General Logic

Discussion in 'General Science' started by Ryan$, Dec 30, 2018.

  1. Ryan$

    Thread Starter Member

    Dec 14, 2018
    178
    2
    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!
     
  2. Papabravo

    Expert

    Feb 24, 2006
    12,158
    2,669
    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
     
  3. wayneh

    Expert

    Sep 9, 2010
    16,099
    6,212
    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.
     
    Last edited: Dec 30, 2018
  4. Papabravo

    Expert

    Feb 24, 2006
    12,158
    2,669
    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)
     
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