# Creative, recursively enumerable

I'm trying to show that the set $K$ is creative. $K$ has to do something with $\phi_x$ and the only thing I can get out of creative is if there is a total recursive $f$ s.t. $f(e)$ is an element of $A$ iff $f(e)$ is an element of $W_e$.

Can someone also explain recursive enumerable vs. creativity? Thanks in advance.

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To show $K$ is creative: let $f(e)=e$ be the function.
$K=\{x:x\in W_{x}\}$, so $e\in K\leftrightarrow e\in W_{e}$, so we choose $f(e)=e$. – Chao Chen Mar 7 '13 at 3:56