Question

In a mathematical induction, can you prove the "n'th case implies n+1'th case" step by contrapositive?

score 156 · Answer 1 · 2026-03-25 12:54:31

156

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In a mathematical induction, can you prove the "n'th case implies n+1'th case" step by contrapositive?

Published on 25 Mar 2026 - 12:54

score 29 · Answer 2 · 2018-07-17 05:19:59

29

Views

Find the incorrectness of the process.

Published on 17 Jul 2018 - 5:19

score 256 · Answer 3 · 2018-07-17 05:35:07

256

Views

Let $I_1, I_2, \cdots$ be any countable collection of intervals, whose union contains some interval $I$, then $\sum P(I_j) \geq P(I)$.

Published on 17 Jul 2018 - 5:35

score 367 · Answer 4 · 2026-03-25 14:32:38

367

Views

Covering space with transitive action is path-connected.

Published on 25 Mar 2026 - 14:32

score 78 · Answer 5 · 2026-03-26 12:08:26

78

Views

Prove that $\sum_{j=1}^{n} \mathbb{P}(I_j) \geq \mathbb{P}(I)$, when $\bigcup_{j=1}^n I_j \supseteq I$.

Published on 26 Mar 2026 - 12:08

score 342 · Answer 6 · 2026-03-26 01:28:35

342

Views

$\frac{x^2+y^2}{x-y}|1995$. Find positive integer $x,y$

Published on 26 Mar 2026 - 1:28

score 216 · Answer 7 · 2026-04-01 22:37:24

216

Views

$f$ is continuous, if $f_n$ continuous and $f_n\to f$ uniformly

Published on 01 Apr 2026 - 22:37

score 3k · Answer 8 · 2018-07-17 18:49:45

3k

Views

Three cards are randomly chosen without replacement from an ordinary deck of 52 playing cards.

Published on 17 Jul 2018 - 18:49

score 152 · Answer 9 · 2026-03-25 16:08:21

152

Views

Proof that $\sum_{n = 0}^{\infty}\dfrac{1}{n(n+1)}$ converges to $1$

Published on 25 Mar 2026 - 16:08

score 44 · Answer 10 · 2026-03-30 23:20:49

44

Views

Show ab is also a unit

Published on 30 Mar 2026 - 23:20

score 82 · Answer 11 · 2026-03-30 15:01:49

82

Views

Show $ax+b=0$ has only one solution

Published on 30 Mar 2026 - 15:01

score 612 · Answer 12 · 2018-07-18 00:46:01

612

Views

Is this proof of $0 * a = 0$ correct?

Published on 18 Jul 2018 - 0:46

score 386 · Answer 13 · 2026-03-25 05:01:32

386

Views

Proof Check for General Topology of Topological Groups

Published on 25 Mar 2026 - 5:01

score 58 · Answer 14 · 2026-03-26 10:46:18

58

Views

Attempt to proof following statement (kernel and image of a matrix)

Published on 26 Mar 2026 - 10:46

score 59 · Answer 15 · 2026-03-26 10:45:13

59

Views

Proof verification of Simplicial homology of $M_g$

Published on 26 Mar 2026 - 10:45

List Question

In a mathematical induction, can you prove the "n'th case implies n+1'th case" step by contrapositive?

Find the incorrectness of the process.

Let $I_1, I_2, \cdots$ be any countable collection of intervals, whose union contains some interval $I$, then $\sum P(I_j) \geq P(I)$.

Covering space with transitive action is path-connected.

Prove that $\sum_{j=1}^{n} \mathbb{P}(I_j) \geq \mathbb{P}(I)$, when $\bigcup_{j=1}^n I_j \supseteq I$.

$\frac{x^2+y^2}{x-y}|1995$. Find positive integer $x,y$

$f$ is continuous, if $f_n$ continuous and $f_n\to f$ uniformly

Three cards are randomly chosen without replacement from an ordinary deck of 52 playing cards.

Proof that $\sum_{n = 0}^{\infty}\dfrac{1}{n(n+1)}$ converges to $1$

Show ab is also a unit

Show $ax+b=0$ has only one solution

Is this proof of $0 * a = 0$ correct?

Proof Check for General Topology of Topological Groups

Attempt to proof following statement (kernel and image of a matrix)

Proof verification of Simplicial homology of $M_g$

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