# Tagged Questions

2answers
59 views

### Induction proof [ little-o notation ]

I have to prove that $2^n = o(n!)$, that is, $\forall c \gt 0 \quad \exists$ $n_0 \in \mathbb N$ such that $\forall n \ge n_0$ we have $2^n \lt c.n!$ Well, this is what I did so far: First I ...
2answers
148 views

### Induction Proof: $\sum_{i=1}^{n+1} i \cdot 2^i = n \cdot 2^{n+2}+2$

Prove by Mathematical Induction . . . $$\sum_{i=1}^{n+1} i \cdot 2^i = n \cdot 2^{n+2}+2$$ for all $n \geq 0$ I tried solving it, but I got stuck near the end . . . a. Basis Step: \$1\cdot 2^1 ...
1answer
230 views

### Strong induction proofs

I'm having trouble understanding strong induction proofs I understand how to do ordinary induction proofs and I understand that strong induction proofs are the same as ordinary with the exception ...
1answer
88 views

### Connected Components Graph proof

I am trying to do this one problem for a homework set, and am not entirely sure how I would even start this proof. Here is the question Prove, by induction on k, that a connected component of k nodes ...
2answers
119 views

### is it possible to prove the method of mathematical induction itself?

Since the method of mathematical induction follows some sort of 'algorithm', would the method itself be provable? namely, give that the method of mathematical induction is as follows: if S is a ...
3answers
193 views

### Statements true for all integers but not provable by induction

Is there any examples of statements P(n) such that "for all $n>1$, P(n)" is provable, but P(n)=>P(n+1) is not provable? (without using some mild deformation of "for all $n>1$, ...
1answer
148 views

### How does adding the full second order induction scheme affect the consistency strength of subsystems of second order arithmetic?

Following on from my question about $\omega$-models, I'm interested in the interaction between subsystems of second order arithmetic with restricted induction such as $\mathsf{RCA}_0$ and those which ...
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