representing Order pairs

Question

I was reading Swokowski's book of calculus

I noted that say [The Set of all order pairs will be denote by $\mathbb{R}*\mathbb{R}$ ]

Does that mean if I have $(a,b)$ and $(c,d)$ then $(a,b)$ and $(c,d)$ = $\mathbb{R}*\mathbb{R}$ ?

Answer 1

The main property for ordered pairs is: If $(a,b)=(c,d)$ then $a=c$ and $b=d.$ The reference to R*R [more typically called $R \times R$] means only that one is considering the components $a,b$ of a given pair $(a,b)$ as being members of $R.$

More generally for sets $E,F$ the notation $E \times F$ refers to the set of all ordered pairs $(x,y)$ with $x \in E$ and $y \in F.$ Sometimes called the "Cartesian product" of $E$ and $F$ (in that order, in case $E \neq F.$)