November 2013
Beginner to intermediate
346 pages
8h 37m
English
Content preview from Natural Language Processing
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CHAPTER 3
Algebraic Structures
Algebraic structures play a major role in mathematics and its
applications. Being a natural generalization of arithmetic operations
with numbers and their properties, different algebraic structures
are used to describe general patterns and behavior of elements and
their operations. This chapter briefl y introduces basic algebraic
structures.
3.1 Functions
Defi nition 3.1.1. A function or map is a triple f = (A, B, F), where A
and B are sets and F ¡ A B is a relation satisfying
(xFy xFy') ² y = y' (Uniqueness of F)
x ¢ A.y ¢ B.xFy (Totality of F)
The set A is called domain of f, B is called codomain of f, and F is ...
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