Euclidean relations: Philosophy Forums

Euclidean relations

taiho
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Joined: May 03, 2008
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Posted 05/03/08 - 09:49 AM: Subject: Euclidean relations	#1
Hello, I'm having a bit of trouble understanding why a reflexive relation that is Euclidean must also be symmetric and transitive. Could someone provide me with an intuitive explanation or a proof showing why? Thank you!

7
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Posted 05/03/08 - 10:58 AM:	#2
A relation is Euclidean iff xRy & xRz -> yRz. For symmetry, I need xRy -> yRx. Assume that I have xRy. Well xRy & xRx -> yRx. For transitivity, I need xRy & yRz -> xRz. Assume that I have xRy and yRz. I also have yRx by symmetry. yRx & yRz -> xRz.

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