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April 13th, 2014, 11:59 AM   #1
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power of 2 zero function

Find a function such that $\displaystyle f(2^n)=0$ for every $\displaystyle n \in Z$ and $\displaystyle f(x)=0$ is not correct.
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April 13th, 2014, 01:13 PM   #2
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Originally Posted by gelatine1 View Post
Find a function such that $\displaystyle f(2^n)=0$ for every $\displaystyle n \in Z$ and $\displaystyle f(x)=0$ is not correct.
Trivial.
$\displaystyle f(x) = 0, x = 2^n$
$\displaystyle f(x) = 1, otherwise$
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April 13th, 2014, 01:59 PM   #3
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Hello, gelatine1!

I suppose we can create functions of the form: $\displaystyle f(x) \,=\,x - x$


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Find a function such that $\displaystyle f(2^n)=0$ for every $\displaystyle n \in Z$ and $\displaystyle f(x)=0$ is not correct.
$\displaystyle f(2^n) \;=\;\sin(2^n) - \frac{1}{\csc(2^n)} $
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April 14th, 2014, 01:45 AM   #4
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I was thinking of $\displaystyle f(x) = 2^{\left \lfloor log(x) \right \rfloor}+2^{\left \lfloor log(x/2) \right \rfloor} - x$
where log is base 2

This is also a fractal function (I just call it like that ). Is this anything that exist ? I mean a fractal function ?
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April 14th, 2014, 03:18 AM   #5
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Whoops I meant $\displaystyle f(x) = 2^{\left \lfloor log(x) \right \rfloor} - x$
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April 14th, 2014, 07:46 AM   #6
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I don't understand what you want. What if x = 2^n? Then f(2^n) = 0 which isn't correct.
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