

Views

Find all the values of $y$ so that $\min\limits_{[1, 2]}\left | x^{3}- 3x+ y \right |= 6$ .

Published on 16 Jun 2020 - 6:16

score 214 · Answer 6 · 2026-03-30 20:42:45

214

Views

Rational points of an circle centred at $(\pi,2)$

Published on 30 Mar 2026 - 20:42

score 42 · Answer 7 · 2026-04-01 13:11:49

42

Views

Given two $3$-distinct-digit-natural numbers. Prove that the probability that at least one of both is a multiple of $10$ is $16/81\simeq 0.197530..$ .

Published on 01 Apr 2026 - 13:11

score 185 · Answer 8 · 2020-06-16 18:28:58

185

Views

Weak limit of non-negative functions is non-negative (without Mazur)

Published on 16 Jun 2020 - 18:28

score 110 · Answer 9 · 2026-03-30 03:56:37

110

Views

Prove that $\frac{1}{\sqrt{1}}+\frac{1}{\sqrt{2}}+\frac{1}{\sqrt{3}}+\frac{1}{\sqrt{4}}+\frac{1}{\sqrt{5}}+\frac{1}{\sqrt{6}}\cdots>\infty$ .

Published on 30 Mar 2026 - 3:56

score 186 · Answer 10 · 2026-03-25 16:03:48

186

Views

Given three real numbers $a,b,c$ so that $\{a, b, c\}\subset [1, 2]$ . Prove that $7abc\geq ab(a+ b)+ bc(b+ c)+ ca(c+ a)$ .

Published on 25 Mar 2026 - 16:03

score 110 · Answer 11 · 2026-03-26 13:42:36

110

Views

Is $\neg$Intro necessary for this proof?

Published on 26 Mar 2026 - 13:42

score 832 · Answer 12 · 2020-06-18 00:28:10

832

Views

Prove that for A, B and C sets, A - ( B - C ) = ( A - B ) ∪ ( A ∩ C ) (Alternative to the proof given)

Published on 18 Jun 2020 - 0:28

score 101 · Answer 13 · 2026-03-25 10:57:24

101

Views

Prove $\frac{a^2}{(a+b)^2} \geqslant \frac{4a^2-b^2-bc+7ca}{4(a+b+c)^2}$

Published on 25 Mar 2026 - 10:57

score 801 · Answer 14 · 2026-02-23 03:59:49

801

Views

A very interesting question: intersection point of $x^y=y^x$

Published on 23 Feb 2026 - 3:59

score 66 · Answer 15 · 2020-06-18 22:39:47

66

Views

Prove that for all sets $A$ and $B$, $( A \cup B ) - B = A$ implies $A \cap B =\varnothing$.

Published on 18 Jun 2020 - 22:39

List Question

Lindelöf and co-countable topology

Solving $2\sin(x)= \cot(5x)$ without finding the intersections of the graphs of the two sides

basis and Hausdorff space

If $A$, $B$ and $C$ are sets, where $A \triangle C = B \triangle C $, then $ A = B $

Find all the values of $y$ so that $\min\limits_{[1, 2]}\left | x^{3}- 3x+ y \right |= 6$ .

Rational points of an circle centred at $(\pi,2)$

Given two $3$-distinct-digit-natural numbers. Prove that the probability that at least one of both is a multiple of $10$ is $16/81\simeq 0.197530..$ .

Weak limit of non-negative functions is non-negative (without Mazur)

Prove that $\frac{1}{\sqrt{1}}+\frac{1}{\sqrt{2}}+\frac{1}{\sqrt{3}}+\frac{1}{\sqrt{4}}+\frac{1}{\sqrt{5}}+\frac{1}{\sqrt{6}}\cdots>\infty$ .

Given three real numbers $a,b,c$ so that $\{a, b, c\}\subset [1, 2]$ . Prove that $7abc\geq ab(a+ b)+ bc(b+ c)+ ca(c+ a)$ .

Is $\neg$Intro necessary for this proof?

Prove that for A, B and C sets, A - ( B - C ) = ( A - B ) ∪ ( A ∩ C ) (Alternative to the proof given)

Prove $\frac{a^2}{(a+b)^2} \geqslant \frac{4a^2-b^2-bc+7ca}{4(a+b+c)^2}$

A very interesting question: intersection point of $x^y=y^x$

Prove that for all sets $A$ and $B$, $( A \cup B ) - B = A$ implies $A \cap B =\varnothing$.

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