LIST OF SYMBOLS

Symbol Application Meaning

€

*

d

0 {} u n

1 1

u

0

X

-»

N R B2 arb. B\

aeA

a$A

A<zB 4 = 0 {*;-} Xufi / InB W

i = l

CM.

(al9...,an)

A x B , 4 - B / : A - B BA

fceN aeR xeB 2 x = arb. f:Bn

2->R

a is an element of set A (also: a belongs to the set A) a is not an element of set A (also: a does not belong to the set A) A is a subset of set B A is an empty set all x such that union of sets A and B intersection of sets A and B number of elements of (finite) set A

union of sets Al,...,An

union of sets Ax for i e /

ordered pair of elements a, b ordered n-tuple of elements ai , . . . , a„ cartesian product of sets A, B mapping (function) of A into B mapping/(function/) of A into B all mappings of A into B k is positive integer a is a real number x assumes value 0 or 1 x assumes value 0 or 1 function which assigns a real number to an n-component vector of zeros and ones

14

Symbol

H) H, ) n,..,) - ,p ( ) - > * ( . ) - i p ( , . . . , V

& => o

\-

V

A

V 3 =

T F

Application

P(x) H*>y) P(Xi,...,X„) -.P(x) -*P(x,y)

)-iP(xu...,xn) PV q

p&q p=>q poq

{X1,...,X„}\-Y

n

VP, i = l

VP, iel

n

A Pi t = i

A Pi iel

Vx 3x C = ^ u B

Meaning

x has property P x and y are in relation P xl9...,x„ are in relation P x does not have property P x and y are not in relation P x!,...,x„ are not in relation P disjunction (alternative) of statements p, q conjunction of statements p, q p implies q p if and only if q (p is equivalent to g) formula Y follows from the class of formulae Xl9..., Xn

disjunction of statements P i » — » P n disjunction of statements p( for 1 6 /

conjunction of statements Pi> •••>P« conjunction of statements p{ for 1 6 / for all x an x exists set C is defined as the union of sets A, B truth value True truth value False