If statements in equations?

Question

When creating an equation is there any way to let someone know that if this number doesn't fit into this then use this other equation? Ex: $x>1$ then use $x+y$, or if $x<1$ then use $x-y$. Or do you just have to find an equation that works for both probability?

Answer 1

Like this:

$$ f(x,y)=\begin{cases} x+y & X>1 \\ x-y & X<1 \end{cases} $$

Answer 2

Yes, you can set up a function like this. For example, like this:

$f(x,y) =\,$ for $x>1\,$ use $x+y\,$ and for $x<1\,$ use $x-y$

Answer 3

A good example is the Kronecker delta.

Answer 4

You could also say $f(x,y) = x + \frac{x-1}{|x-1|}y$ for your particular example.