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January 8th, 2010, 03:31 PM   #1
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equivalence relation

n R m in Z+ if n and m have the same final digit in the usual base ten notation.
a) Determine whether the given relation is an equivalence relation and describe the partition arising from each equivalence relation.
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January 11th, 2010, 09:24 AM   #2
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Re: equivalence relation

That this is an equivalence relation is obvious from the definition of an equivalence relation (reflexivity, symmetry, transitivity). The structure obtained will have ten elements which will function as 0,1,2,...,9. Essentially you get arithmetic modulo ten (depending on the operators you started with of course).
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