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Erschienen in:
2011 | OriginalPaper | Buchkapitel
Relations
verfasst von : Ulrich Daepp, Pamela Gorkin
Erschienen in: Reading, Writing, and Proving
Verlag: Springer New York
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In the last chapter we introduced relations. We will now look at three useful properties of relations. Recall that “
S
is a relation on a set
X
” is one way of saying that
S
is a subset of
X
×
X
, and therefore the elements of
S
are ordered pairs, (
x
,
y
). Many authors write
x
~
y
rather than
$$(x,y)\, \in \,S.$$
Sometimes we will write
x
~
y
and other times we will write
$$(x,y)\, \in \,S,$$
and this is exactly the same thing. So why do it? Because sometimes one notation is more convenient than the other. Use the next exercise to familiarize yourself with both notations.