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# Function defined over all a set (NOTATION)

2017-12-03 03:03:34

I want to write down symbolically a function that is defined over a set (all the set, no just an element of it) to the natural numbers.

The function is something like this:

For example $X\subset \mathbb{Z}^+$ is a set with finite number of elements. My function $R(\cdot)$ take the set $X$ and draw an element from it at random. For example $R(\{1,2,3\})=2$

I want to use the notation $$f : A \to B$$

But i don't know what to put in the place of $A$.

Use power set:

$R: \mathcal{P}(A) \to A$ such that $R(X) \in X$.

Another notation to power set is $2^A$.

$f:2^A\rightarrow B$ defines a function that maps every subset of $A$ to an element of $B$.

• Use power set:

$R: \mathcal{P}(A) \to A$ such that $R(X) \in X$.

Another notation to power set is $2^A$.

2017-12-03 04:02:10
• $f:2^A\rightarrow B$ defines a function that maps every subset of $A$ to an element of $B$.

2017-12-03 05:12:00