1. Set Theory
The first mathematical topic that we have to look at in order to understand how search
engines work is the topic of
sets
. We need this because the first step that any search
engine does in trying to answer your question, is to identify a collection of web pages
that in some way seem to match your question. That collection is a
set
. The way that the
engine finds that set involves certain basic mathematical operations that can be
performed on sets. So here we go.
Definition: A set is a collection of objects.
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Examples of collections of objects:
My cat, my dog, and my elephant.
All cats.
The animal types {cat, dog, cow, tiger}
All students in ITI 111
The students {John, Maria, Pedro, Paul}.
Students whose names are John, Maria, Pedro and Paul.
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There are two important ways to specify a set, by a list, and by a rule.
The first way to specify a set is by listing all of the objects that are in it. This is done, on
a page, by using curly braces to represent the beginning and end of the set and listing the
things that are in the set, or their names, usually separated by commas. So we might
have a set that contains the letters a,b,c,d,e,f,w. We could give that set a name (C)
and
write in equations something like
C={a,b,c,d,e,f,w}.