Appendix B
Sets and Functions
B.1 Se
The conce
even prer
be able
all ob.i
logier
basiAlgebra of Sets
.nost basic of all mathematical concepts. Indeed, it
in order to be able to count "how many," one must
ne objects being counted as somehow separated from
.ounted. Thus, it is natural that the algebra of sets is
e the algebra of numbers. This section will review the
1tions, and relations of sets.
Jut that the word "set" is an undefined term in our context.
T .e that the reader has an understanding of the word without
.on. The notion of "set" conforms to certain axioms, but to de-
sc110e tnese axioms is beyond the scope of this book. One of them, however,
states that a set is completely determined by its elements (or its members);
that is, by what belongs to it.NOTATION: We usually denote sets by capital letters and their elements
by lowercase letters.
The symbol "E" is used to denote "is an element of." Thus,xEA
is the statement "x is an element of A,'' or "x belongs to A."
To describe a set it is sufficient to list its members, in any order. When we
do so, it is customary to enclose its member in "braces." Thus, for example,
the set of integers from 1 through 10 can be denoted
A= {l, 2, 3, 4, 5, 6, 7, 8, 9, 10} or A= {5, 2, 8, 10, 4, 3, 9, 7, 1, 6}.
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