07-01-2013, 06:57 AM
(This post was last modified: 07-01-2013, 07:14 AM by Guy1234567890.)
(06-30-2013, 09:01 PM)Thor23 Wrote: But you can't assume it works for all n = k because you don't know if that's true. You can only assume it works for one k, then show that if - based off that assumption - k+1 also happens to be true, then it will work for whatever k happens to be. If k+1 doesn't work, then your assumption must have been wrong.
Actually, the assumption is not that it works for all n. Rather, it is that it works for all k+1. Then after showing this to be true, and because you know it works for a specific k, you must therefore know that it works for all whole number values greater than the "seed" value.
Effectively, you show it to work for n=0, and hence n=1, and hence n=2 etc. because each time you show it works for a specific n, it therefore also works for that n+1, and hence for that n+1 and so on.