Question

Modulo fix-point by induction

score 59 · Answer 1 · 2018-06-21 09:05:47

59

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Modulo fix-point by induction

Published on 21 Jun 2018 - 9:05

score 98 · Answer 2 · 2018-06-21 14:11:23

98

Views

$(\forall n, {\rm T} \vdash P(n)) \Rightarrow ({\rm T} \vdash \forall n, P(n))$ Why is it false?

Published on 21 Jun 2018 - 14:11

score 116 · Answer 3 · 2018-06-22 00:10:48

116

Views

Show by mathematical induction that $(2n)! > 2^n*n!$ for all $n \geq 2$

Published on 22 Jun 2018 - 0:10

score 1.3k · Answer 4 · 2018-06-22 11:18:02

1.3k

Views

For any two finite sets $X$ and $Y$, prove that $\#(Y^X)=\#(Y)^{\#(X)}$ by induction

Published on 22 Jun 2018 - 11:18

score 7.6k · Answer 5 · 2026-03-25 22:30:50

7.6k

Views

Prove by induction that $n^4-4n^2$ is divisible by 3 for all integers $n\geq1$.

Published on 25 Mar 2026 - 22:30

score 139 · Answer 6 · 2018-06-23 12:53:24

139

Views

Consider the next succession and prove by induction

Published on 23 Jun 2018 - 12:53

score 81 · Answer 7 · 2018-06-23 14:22:07

81

Views

Preserving addition of one in inductive step of modulo

Published on 23 Jun 2018 - 14:22

score 82 · Answer 8 · 2026-03-26 17:53:31

82

Views

Alternative proof of $\sum_{k=0}^{n}{\binom{2n+1}{k}}2^{n-k} = \sum_{k=0}^{n}{\binom{n+k}{k}}3^{n-k}$

Published on 26 Mar 2026 - 17:53

score 93 · Answer 9 · 2018-06-25 01:03:25

93

Views

I’m stuck on an induction proof and need some help on proofs in general

Published on 25 Jun 2018 - 1:03

score 115 · Answer 10 · 2018-06-25 07:31:14

115

Views

Prove $ \frac{1}{2\sqrt{1}}+\frac{1}{3\sqrt{2}}+\dots+\frac{1}{(n+1)\sqrt{n}}<2$

Published on 25 Jun 2018 - 7:31

score 388 · Answer 11 · 2018-06-25 08:27:01

388

Views

Cauchy's induction principle

Published on 25 Jun 2018 - 8:27

score 77 · Answer 12 · 2018-06-25 19:47:00

77

Views

Prove by induction for $\forall n\in \Bbb N_1 $ that $2^n \ge 1+n $.

Published on 25 Jun 2018 - 19:47

score 123 · Answer 13 · 2018-06-25 21:34:23

123

Views

Considering the next succession, prove by induction that $b_n<0$ for $n \ge 2$ - Is this correct?

Published on 25 Jun 2018 - 21:34

score 107 · Answer 14 · 2018-06-26 10:20:14

107

Views

Proving after some minutes nobody will change her marker

Published on 26 Jun 2018 - 10:20

score 101 · Answer 15 · 2026-03-25 16:00:22

101

Views

How can I create new identities with sums?

Published on 25 Mar 2026 - 16:00

List Question

Modulo fix-point by induction

$(\forall n, {\rm T} \vdash P(n)) \Rightarrow ({\rm T} \vdash \forall n, P(n))$ Why is it false?

Show by mathematical induction that $(2n)! > 2^n*n!$ for all $n \geq 2$

For any two finite sets $X$ and $Y$, prove that $\#(Y^X)=\#(Y)^{\#(X)}$ by induction

Prove by induction that $n^4-4n^2$ is divisible by 3 for all integers $n\geq1$.

Consider the next succession and prove by induction

Preserving addition of one in inductive step of modulo

Alternative proof of $\sum_{k=0}^{n}{\binom{2n+1}{k}}2^{n-k} = \sum_{k=0}^{n}{\binom{n+k}{k}}3^{n-k}$

I’m stuck on an induction proof and need some help on proofs in general

Prove $ \frac{1}{2\sqrt{1}}+\frac{1}{3\sqrt{2}}+\dots+\frac{1}{(n+1)\sqrt{n}}<2$

Cauchy's induction principle

Prove by induction for $\forall n\in \Bbb N_1 $ that $2^n \ge 1+n $.

Considering the next succession, prove by induction that $b_n<0$ for $n \ge 2$ - Is this correct?

Proving after some minutes nobody will change her marker

How can I create new identities with sums?

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