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Supplementary Lecture Notes for Math 125-1 - Alexei V. Samsonovich 2/1/2007 6
Lecture 2: Sets, Relations and Functions
A set S is a collection of distinct objects x
1
, x
2
, . called elements (or members) of the
set. This is written as follows: S = {x
1
, x
2
, .}, and the expression x
1
? S says that x
1
is a
member of S (belongs to S). The notion of a set does not allow for multiple instances
(repetitions) of the same element in the set, while the notion of a sequence (an ordered
collection) does. The notion of a set does not relate to the notion of continuity, while at
the same time it provides a basis for all concepts of continuous data structures (which are
not a topic here). As far as the set theory per se is concerned, the nature of elements is
irrelevant: all that matters is how many elements are and whether two elements x and y
are one and the same element (x = y) or not (x ? y). For example, a set may contain
another set (or even itself) as its element. A set ...

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