Simple question about induction .

  • Thread starter Andrax
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  • #1
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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).
 

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  • #2
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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.
 
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  • #3
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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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