Rational and Irrational Numbers

Q = {a/b : a, b ∈ Z, b ≠ 0}

R = Q ∪ Q̄

a/b = c/d ⇔ a × d = b × c

a/b > c/d ⇔ a × d > b × c

d = (y - x)/(n + 1)

n rational numbers between x and y: x + d, x + 2d, x + 3d, ..., x + nd

(a + c)/(b + d)

Non-terminating and non-recurring decimal

√m is irrational if exact square root of m does not exist

√ab

(a + b)/2

R = Q ∪ Q̄

Rational numbers = terminating or recurring decimals