Question

Proof: For any integer $n$ with $n \ge 1$, the number of permutations of a set with $n$ elements is $n!$.

score 7k · Answer 1 · 2018-12-28 16:19:23

7k

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Proof: For any integer $n$ with $n \ge 1$, the number of permutations of a set with $n$ elements is $n!$.

Published on 28 Dec 2018 - 16:19

score 33 · Answer 2 · 2018-12-29 03:37:22

33

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Inductive proof verification

Published on 29 Dec 2018 - 3:37

score 289 · Answer 3 · 2018-12-29 17:01:13

289

Views

Prove through induction that $a \in A_1 \triangle A_2 \triangle \ldots \triangle A_n $ $\iff$ $|{\{i|a \in A_i}\}| $ is odd

Published on 29 Dec 2018 - 17:01

score 86 · Answer 4 · 2026-03-26 01:02:08

86

Views

Prove that $a_n \in [0,2)$

Published on 26 Mar 2026 - 1:02

score 119 · Answer 5 · 2026-03-26 09:50:06

119

Views

Prove $x_1^2 + x_2^3 + ... + x_{n - 1}^n + \frac{1}{x_1^2 x_2^3 ... x_{n - 1}^n} \geq n + (x_1 - 1)^2 + 2(x_2 - 1)^2 + ... + (n - 1)(x_{n - 1} - 1)^2$

Published on 26 Mar 2026 - 9:50

score 1.5k · Answer 6 · 2026-03-26 06:23:10

1.5k

Views

Prove for the Fibonacci sequence: $F(m+n) = F(m-1) \cdot F(n) + F(m) \cdot F(n+1)$

Published on 26 Mar 2026 - 6:23

score 381 · Answer 7 · 2019-01-02 09:23:21

381

Views

Strong induction and vacuous truth

Published on 02 Jan 2019 - 9:23

score 104 · Answer 8 · 2019-01-03 09:02:45

104

Views

How to show the number of domains the disk is split into is $1+ C_n^2 + C_n^4$?

Published on 03 Jan 2019 - 9:02

score 736 · Answer 9 · 2026-02-23 01:03:56

736

Views

Proving That Consecutive Fibonacci Numbers are Relatively Prime

Published on 23 Feb 2026 - 1:03

score 97 · Answer 10 · 2019-01-04 12:02:43

97

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$Q(n)$: "$P(k)$ holds for all $k<n$". Then why is $Q(0)$ clearly true?

Published on 04 Jan 2019 - 12:02

score 314 · Answer 11 · 2026-03-26 08:02:17

314

Views

Proving the Fibonacci identity $(−1)^{m−k}(F_{m+k+1}F_{m−k−1}−F_{m+k}F_{m−k}) =F_{k}^2+F_{k+1}^2$

Published on 26 Mar 2026 - 8:02

score 43 · Answer 12 · 2019-01-05 13:04:12

43

Views

Is my proof by induction of even number arithmetic progression correct?

Published on 05 Jan 2019 - 13:04

score 116 · Answer 13 · 2026-03-25 19:05:55

116

Views

How to prove $a_{n+1}=(1+a_n+a^2_{n-1})/3$ is a non-decreasing sequence?

Published on 25 Mar 2026 - 19:05

score 91 · Answer 14 · 2019-01-07 11:48:44

91

Views

Is the following Strong Induction conclusion true?

Published on 07 Jan 2019 - 11:48

score 36 · Answer 15 · 2019-01-07 12:14:19

36

Views

Proof by simple induction, question concerning the inductive step

Published on 07 Jan 2019 - 12:14

List Question

Proof: For any integer $n$ with $n \ge 1$, the number of permutations of a set with $n$ elements is $n!$.

Inductive proof verification

Prove through induction that $a \in A_1 \triangle A_2 \triangle \ldots \triangle A_n $ $\iff$ $|{\{i|a \in A_i}\}| $ is odd

Prove that $a_n \in [0,2)$

Prove $x_1^2 + x_2^3 + ... + x_{n - 1}^n + \frac{1}{x_1^2 x_2^3 ... x_{n - 1}^n} \geq n + (x_1 - 1)^2 + 2(x_2 - 1)^2 + ... + (n - 1)(x_{n - 1} - 1)^2$

Prove for the Fibonacci sequence: $F(m+n) = F(m-1) \cdot F(n) + F(m) \cdot F(n+1)$

Strong induction and vacuous truth

How to show the number of domains the disk is split into is $1+ C_n^2 + C_n^4$?

Proving That Consecutive Fibonacci Numbers are Relatively Prime

$Q(n)$: "$P(k)$ holds for all $k<n$". Then why is $Q(0)$ clearly true?

Proving the Fibonacci identity $(−1)^{m−k}(F_{m+k+1}F_{m−k−1}−F_{m+k}F_{m−k}) =F_{k}^2+F_{k+1}^2$

Is my proof by induction of even number arithmetic progression correct?

How to prove $a_{n+1}=(1+a_n+a^2_{n-1})/3$ is a non-decreasing sequence?

Is the following Strong Induction conclusion true?

Proof by simple induction, question concerning the inductive step

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