Theory:

Consider the set of all natural numbers.
 
Roaster form of the set: A=1,2,3,4,5,....
 
Set builder form:A=x:xisanaturalnumber}.
 
Thus, it can be concluded that \(1, 2, 3,...\) are belongs to the set \(A\).
 
But the element \(0\) doesn't belongs to the set \(A\).
Here comes the list of symbols we often use to denote the sets.
Symbol
Meaning
Example
belongs toSuppose A={3,4,5} then \(3\)\(A\).
does not belongs toSuppose A={3,4,5} then \(6\)\(A\).
\(:\) or \(|\)such thatThe set builder form A={3,4,5} is A={x:xisanaturalnumber,3x5
the set of all natural numbers={1,2,3,...}
\(W\)the set of all whole numbers\(W = {0, 1, 2, 3,...}\)
orIthe set of all integers={...,3,2,1,0,1,2,3,...}
+the set of all positive integers+={1,2,3,4,...}
the set of rational numbers={pq,q0withpandqareintegers
+the set of positive rational numbers+={pq,q0withpandqsamesignintegers
the set of real numbers={x|x}
+the set of positive real numbers+={x|0<x