Double Assumption vs Hard Induction?!?! (1 Viewer)

[Jacob1991]

i think that's what they're called.so say im using MI to prove something like a Fibonacci seriesin assumption step do u use double assumption as in assume true for n= k-1, and n=k or hard induction as in assume true n=1 to n=k.PLZ HELP!!!

 

[untouchablecuz]

its termed "strong induction"
if you have a statement S(n) and you want to prove it true for S(k+1), you not only assume S(k) true, but also, S(k-1), S(k-2),...S(2), S(1).

 

[Aerath]

i think that's what they're called.so say im using MI to prove something like a Fibonacci seriesin assumption step do u use double assumption as in assume true for n= k-1, and n=k or hard induction as in assume true n=1 to n=k.PLZ HELP!!!

OK, Jacob, that's just like...beyond freaky. Although, with people like you, I guess I do feel safe for Maths given that you're gonna scale all 120 of us who do 4U up.

 

[untouchablecuz]

i think that's what they're called.so say im using MI to prove something like a Fibonacci seriesin assumption step do u use double assumption as in assume true for n= k-1, and n=k or hard induction as in assume true n=1 to n=k.PLZ HELP!!!

sorry, i misinterpreted your Q
im under the presumption that you would use strong induction which will then allow you to use a "double or triple (etc) assumption"
mostly used for recursive formulas, where you, for example, have S_k+2 in terms of not only S_k, but also S_k+3 and S_k+4 etc etc etc

 

[untouchablecuz]

Strong Mathematical Induction
have a look at this

 

[charlen]

this method is called a variation of induction by second principle cause the actual induction by second principle is look super hard and confusing