What is this codomain?

Question

I was presented with a function $f:X$-->$2^X$ and I'm not sure what is meant by the codomain $2^X$. Any ideas?

this is the defenition of codomain of a fucntion https://en.wikipedia.org/wiki/Codomain — Varazda, Oct 28 '18 at 18:56

score 2 · Answer 1 · answered Oct 28 '18 at 18:55

2

answered Oct 28 '18 at 18:55

Soby

Thanks for the response. Not sure what is meant by "$2$ being defined as ${0,1}$, but in this case, would $f$ then be a function that takes an element of $X$ and returns a function $g:X$-->${a,b}$ for $a,b$ in $R$? – Oct 28 '18 at 19:06
The reason why "2" can be viewed as ${0,1}$ is due to the way natural numbers are constructed. https://en.wikipedia.org/wiki/Set-theoretic_definition_of_natural_numbers To answer your question, we can view $2^S$ as the set of all functions $f:S \rightarrow {0,1}$ from $S$ to ${0,1}$. (This notation is confusing but just accept it for now). Now consider a subset $X \subset S$. We identify each $s\in S$ as 0 if $s\in X$ and 1 if $s\notin X$. This way you see that $X$ induces a map $f:S\rightarrow {0,1}$ mapping each $s\in S$ just the way we defined above. – Soby Oct 29 '18 at 12:48

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