Variable

Let (see what let means) a variable be a symbol that represents a literal thing.

I can define what number it represents by saying “it’s equal to this”

Example:

Let

\begin{gather*} x\triangleq1 \end{gather*}

Note that the equals sign with a triangle on top means that we "let" it be that. This is to avoid confusion. If I write something like this, we know it is derivable from $x\triangleq 1$ (which cannot be derived from something earlier)

x+3=4

Now if I add something to that variable, I’m going to write a double arrow “ $\Rightarrow$ ” on the left of it to show that “Therefore this is true”

Example:

\begin{gather*} x\triangleq 1\\ \Rightarrow x+1=1+1\\ \Rightarrow x+1=2 \end{gather*}