"in X, **such that**..."

An associative function $~$f : X \\times X \\to X$~$ is a binary operation for all $~$x, y, z$~$ in $~$X$~$, $~$f(x, f(y, z)) \= f(f(x, y), z)$~$\. For example, $~$+$~$ is an associative function, because $~$(x + y) + z \= x + (y + z)$~$ for all values of $~$x, y,$~$ and $~$z$~$\.

in X, such that…