## A Conversation for Equivalence Relations - The mathematics of distinction

### Gemini's - we'all the same!

Kul_Tegin Started conversation Feb 23, 2004

A very useful entry. Equivalence relation is one of the most important concepts in the mathematics at all levels.

An example I used when teaching Discrete Maths is the Horoscope. Astrologers divide the set of all humans into 12 equivalence classes generated by the equivalence relation 'Having the same sign of the zodiac'. Everyone in the same equivalence class e.g. Gemini are all equivalent. But not 'the same as' i.e. equality/identity (strong equivalence) requires one other property i.e. substitutivity. 'Your milkman may be a Gemini like you Doctor but he's not going to operate on me while you go for lunch!"

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### Gemini's - we'all the same!

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