?

Implies.

Z

Integers {..., -2, -1, 0, 1, 2, 3, ...}.

N

Natural numbers {0, 1, 2, ...}.

#S

The number of elements in the set S.

gcd( p, q)

Greatest common divisor of p and q.

? x ?

Least integer greater than or equal to x.

? x ?

Greatest integer less than or equal to x.

R

Real numbers.

R ⁺

Nonnegative real numbers; [0, ?[.

T

The circle of unit circumference; also, the interval [0, 1].

C

Complex numbers; the complex plane.

] a, b[

The open interval { x : a < x < b}.

[ a, b]

The closed interval { x : a ? x ? b}.

] a, b]

The half-open interval { x : a < x ? b}.

[ a, b[

The half-closed interval { x : a ? x < b}.

B _?( ?)

The ball of radius ? centered at ?.

E

Lebesgue measure of a set E, E ? R ^d.

diam E

Diameter of a set E; inf{ R : s, t ? E ? s - t ? R}.

sup X

Supremum of a set X; the least L ? R with x ? L for all x ? X.

inf X