June 2014
Intermediate to advanced
464 pages
11h 15m
English
book
Mathematical Foundations of Image Processing and Analysis, Volume 1
by Jean-Charles Jean-Charles Pinoli Pinoli
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7
Basic Reminders in Set Theory
This chapter aims to briefly summarize the basic notions of Set Theory that should be necessary for presenting the mathematical imaging frameworks for both gray-tone and binary images.
7.1. Mathematical disciplines
The mathematical discipline of reference is the theory of sets, or for short Set Theory [RUB 67, DEV 93, BOU 04c]. The notion of set is fundamental in modern Mathematics because most of the mathematical entities (numbers, relations, operations, functions, etc.) are defined in terms of sets.
7.2. Sets and elements
A set, denoted as 
is a collection of well-defined and distinct elements, denoted 
A subset of a set 
is a subcollection of well-defined and distinct elements of . A singleton is also a set with exactly one element. For example, the set 
is a singleton related to the element 
The empty set is denoted by Ø.
7.2.1. Membership
The first concept ...
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I'm always learning. So when I got on to O'Reilly, I was like a kid in a candy store. There are playlists. There are answers. There's on-demand training. It's worth its weight in gold, in terms of what it allows me to do.