A student writes,
Some of the stuff I'm working on right now involves 'equivalence relations'.
I have seen that they must be transitive, symmetrical and reflexive, but I don't
understand any of these words, or the importance of an equivalence relation, or
what an equivalence relation really is at all!
Could I have an explanation please?
Transitive means: if aRb and bRc then aRc.
Example: the relation > (greater than) is transitive. if a>b and b>c then a>c.
Symmetric means: if aRb then bRa.
Example: the relation != (not equal to) is symmetric. if a!=b then b!=a.
Reflexive means: aRa
Example: the relation >= (greater than or equal) is reflexive. a>=a.
None of these examples, however, is an equivalence relation, because in each case I chose an example in which the particular property applies, but not all three properties.
Sets, Set Description Notation
Set Theory - Groups, group operation has properties: Closure, Associativity, Identity, Inverse.
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