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Hoping you guys could help me with a small issue. No matter how hard I try, I don't seem to fully understand the notion of an equivalence relation, and henceforth an equivalence class. What I do understand that, in order to have and equivalence relation, it is defined to satisfy three rules, symmetry, transitivity....forgot the name of the last one...the one where A~B, B~C, implies A~B. I have read that the equivalence class is the set of those elements which satisfy those definition rules.....can someone please elaborate, none of the literature I have helps which a less abstract full definition (or at least my interpretation of one).

The books I do have are James Munkres, Topology, and Nakaharas Geometry Topology and physics. Both books arent helping. ALSO, if a kind soul has a little more time, the main reason why I question my understanding of equivalence relations is due to an example in Nakaharas p94, where he gives some x-y belonging to a subgroup of G....then defines a relation on them....im confused by this.

Thanks for any help

Cheers

Reza

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# Equivalence relations and equivalence classes

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