Tagged Questions
1
vote
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 ...
2
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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 ...
1
vote
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 ...
2
votes
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 ...
0
votes
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 ...
3
votes
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 $n>1$, ...
3
votes
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 ...
