• R - the set of all real numbers

• R

+

- the set of all positive real numbers

• Z - the set of all integers

• N - the set of all positive integers

• Q - the set of all rationals

• (a, b) - open interval with the endpoints a and b

• [a, b] - closed interval with the endpoints a and b

• [x] - the integral part of a real number x

• For x e R,

sgnx =

( 1 for x 0,

- 1 for x 0,

0 for x = 0.

For n e N,

n! = 1 -2-3-...-n ,

(2n)!! = 2 • 4 • 6 •... • (2n - 2)(2n) and

(2n - 1)!! = 1 • 3 • 5 • ... • (2n - 3)(2n - 1).

If A c K is nonempty and bounded from above, then sup A

denotes the least upper bound of A. If a nonempty set A is

not bounded above, then we assume that sup A = -foo.

xin