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(mathematics) super exponential function, wtfhelp?
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my teacher told me this, and i'm quite sure he isn't pulling my leg, but i just don't get it... firstly f(x)=x^x^x^x^x...this goes on forever. and he says there's a value for x that makes f(x)=2. what the hell is it? any way i look at it, that's a downright outrageous claim... |
Aramis|
Re: (mathematics) super exponential function, wtfhelp?
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by
on 2007-02-28 11:42:35 (edited 2007-02-28 11:51:34)
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f(0) = 1 because anything raised to the 0th power is 1. f(1) = 1 because 1 raised to the anything power is 1. f(2) = infinity because 2 multiplied by itself is greater than 2. therefore, this being done an infinite number of times would produce an infinitely large product. somewhere in-between f(1) and f(2) there may be an example that converges on 2. it seems at first unlikely. i will put more thought into it, and edit this post if i find a solution. EDIT: the limit of the Infinitely high power towers f(√2) is 2! notice: the square root of 2 lies between 1 and 2, so my previous assumption was correct ^_^ 
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