Question

Write an inductive proof that if there is a surjection $ f : \lceil m \rceil → \lceil n \rceil $ then $m ≥ n$.

score 271 · Answer 1 · 2026-04-17 07:13:22

271

Views

Write an inductive proof that if there is a surjection $ f : \lceil m \rceil → \lceil n \rceil $ then $m ≥ n$.

Published on 17 Apr 2026 - 7:13

score 243 · Answer 2 · 2026-04-14 12:50:04

243

Views

How to show that $6^n$ always ends with a $6$ when $n\geq 1$ and $n\in\mathbb{N}$

Published on 14 Apr 2026 - 12:50

score 183 · Answer 3 · 2026-04-16 07:36:51

183

Views

Prove that if $k \in \mathbb{N}$, then $k^4+2k^3+k^2$ is divisble by $4$

Published on 16 Apr 2026 - 7:36

score 455 · Answer 4 · 2026-04-14 19:03:55

455

Views

Prove by induction that $u_n=3\times2^{n-1}-1$ for all $n\ge1$

Published on 14 Apr 2026 - 19:03

score 85 · Answer 5 · 2026-04-14 01:53:52

85

Views

Show that $\sum_{r=1}^nu_r=u_{n+1}-(n+2)$

Published on 14 Apr 2026 - 1:53

score 69 · Answer 6 · 2026-04-12 12:41:42

69

Views

Axiom of Induction Question

Published on 12 Apr 2026 - 12:41

score 1.1k · Answer 7 · 2026-04-14 16:31:48

1.1k

Views

Proving by strong induction for a sequence of integers, $2^n$ divides term $n$

Published on 14 Apr 2026 - 16:31

score 108 · Answer 8 · 2026-04-16 13:45:45

108

Views

Show that $\sum_{r=1}^nu_r=u_{n+1}-(n+2)$ given $u_1=2\,,u_{k+1}=2u_k+1\,,u_n=3\times2^{n-1}-1$

Published on 16 Apr 2026 - 13:45

score 159 · Answer 9 · 2026-04-15 05:30:23

159

Views

Prove that $(n!)^{\frac{1}{n}} < ((n+1)!)^{\frac{1}{n+1}}$

Published on 15 Apr 2026 - 5:30

score 2.2k · Answer 10 · 2026-04-17 12:00:16

2.2k

Views

Proving that for Fibonacci numbers $a_n \lt (\frac {1 + \sqrt 5} 2)^n$ for $n \ge 1$

Published on 17 Apr 2026 - 12:00

score 165 · Answer 11 · 2026-04-15 20:23:36

165

Views

Trouble with induction on the length of a word

Published on 15 Apr 2026 - 20:23

score 109 · Answer 12 · 2026-04-12 03:16:20

109

Views

Proving by induction $2^k - 1 = 1+\cdots +2^{k-1}$

Published on 12 Apr 2026 - 3:16

score 538 · Answer 13 · 2026-04-11 18:41:28

538

Views

Transfinite Induction in Peano Arithmetic

Published on 11 Apr 2026 - 18:41

score 31 · Answer 14 · 2026-04-14 00:39:05

31

Views

For any prime $p ≠ 2,5$, prove there are at most four values of the last digit of any power $p^{i}$?

Published on 14 Apr 2026 - 0:39

score 561 · Answer 15 · 2026-04-15 01:21:44

561

Views

If there is an injection $f: X \to Y$ with $m=n$ then $f$ is a bijection.

Published on 15 Apr 2026 - 1:21

List Question

Write an inductive proof that if there is a surjection $ f : \lceil m \rceil → \lceil n \rceil $ then $m ≥ n$.

How to show that $6^n$ always ends with a $6$ when $n\geq 1$ and $n\in\mathbb{N}$

Prove that if $k \in \mathbb{N}$, then $k^4+2k^3+k^2$ is divisble by $4$

Prove by induction that $u_n=3\times2^{n-1}-1$ for all $n\ge1$

Show that $\sum_{r=1}^nu_r=u_{n+1}-(n+2)$

Axiom of Induction Question

Proving by strong induction for a sequence of integers, $2^n$ divides term $n$

Show that $\sum_{r=1}^nu_r=u_{n+1}-(n+2)$ given $u_1=2\,,u_{k+1}=2u_k+1\,,u_n=3\times2^{n-1}-1$

Prove that $(n!)^{\frac{1}{n}} < ((n+1)!)^{\frac{1}{n+1}}$

Proving that for Fibonacci numbers $a_n \lt (\frac {1 + \sqrt 5} 2)^n$ for $n \ge 1$

Trouble with induction on the length of a word

Proving by induction $2^k - 1 = 1+\cdots +2^{k-1}$

Transfinite Induction in Peano Arithmetic

For any prime $p ≠ 2,5$, prove there are at most four values of the last digit of any power $p^{i}$?

If there is an injection $f: X \to Y$ with $m=n$ then $f$ is a bijection.

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