Set Properties: Formal Semantics of Programming Languages What is the difference between the two notations below?
{x | x (is an element of) X & P(x)}

vs.
X = {x | P(x)}

These both seems to say to me x is in X as long as it abides by property P. The top one is defined as a comprehension and the bottom one is used as a lead into Russle's paradox.

The first is an object, namely a set.  In particular, it can't be true or false.  The second is an equation, which is a type of statement.  The difference between the two is the same as the difference between "dog" and "my dog has four legs."
