How to prove that this function is primitive recursive?

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How to prove that this function is primitive recursive?

How can I solve the following problem: Let $f, \pi, g$ accept one, two and three arguments respectively. If you know that $f, \pi, g$ are primitive recursive functions prove that $h$ defined as: $$ \begin{align*} h(0, y) &\simeq f(y) \\ h(x + 1, y) &\simeq g(x, y, h(x, \pi(x, y))) \end{align*} $$ is also primitive recursive function. The definition of primitive recursion I know is: $$ \begin{align*} h(\bar{x}, 0) &\simeq f(\bar{x}) \\ h(\bar{x}, y + 1) &\simeq g(\bar{x}, y, h(...

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It may seem silly to post a second answer to a question that seems no longer to interest anybody, not...

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How should one prove a curve's function?

So you know how we have theorems? For example, a questions gives us a statement and demands us to prove the statement right? Similarly, can we do it for curves too? I mean, if a graph of a curve is given and the question demands us to prove that its...

Answer:

Can't be done in general, because the curve is going to be specific by some finite geometric means,...

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How to prove log(x)*log(1-x) is a concave function ?

I want to prove that log(x)*log(1-x) is a concave function, although the excel shows that it is a concave function, I can't prove that. Please help :(

Answer:

just double differentiate it you will see that the double differentiation attains only negative values...

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How do I prove this conjecture for a general quartic function?

How do I prove that for every quartic function the following is true: If R and Q are the points of inflection and P and S are the points colinear to the points of inflection that reintersect the function then the ratio always is the following PQ:QR:RS...

Answer:

Given the general quartic: Y = AX^4 + BX^3 + CX^2 + DX + E, divide by A and put X = x - (A/4) to obtain...

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Answer:

Well, a local max or min would require a critical point---a place where f ' (x) = 0 or is undefined...

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Michelle at Yahoo! Answers Mark as irrelevant Undo

[Discrete Mathematics] How to prove a function is big-theta(n^3/2)?

The function I was given is (n+1)3/2. I understand that I have to prove that it is both big-O(n3/2) and big-Omega(n3/2). I know how to do this for polynomial functions such as n2 and ...show more

Answer:

Upper bound. For all n > 1: (n+1)^(3/2) < (n+n)^(3/2) = 2^(3/2) * n^(3/2). Lower bound. For all...

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JK54GL7XXY2Z26X4URCSVXVZFY at Yahoo! Answers Mark as irrelevant Undo

How to prove this function is always negative?

hello! f(x) = ln (1+x) - x how to prove this function for all x>0 is always negative? i think to use that f is continous and so it has a maximum, but the maximum is 0 and is not ...show more

Answer:

Your function is f(x) = ln (1 + x) - x if you differenciate it wrt x, then f'(x) = 1/(1+ x) - 1 now...

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Answer:

The first condition you gave, f(¯¯¯¯A)⊆¯¯¯¯¯¯¯¯¯¯¯f(A)f(A¯)⊆...

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Josh Alman at Quora Mark as irrelevant Undo

How do you show/derive/prove this vector-valued function identity?

R(t) is a vector-valued function. Please show that d/dt (||R(t)||) = [R(t) · R'(t)] / ||R(t)|| Note: R is supposed to have an arrow above it and || || means absolute value. * I cannot answer this exercise . Please help me. I've tried using implicit...

Answer:

Hmm, it looks like the scalar projection formula scalar projection of vector b on vector a = a.b/|a...

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Lindsay at Yahoo! Answers Mark as irrelevant Undo

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The two variables are complements factors (or supporting factors) in a particular production process...

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