Math Help - Induction question

1. Induction question

If you have an equation like
n<2^n for n>=0

do you just work one side of the equation at a time like

n<2^(n+1) ....

or do you do both sides like

n+1<2^(n+1) ......

Thanks for the help.

2. Originally Posted by smellatron
If you have an equation like
n<2^n for n<=0

do you just work one side of the equation at a time like

n<2^(n+1) ....

or do you do both sides like

n+1<2^(n+1) ......

Thanks for the help.
are you sure this is for n <= 0? that would mean we are doing induction for negative integers, not completely strange, but very uncommon. also, it is trivial to use induction for such a claim, since 2^n is always positive, while n is nonpositive for n<=0. clearly it will always be the case 2^n > n under such conditions.

3. Originally Posted by smellatron
If you have an equation like
n<2^n for n>=0

do you just work one side of the equation at a time like

n<2^(n+1) ....

or do you do both sides like

n+1<2^(n+1) ......

Thanks for the help.
Hi smellatron.

In an induction proof, the statement $n<2^n$ is what you assume as your inductive hypothesis and the statement $n+1<2^{n+1}$ is what you then try to prove. There is no value in considering $n<2^{n+1}.$