Foundations of Semantic Web Technologies

Appendix B

Set Theory

This appendix briefly introduces basic notations and notions of se t theory

used in this bo ok.

B.1 Basic Notions

The notion of a set as a mathematical term was introduced by Georg Cantor

in 1877 who defined a set as “a collection of certain well-distinguished objects

of cognition or thinking, which will be called elements, to a whole.”

Conventionally sets are represented by capital letters whereas lowercase

letters are used to denote their elements. In order to expres s that an entity e

is an element of a set S, we write e ∈ S (the contrary would be displayed as

e 6∈ S).

Note that a set cannot contain an element twice or many times, ...