Ordered Pairs

To denote an ordered pair of real numbers, you write the numbers separated by a comma inside a pair of parentheses. For example, $(7,3)$ is an ordered pair whose first coordinate is 7 and whose second coordinate is 3. In general, an ordered pair of real numbers with a as first coordinate and b as second coordinate is written as $(a,b).$

What is the difference between braces $\left\{\right\}$ and parentheses $()$ ? You learned that braces are used to denote a set. When numbers are listed inside braces, the order in which they appear is not important. Thus, the set $\{4,-8\}$ is the same as $\{-8,4\}.$ Moreover, the set $\{7,7\}$ can be simply written as {7}. Similarly, the set $\{1,2,1,2\}$ can be simply written as $\{1,2\}.$

On the other hand, an ordered pair whose first and second coordinates are both equal to 7 is written as $(7,7)$ and not as (7).