Confused about class definition

Question

I find this in my Set theory material:

[0] = {x:0==x(mod2)} = {x:2|0-x}

, where I'm replacing equivalence sign ("=" with extra horizontal line) with double equality sign "==" because I don't know how to input the proper symbol.

I'm reading it as

class 0 includes (all x that are defined by 0 being equivalent to x%2) which is equal to (all x that are defined by 2 being such that 0-x)

I am confused about this part:

{x:2|0-x}

Shouldn't there be be a boolean statement to the right of "|"? Or am I misreading?

Answer 1

$|$ in this case means 'divides': https://en.wikipedia.org/wiki/Divisibility#Definition

Answer 2

The usual convention for defining a class is this $$\Bigl\{\textbf{variable }\Large\text{separator }\normalsize\textbf{condition on the variable}\Bigr\}$$

The separator can be $:$ (colon) or it can be $\mid$ (pipe). In this case, the symbol $\mid$ is already used to denote the divisibility relation, therefore $:$ was used.