0 like 0 dislike
0 like 0 dislike
Using multiple base cases in weak induction

1 Answer

0 like 0 dislike
0 like 0 dislike
The number of basis cases does not determine which inductive method you're using, rather the inductive hypothesis.



With weak induction on a natural number n, we wish to assume that k<n is true for *some*  k and show that k+1 is true.


With strong induction on a natural number n, we wish to assume that for any c =< k < n, k+1 is true *for all*  k, where c is the value of one of our basis cases, and show that k+1 is true.



The tried-and-true domino allegory works well here. Weak induction ensures that if I pick any one domino to knock over, the next one must fall as well. Strong induction ensures that if I knock down one domino, every single domino afterward must also fall.
by

Related questions

0 like 0 dislike
0 like 0 dislike
0 answers
MorganHoover_ asked Jun 21
"Previous comparison of change in CAPS score between sertraline and placebo showed effect sizes of 0.31 and 0.37 (ref. 16). Similarly, comparison of change in CAPS score ...
MorganHoover_ asked Jun 21
0 like 0 dislike
0 like 0 dislike
1 answer
TylerReddick asked Jun 21
Hello Stats, I am trying to model frequency of an event, and I am looking for the best way to do this. My response variable is frequency, and I am fitting it with Poisson...
TylerReddick asked Jun 21
0 like 0 dislike
0 like 0 dislike
1 answer
_moadams asked Jun 21
I am running a LGCM and have identified a best fitting, two-class trajectory. The problem is that when I open the plots to see the estimated means and observed individual...
_moadams asked Jun 21
0 like 0 dislike
0 like 0 dislike
1 answer
ansaeuropa asked Jun 21
Hi! I thought that this would be a perfect place to discuss about my current project I'm thinking of doing. I have the chance to explore Trackman data, (trackman is a dev...
ansaeuropa asked Jun 21
0 like 0 dislike
0 like 0 dislike
26 answers
PawSox asked Jun 21
I have training in physics and maths and have been looking at statistical programming jobs in the private sector (mostly biotech), and it seems like every single company...
PawSox asked Jun 21
by PawSox

24.8k questions

103k answers

0 comments

33.7k users

OhhAskMe is a math solving hub where high school and university students ask and answer loads of math questions, discuss the latest in math, and share their knowledge. It’s 100% free!