Hi guys ; there's something I'm confused with and I would by your help to eliminate thats confusion and comprehend it;

Lets say I'm having a general function which it's like n(h)=2^h-1 ; lets assuming according to n=7 then h=20 "assuming !" , why saying what's h according to n=7 is the same saying what's n according to h=20! , how is that reflected logically between two statements of "saying" ?!


thanks!

 

n(h) and h cannot be chosen independently if there is a functional relationship. If you specify one of the values, the other value is fixed. Your example posits a case which cannot exist. You cannot simultaneously have h=20 and n(h)=7.
If h=20 then n(20)= 1,048,575
If n=7 then h=3, because 2^(3)=8, and 8-1=7

 

To say it another way, you have one equation and one unknown and therefore zero degrees of freedom. Once the independent variable h is specified, there's no freedom to choose n. It's already defined by the choice of h and the equation.

 

To say it another way, you have one equation and one unknown and therefore zero degrees of freedom. One the independent variable h is specified, there's no freedom to choose n. It's already defined by the choice of h and the equation.

Since the function has an inverse, it is also true that if you choose a value for n(h), then h is uniquely determined as well. Even if h is not an integer. It is the logarithm to the base 2 of (n(h) +1)