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Math Help - Help Please?? Show that A(1, n) = 2^(n) whenever n >= 1?

  1. #1
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    Help Please?? Show that A(1, n) = 2^(n) whenever n >= 1?

    I am stuck on this same problem as the other guys topic. But I think we do use induction.I have this so far:

    Base Case:
    A(1, n) = n + 2
    n + 2 = 2^(n) Let n = 2
    2 + 2 = 2^(2)
    4 = 4 Base case holds

    Induction Hypothesis:
    We going to assume P(k) is true for all integers of k > 1

    Induction Step (Confused Here):
    We must prove for P(k+1)

    What do I do next b/c I cant solve this?
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  2. #2
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    Grandad's Avatar
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    More information please

    Hello Grillakis

    Please tell us what you mean by A(1, n).

    Grandad
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  3. #3
    Like a stone-audioslave ADARSH's Avatar
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    Quote Originally Posted by Grandad View Post
    Hello Grillakis

    Please tell us what you mean by A(1, n).

    Grandad
    Ackermann's function
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    Quote Originally Posted by Grandad View Post
    Hello Grillakis

    Please tell us what you mean by A(1, n).

    Grandad
    well A(1, n) is Ackermann function. So I am assuming it wants us to prove that A(1, n) = 2^(n)

    Heres a link to Ackermanns Function:
    Ackermann Function -- from Wolfram MathWorld

    (Edit: Sorry! you already gave the link. I think its asking me to prove using Induction, which I tried in the 1st post. Doesn't help in the book but it shows 1 using Induction.)
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  5. #5
    Like a stone-audioslave ADARSH's Avatar
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    Quote Originally Posted by Grillakis View Post
    I am stuck on this same problem as the other guys topic. But I think we do use induction.I have this so far:

    Base Case:
    A(1, n) = n + 2
    n + 2 = 2^(n) Let n = 2
    2 + 2 = 2^(2)
    4 = 4 Base case holds

    Induction Hypothesis:
    We going to assume P(k) is true for all integers of k > 1

    Induction Step (Confused Here):
    We must prove for P(k+1)

    What do I do next b/c I cant solve this?
    ----------------------------------
    You know that A(1,n) = n + 2

    You are trying to prove
    A(1,n) = 2^{n}

    --------------------------
    If you agree with this than I dont agree with you

    because

    n+2 \ne 2^{n} for n>= 1 , example put n = 3
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  6. #6
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    Quote Originally Posted by ADARSH View Post
    ----------------------------------
    You know that A(1,n) = n + 2

    You are trying to prove
    A(1,n) = 2^{n}

    --------------------------
    If you agree with this than I dont agree with you

    because

    n+2 \ne 2^{n} for n>= 1 , example put n = 3
    That's what its asking me from the book word for word is show that it =. I can pop a link to show you, and it shows 1 example using Induction, but the example they show I don't understand.

    Heres a link (it's at the bottom of the page: #50 on page 10/10):
    http://isis.poly.edu/courses/discretemath/problems4.pdf

    (This is what we confused on.)

    I agree with you its not correct b/c when I tried 1 since n >= 1 I would have LHS:1 + 2 = 3 = 2^(1) = 2RHS which is not equal, but it does work when n = 2, but like you also mention doesn't work with 3.
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  7. #7
    Like a stone-audioslave ADARSH's Avatar
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    Quote Originally Posted by Grillakis View Post
    That's what its asking me from the book word for word is show that it =. I can pop a link to show you, and it shows 1 example using Induction, but the example they show I don't understand.

    Heres a link (it's at the bottom of the page: #50 on page 10/10):
    http://isis.poly.edu/courses/discretemath/problems4.pdf

    (This is what we confused on.)

    I agree with you its not correct b/c when I tried 1 since n >= 1 I would have LHS:1 + 2 = 3 = 2^(1) = 2RHS which is not equal, but it does work when n = 2, but like you also mention doesn't work with 3.
    It is a misprint "most probably" ,As far as I can induce you should try proving that
    A(1,n) = 2 + n
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  8. #8
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    Quote Originally Posted by ADARSH View Post
    It is a misprint "most probably" ,As far as I can induce you should try proving that
    A(1,n) = 2 + n
    OK ADARSH. I hope it is a misprint because thats why me and that other gentlemen was asking about this. Let me try this bad boy again then with 2 + n.
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