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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. Tags function, power Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post kannan19 Calculus 6 April 29th, 2013 01:37 PM Vasily Calculus 6 July 22nd, 2012 11:31 AM LAPOSH42 Calculus 2 June 28th, 2012 03:16 PM icemanfan Applied Math 5 February 29th, 2012 09:07 AM kannan19 Trigonometry 0 December 31st, 1969 04:00 PM

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