Recent content by MitsuZero

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    Trouble with Planetmath's Images?

    Just wondering if anyone else has been experiencing problems viewing any of the images on planetmath.com? Take for example: http://planetmath.org/encyclopedia/GammaFunction.html All the images (and hence the bulk of the information) simply does not appear. This seems to be the case...
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    Decay length of Half Square Well

    If one wall is at infinite potential, and the other at some finite potential, what is the decay length outside of the well? I was thinking it might be twice that for a finite square well. Also can anyone provide some information regarding these wells? Google is (surprisingly) devoid of any...
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    Using bijectiveness to prove congruence relation

    Dick I do apologize. I'm not sure why I saw David in place of Dick. Rs1n, I'll be sure to update the proof before I submit it. I emailed my professor with the same proof I posted, and he responded: "Your proof on the first problem looks good. It's a bit more "brute force" than a proof using...
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    Using bijectiveness to prove congruence relation

    I can't thank you guys enough for your help. David, your absolutetly correct in that a lot of my previous work was...illogical. Rather it was a mish-mash of ideas with no concrete direction. rs1n, your explanation was absolutetly invaluable. Furthermore you helped me to understand the...
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    Using bijectiveness to prove congruence relation

    Hi Ivy (may I call you Ivy?), first off I really appreciate your response. It would seem that sometimes we simply require a nudge. I think I understand what your getting at (that eureka moment). I had actually noticed that bijective "symmetry" your talking about (forgive my diction). Here...
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    Using bijectiveness to prove congruence relation

    Homework Statement \forall x\in Z, if x is odd, \exists y\in Z, such that xy\equiv1(mod 16) The attempt at a solution I tried to prove this by using the fact that if you got a set of odd integers R = {1, 3, 5, ..., 15}, and if x, y, f(r) \in R, then xy\equiv f(r)(mod 16). This...
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    Proof through Induction with Inequality

    I believe I used just about all the hints my professor gave. Though whether I used them correctly is questionable. For the first hint I multiplied both sides by 2^(n-1) in order to fit the form he gave -- i.e. 2^(n-1)^2 * 2^(n-1) > (n-1)^(n-1) * 2^(n-1) For the second hint, I got rid of the...
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    Proof through Induction with Inequality

    Homework Statement Original Problem Text: http://img264.imageshack.us/img264/5882/problem3pn7.th.gif Prove that, if [SIZE="3"]n \in N and [SIZE="3"]n \geq 2, then [SIZE="3"]2^(n^2) > n^(n). Homework Equations Some Hints: *** (n-1)^(n-1) * 2^(n-1) = (2n - 2)^(n-1) *** If n >=...
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