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 April 13th, 2014, 11:59 AM #1 Senior Member   Joined: Mar 2012 From: Belgium Posts: 654 Thanks: 11 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.
April 13th, 2014, 01:13 PM   #2
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Quote:
 Originally Posted by gelatine1 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.
$\displaystyle f(x) = 0, x = 2^n$
$\displaystyle f(x) = 1, otherwise$

April 13th, 2014, 01:59 PM   #3
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Hello, gelatine1!

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

Quote:
 Find a function such that $\displaystyle f(2^n)=0$ for every $\displaystyle n \in Z$ and $\displaystyle f(x)=0$ is not correct.
$\displaystyle f(2^n) \;=\;\sin(2^n) - \frac{1}{\csc(2^n)}$

 April 14th, 2014, 01:45 AM #4 Senior Member   Joined: Mar 2012 From: Belgium Posts: 654 Thanks: 11 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 ?
 April 14th, 2014, 03:18 AM #5 Senior Member   Joined: Mar 2012 From: Belgium Posts: 654 Thanks: 11 Whoops I meant $\displaystyle f(x) = 2^{\left \lfloor log(x) \right \rfloor} - x$
 April 14th, 2014, 07:46 AM #6 Math Team   Joined: Apr 2010 Posts: 2,780 Thanks: 361 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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