1549901369-Elements_of_Real_Analysis__Denlinger_

Glossary of Symbols 721

FUNCTIONS

Symbol Meaning Defined on page

f : A ~ B f is a function from A to B

V(j), R(f) domain off, range off

J(C) {f(x): x EC}

f-^1 (D) {x: f(x) E D}

F(S,JR) {all functions f : S ~JR}

f ± g , r f , f g, f / g algebraic combinations of f and g

/JI absolute value of a function

min{f,g}, max{f,g} minimum (maximum) off and g

g o f composite of f and g

identify function on A

inverse function of f

THE REAL NUMBER SYSTEM

619

619

188 , 620

188,620

541,625

626

626

626, 627

629

631

631

Symbol Meaning Defined on page

p

<,>,::;,~

multiplicative inverse of x

set of all positive elements of an ordered field

less than, greater than, etc.

/x/ absolute value of x

[a, b], (a, b), etc. (bounded) intervals

(-oo,a), [b,+oo), etc. (unbounded) intervals

G)

Zp

Qp

N,Z,Q

minA, maxA

sup A

inf A

JR

+oo, - oo

e

set of all natural numbers of ordered field F

n factorial

binomial coefficient, for 0 ::; k ::; n E N

set of all integers of ordered field F

set of all rational numbers of ordered field F

natural numbers, integers, rational numbers

minimum and maximum elements of A

least upper bound of A

greatest lower bound of A

set of all real numbers

sup or inf of unbounded sets

lim (1+1/nt, often called Euler's number

n-->oo

2 sin-^11

Euler's constant

6

11

11

16

18, 19

18 , 19

21

27

27

28

28

4, 24 , 29

35

37

37

42

43

96

429

475