9 Binary relations and binary relationships 10 Binary relationships

Example 9.1. Here are some relationships that might hold between two real numbers x and y: x is less than y, abbreviated x < y. Similarly x ≤ y, x ≥ y and x > y. y is the square of x, which is abbreviated by y = x, x is within ε of y. Here ε ≥ 0 and this relationship means |x− y| ≤ ε. y is the image of x under f , where f is a function from R to R. This relationship is abbreviated y = f(x). Note that the relationship “y is the square of x” is a special case of this one. Any equation or inequality involving x and y, such as “|x − y| ≤ 1”, “x + y = 1” or “(x+ y) ≤ x” defines a relationship between x and y.