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Post by sparkpowder on Mar 14, 2011 17:35:16 GMT
I [or a user who can] asks a math question. The first person to get the correct math answer wins a point. People who may ask questions:
Me General Veers Micro Farad Memzak
Point bearers:
Me: Infinite [for being game creator]
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Post by Rock on Mar 14, 2011 19:20:02 GMT
Wrong board. I'm moving this.
And you realize the game isn't going to start unless you provide a problem?
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Post by ganondorfchampin on Mar 14, 2011 19:30:09 GMT
Problem: What continuous function when composed on itself generates the exponential function?
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Post by Qwerty on Mar 14, 2011 22:26:32 GMT
Why exactly did you give yourself infinite points? That just ruins it. Now nobody can ever possibly win except you, or even do well relative to your point value.
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Post by Anonymousperson5 on Mar 19, 2011 22:12:53 GMT
I find this pointless, as only a small number of people can ask questions, which I find unfair. Should this thread be locked?
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Post by Elmach on Mar 22, 2011 1:12:50 GMT
1. I'm still waiting for a question. 2. There is no continuous function which when composed with itself generates the exponential function, because:
If there was, let's call the function f(x)
So we have f(f(x))=ex.
Since ln(0) does not exist, there is no such x such that f(f(x))=0. Since ln(everything else) exists, there must be x such that f(f(x))=everything else.
Let h(x)=ln(f(x)). Since f(C), where C is the complex plane, does not contain 0, and f(x) is continuous, h(x) is continuous.
Then h(eh(x))=ln(f(f(f(ln(f(x)))))=ln(f(eln(f(x))))=ln(f(f(x)))=ln(ex)=x+2πik. (k is an integer.)
However, since h(eh(x)) is continuous, k is a constant.
Ergo, h(x) takes all values. Ergo, there exists a such that h(a)=0, and b such that h(b)=2πi.
Thus, a+2πik = h(eh(a)) = h(e0) = h(e2πi) = h(eh(b)) = b+2πik.
Ergo, a=b.
Ergo, 0=2πi.
CONTRADICTION.
Ergo, there is no continuous f(x) such that f(f(x))=ex.
Just an amusing tangent.
Anyways...
3. I am waiting for a question.
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