# Validity of notation from the aspect of function description

I have the following notation that should describe the nature of my function

$for \forall a \in A \exists f:A \rightarrow S, A \subset N, S \subset [0,1]^n,|S|=n$

Can anyone tell me is the notation correct for the descriptive definition below.

Function takes a natural number as an input(from set A) and outputs a vector of probabilities for each state(from set S).The size of the vector is the size of a set S. The probabilities should be all rational numbers from 0 to 1 inclusive.

M.

You are not using $a$ at all. Also, your restriction on $A$ should be quantified. Did you mean to start with

$\forall A \subset \mathbb{N} \cdots$ ?

You are slightly mixing what you are defining and what you are claiming anyway. As far as I can tell your statement is that:

for each such $A$, there is a subset $S \subset [0, 1]^n$ and a function $f: A \to S$ such that $|S| = n$.

Or is it

for each such $A$, and for each subset $S \subset [0, 1]^n$ such that $|S| = n$ there is a function $f: A \to S$?

Or is it

for each such $A$, for each $S \subset [0, 1]^n$ there exists a function such that $f: A \to S$ and $|S| = n$?

Feel free to pick any of these alternatives, they translate quite literally into $\forall$ and $\exists$ statements the way I have written them.

• Thank you. I'm claiming the first one. How should I state the quantification of A, since it's a subset of the set of natural numbers. It has a finite number of members. Nov 18 '13 at 20:46
• Thank you again. Can you please verify the latex that I've produced based on your first suggestion? $\forall A \subset N \exists S \subset [0,1]^n \land \exists f:A \rightarrow S,|S|=n$ Nov 18 '13 at 21:19