Function

Also let us notate a state as a function of time. What’s a function?

Example:

if i let $f$ be a function that accepts $x$ as an argument, like this

\begin{gather*} f(x)=4x \end{gather*}

then

\begin{gather*} f(5)=4(5)=20 \end{gather*}

A function $f$ , can also be thought of mapping numbers from a Set $A$ to set $B$ . It’s written like this

\begin{gather*} f:A\rightarrow B \end{gather*}

A map just links a thing to another thing.

Example

Let $q$ be a function

\begin{gather*} q:\mathbb{Z}\rightarrow\mathbb{Z}\\ q(x)=3x \end{gather*}

q essentially maps all integers to another integer, which is three times itself.

\begin{gather*} q(67)=201 \end{gather*}