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Old 2006-02-22, 12:50   #4
Dougy
 
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Aug 2004
Melbourne, Australia

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Quote:
Originally Posted by Dougy
...for example, f(x)=\frac{3}{2}x+\frac{1}{2}, if m=3 then f^n(m) will still always be a natural number.
After I posted it I noticed that this was incorrect. So I'll give another example of a function f which would not be included if f:\mathbb{N} \rightarrow \mathbb{N}. Eg. f(x)=2^{x-2}+1 has the property that f(1) is not a natural number, while f(x) \in \mathbb{N} when x \in \mathbb{N} and x>1.

It is possible to create a related function g:\mathbb{N} \rightarrow \mathbb{N} such that g(x)=f(x) whenever f(x) \in \mathbb{N}, and g(x)=1 whenever f(x) is not a natural number. But then this would be asking a different question.

Last fiddled with by Dougy on 2006-02-22 at 12:52
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