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Re: Recursive Functions Proof Trouble
Posted:
May 6, 2013 3:13 PM



Multiplication of polynomials:
f.g=c_n k_p x^{n+p} + (c_{n1} k_p + k_{p1} c_n )x^{n+p1}+...+c_0 k_0 x^0. The argument that the coefficients are positive integers still works fine.
To prove the if part:
All polynomials with positive integer coefficients of degree 0 are in S since a_0 = 1+ (a_01)*1, i.e letting c=a_01, f=g=1 . For all k, x^k is in S since x is in S and if x^i is in S then x^{i+1}=x.x^i .
If all polynomials of degree n are in S, then any polynomial of degree n+1 can be written as f + a_{n+1} x^{n+1}, where f is of degree n, and letting c=a_{n+1} and g=x^{n+1} this is seen to be in S too.
________________________________ From: Nicolas Manoogian <discussions@mathforum.org> To: discretemath@mathforum.org Sent: Monday, May 6, 2013 6:23 PM Subject: Recursive Functions Proof Trouble
I'm having some difficulty with a proof, would anyone mind telling me where I'm going wrong?
I've attached the PDF and the TeX.



