- #1
finkeljo
- 10
- 0
Hey all, I got a proposition I am supposed to prove by induction but am just a bit confused. The problem is as follows:
Prove by the principle of mathematical induction that if m is a natural number, then for each natural number n, there exists an integer a greater or equal to zero such that,
n*2^m <= (n+a)*2^m
The inequality is not that difficult but I am just unsure as to which variable I would be doing the induction on. I assume its n, since the proposition is making a statement for all n. Any thoughts otherwise?
And additionally if I did do induction on n, how would I then show existence for a??
Thanks for the help.
Prove by the principle of mathematical induction that if m is a natural number, then for each natural number n, there exists an integer a greater or equal to zero such that,
n*2^m <= (n+a)*2^m
The inequality is not that difficult but I am just unsure as to which variable I would be doing the induction on. I assume its n, since the proposition is making a statement for all n. Any thoughts otherwise?
And additionally if I did do induction on n, how would I then show existence for a??
Thanks for the help.