Algebra I - A Verbose Approach/Relations and Functions/Relations and Equations

Understanding Relations

In algebra, one of the first concepts one learns is the relation. What is a relation? In day-to-day life, one thinks of aunts and uncles. For instance, Sally, my aunt, is my mother's sister. In mathematics, a relation is defined between sets of numbers. A set of numbers A is defined using braces, and simply lists each number in the set, separated by commas. {a, b, c, d,...z} Order of numbers in sets is irrelevant. That is, {1,2,3} and {1,3,2} are the same set. Formally, a relation is defined over any two sets A and B. We write a relation R as $R\subseteq A\times B$ But let's use a more concrete example. Suppose you have a list of prices of apples that we'll call A, and list of the prices of oranges that we'll call B. You want to show that for any price of an apple, there is an orange that costs twice as much. Thus, we have, $A=2\times B$