Section 1

Numbers and algebraic properties

fundamentalviz

a + b = b + a; ab = ba

Order does not change a sum or a product.

fundamentalviz

(a + b) + c = a + (b + c); (ab) c = a (b c)

Grouping does not change sums or products.

fundamentalviz

a (b + c) = ab + a c

Relates multiplication to addition and is the basis of expansion and factorization.

fundamental

a + 0 = a; a \cdot 1 = a

Zero is the additive identity and one is the multiplicative identity.

fundamental

a + (- a) = 0; a \cdot \frac{1}{a} = 1 (a \neq = 0)

Every number has an additive inverse; nonzero numbers have a multiplicative inverse.

fundamentalviz

∣ x ∣ = {x, - x, x \geq 0 x < 0

Represents the distance from a number to zero.

fundamentalviz

d (a, b) = ∣ a - b ∣

Measures the distance between two real numbers.