List questions from induction

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Handshaking puzzle

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Using Bernoulli's Inequality to prove $n^{\frac{1}{n}} < 2-\frac{1}{n}$

Published on 06 Jul 2020 - 21:54

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Strong induction and mistake

Published on 11 Apr 2026 - 16:39

243

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Completing the proof using strong induction for $E = \bigcap_{n=1}^\infty E_n $

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I need to prove that in a complete oriented graph , you can change the orientation of one edge so that the resulting graph is connected.

Published on 08 Jul 2020 - 20:03

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Prove that if the graph on $n$ vertices has at least $(n / 2)^2 + 1$ edges, then it has a triangle in it.

Published on 09 Jul 2020 - 5:15

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Sigma index (Induction)

Published on 11 Apr 2026 - 18:02

194

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Induction and recursion - right out of the set theory starting gate after defining finite sets.

Published on 29 Mar 2026 - 17:44

199

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Prob. 3 (d), Sec. 1, in G.F. Simmon's INTRO TO TOPOLOGY & MODERN ANALYSIS

Published on 01 Apr 2026 - 4:38

61

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Induction on 3D grid with one cube missing

Published on 08 Apr 2026 - 18:36

41

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Prove for some finite $k$, $f^k(n)=1 \forall n \in \mathbb{N} $

Published on 07 Apr 2026 - 21:23

89

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Path induction for homotopies between functions

Published on 15 Mar 2026 - 9:43

54

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Proof the theorem from linear algebra

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Why is $f_1^2=f_1f_2=1$?

Published on 14 Jul 2020 - 14:01

List Question

Show that: The set of all finite subsets of $\mathbb{N}$ is a countable set

Handshaking puzzle

Using Bernoulli's Inequality to prove $n^{\frac{1}{n}} < 2-\frac{1}{n}$

Strong induction and mistake

Completing the proof using strong induction for $E = \bigcap_{n=1}^\infty E_n $

I need to prove that in a complete oriented graph , you can change the orientation of one edge so that the resulting graph is connected.

Prove that if the graph on $n$ vertices has at least $(n / 2)^2 + 1$ edges, then it has a triangle in it.

Sigma index (Induction)

Induction and recursion - right out of the set theory starting gate after defining finite sets.

Prob. 3 (d), Sec. 1, in G.F. Simmon's INTRO TO TOPOLOGY & MODERN ANALYSIS

Induction on 3D grid with one cube missing

Prove for some finite $k$, $f^k(n)=1 \forall n \in \mathbb{N} $

Path induction for homotopies between functions

Proof the theorem from linear algebra

Why is $f_1^2=f_1f_2=1$?

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