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Topic: Recursive Functions Proof Trouble
Replies: 2   Last Post: May 6, 2013 7:00 PM

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Angela Richardson

Posts: 42
From: UK
Registered: 6/22/11
Re: Recursive Functions Proof Trouble
Posted: May 6, 2013 3:13 PM
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att1.html (2.5 K)

Multiplication of polynomials:

f.g=c_n k_p x^{n+p} + (c_{n-1} k_p + k_{p-1} c_n )x^{n+p-1}+...+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_0-1)*1, i.e letting c=a_0-1, 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.



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