Question

$\mathbb{N} ⊇ A_1 \supset A_2 \supset A_3 \supset \cdots$ but $\bigcap_{n=1}^∞ A_n$ is infinite?

score 365 · Answer 1 · 2019-10-05 04:26:54

365

Views

$\mathbb{N} ⊇ A_1 \supset A_2 \supset A_3 \supset \cdots$ but $\bigcap_{n=1}^∞ A_n$ is infinite?

Published on 05 Oct 2019 - 4:26

score 135 · Answer 2 · 2026-03-23 03:51:29

135

Views

Solve in $\mathbb N^{2}$ the following equation : $5^{2x}-3\cdot2^{2y}+5^{x}2^{y-1}-2^{y-1}-2\cdot5^{x}+1=0$

Published on 23 Mar 2026 - 3:51

score 392 · Answer 3 · 2026-03-15 22:30:39

392

Views

I can't understand how can there be languages of infinite size yet containing only words of finite length.

Published on 15 Mar 2026 - 22:30

score 31 · Answer 4 · 2019-10-09 15:31:50

31

Views

Given $A=\{0,1,2,3\}$ and $B=[-\pi,\pi]$, is $A\cup B=B$ true? $\Bbb{Z}\cap B=\{−3,−2,−1,0,1,2,3\}$? (and three others)

Published on 09 Oct 2019 - 15:31

score 160 · Answer 5 · 2026-03-26 14:42:37

160

Views

Solve $0.9^n+0.8^n \leq 0.1$

Published on 26 Mar 2026 - 14:42

score 80 · Answer 6 · 2026-03-25 15:57:23

80

Views

Possible monoidal structures on ordinal numbers

Published on 25 Mar 2026 - 15:57

score 185 · Answer 7 · 2019-10-12 08:24:30

185

Views

Prove that $n! \geq n^{\frac{n}{2}}$

Published on 12 Oct 2019 - 8:24

score 158 · Answer 8 · 2019-10-13 16:48:45

158

Views

Does there exist a natural number $n$ such that all numbers $2n+1, 2n+3, 2n+5, ... , 2n+2015$ be nonprime?

Published on 13 Oct 2019 - 16:48

score 163 · Answer 9 · 2019-10-13 18:26:11

163

Views

$T_1=1,T_2=3,T_n=2T_{n-1}+T_{n-2}$, where $n\ge3$ GCD$(T_n,T_{n-1})=1$

Published on 13 Oct 2019 - 18:26

score 152 · Answer 10 · 2019-10-17 09:17:30

152

Views

Let set A is subset of set $\{{1,2,3,...,100}\}$ which has $55$ different elements.

Published on 17 Oct 2019 - 9:17

score 85 · Answer 11 · 2019-10-19 12:45:59

85

Views

Set theoretical proof about cardinalities of natural numbers

Published on 19 Oct 2019 - 12:45

score 84 · Answer 12 · 2019-10-22 17:55:02

84

Views

Growth rate of primes of the form $a n+1$, with $n$ fixed

Published on 22 Oct 2019 - 17:55

score 981 · Answer 13 · 2019-10-24 17:01:37

981

Views

Prove that the set of partial sums of the sequence $(1/n)_n$ is closed

Published on 24 Oct 2019 - 17:01

score 540 · Answer 14 · 2019-10-30 16:26:03

540

Views

Gradient of $\ln(y^2)=\frac{1}{2}x\ln(x-1)$ at point $x=4$

Published on 30 Oct 2019 - 16:26

score 225 · Answer 15 · 2019-10-30 21:40:00

225

Views

Is the infinite union of Cartesian products of countable sets, countable?

Published on 30 Oct 2019 - 21:40

List Question

$\mathbb{N} ⊇ A_1 \supset A_2 \supset A_3 \supset \cdots$ but $\bigcap_{n=1}^∞ A_n$ is infinite?

Solve in $\mathbb N^{2}$ the following equation : $5^{2x}-3\cdot2^{2y}+5^{x}2^{y-1}-2^{y-1}-2\cdot5^{x}+1=0$

I can't understand how can there be languages of infinite size yet containing only words of finite length.

Given $A=\{0,1,2,3\}$ and $B=[-\pi,\pi]$, is $A\cup B=B$ true? $\Bbb{Z}\cap B=\{−3,−2,−1,0,1,2,3\}$? (and three others)

Solve $0.9^n+0.8^n \leq 0.1$

Possible monoidal structures on ordinal numbers

Prove that $n! \geq n^{\frac{n}{2}}$

Does there exist a natural number $n$ such that all numbers $2n+1, 2n+3, 2n+5, ... , 2n+2015$ be nonprime?

$T_1=1,T_2=3,T_n=2T_{n-1}+T_{n-2}$, where $n\ge3$ GCD$(T_n,T_{n-1})=1$

Let set A is subset of set $\{{1,2,3,...,100}\}$ which has $55$ different elements.

Set theoretical proof about cardinalities of natural numbers

Growth rate of primes of the form $a n+1$, with $n$ fixed

Prove that the set of partial sums of the sequence $(1/n)_n$ is closed

Gradient of $\ln(y^2)=\frac{1}{2}x\ln(x-1)$ at point $x=4$

Is the infinite union of Cartesian products of countable sets, countable?

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