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Equivalence Relations
4 páginas
Publicado por
sharma deepak
Equivalence Relations
Tutorcircle.
com Page No.
: 1/4
Equivalence Relations
A relation on A is an equivalence relation if it is reflexive, symmetric and transitive.
An
example of such is equality on a set.
One might think of...
[Más]
Equivalence Relations
Tutorcircle.
com Page No.
: 1/4
Equivalence Relations
A relation on A is an equivalence relation if it is reflexive, symmetric and transitive.
An
example of such is equality on a set.
One might think of equivalence as a way to glob together
elements that can be considered the same relative to a property.
That is elements become
indistinguishable relative to the relation.
For example in arithmetic we don t think twice about
1/2 and 2/4 as having the same value but they are different objects.
In geometry, similarity of
triangles is an equivalence relation.
A right angled triangle with legs of length 3 and 4 and
hypotenuse of length 5 is not the same as one with lengths 6, 8 and 10.
Yet, we think of them
as equivalent because the ratios of the corresponding sides are the same.
For each , we define the equivalency class containing a to be the set of those elements
which are equivalent to a.
We denote this set by [a] although you should be aware that there
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