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Simple question about induction .

  1. Sep 6, 2013 #1
    This is from a functional equation , i think there is no points in posting it here this is what i ant to prove the functions is from N to N .

    let x be a natural number
    i want to prove that f(x)=[tex]x^2[/tex]

    By induction
    suppose that f(x)=[tex]x^2[/tex]
    f(0)=0 holds (from the functional equation)

    i want to prove that f(x)= [tex](x+1)^2[/tex]

    when putting (x,1)(we have f(x+y)+f(x-y) in the equation) I need to know the value of f(x-1) ,does the assumption that f(x)=[tex]x^2[/tex], imply that f(x-1)=[tex](x-1)^2[/tex]
    (this is not a homework i just saw this excercise online and decided to do it).
  2. jcsd
  3. Sep 6, 2013 #2


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    2017 Award

    Staff: Mentor

    Where is the functional equation?
    Do you have a question, or do you want to start a discussion (about what?)?

    If you want to prove f(x)=x2, you cannot just assume that this is true (without additional statement, this means "for all (natural) x"). It ruins the idea to prove it.
  4. Sep 6, 2013 #3
    i solved the issue now , thanks ,everything is clear,
    ( i meant for an unspecific x let f(x))=x^2 then i'd have to prove by induction ..
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