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
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