In mathematics, some sets are referred to so commonly that they are denoted by special symbols. Some of
these numerical sets include:


<ul>
<li>$\mathbb{P}$ denotes the set of all prime numbers: $\{2,3,5,7,11,...\}$.</li>
<li>$\N$ denotes the set of all natural numbers: $\{0,1,2,3,...\}$.</li>
<li>$\Z$ denotes the set of all integer numbers: $\{...,-2,-1,0,1,2,...\}$.</li>
<li>$\Q$ denotes the set of all rational numbers: $\{\frac{a}{b} \,| \, a,b \in \Z, \, b \neq 0\}$</li>
<li>$\R$ denotes the set of all real numbers.</li>
<li>$\I$ denotes the set of all complex numbers.</li>
</ul>

In addition, the Cartesian product (also called the cross product) of two sets $A$ and $B$, written as $A \times B$,
is the set of all pairs whose ﬁrst component is an element of $A$ and whose second component is an element
of $B$. In set notation, $A \times B = \{(a;b) \, | \ a \in A,b \in B\}$. For example, if $A = \{1,2,3\}$ and $B = \{u,v\}$, then
$A \times B$ = $\{(1,u), \, (1,v), \, (2,u), \, (2,v), \, (3,u), \,(3,v)\}$. Given a set $S$, another signiﬁcant set is the power set of $S$,
denoted by $\mathcal P \left({S}\right)$, is the set of all subsets of $S: \{T \, | \ T \subseteq S \}$. For example, if $S = \{1,2,3\}$, 
then the power set of $S$ is: $\mathcal P \left({S}\right) = \{\{\},\{1\},\{2\},\{3\},\{1,2\},\{1,3\},\{2,3\},\{1,2,3\}\}$. 
It is interesting to note that, if $|S| = k$, then $|\mathcal P \left({S}\right)| = 2^k$

Signiﬁcant Sets