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January 16th, 2014, 10:09 PM  #1 
Newbie Joined: Jan 2014 Posts: 16 Thanks: 0  Equivalence relation
Let Let . We say that if there is a nonzero real number with . Show that is an equivalence relation on What are the equivalence classes? I am not sure how to do this particular problem. I know I must show reflexive, symmetry and transitivity but would reflexive work here? Also the second part confuses me as well. How can I prove this? Thank you! 
January 17th, 2014, 03:35 PM  #2 
Global Moderator Joined: May 2007 Posts: 6,766 Thanks: 698  Re: Equivalence relation
Reflexive: v ~ ?v, when ? = 1. Symmetric: v ~ ?w then w ~ (1/?)v, since ? ? 0.

January 17th, 2014, 04:27 PM  #3 
Member Joined: Sep 2013 Posts: 32 Thanks: 0  Re: Equivalence relation
Thanks mathman!

January 17th, 2014, 04:30 PM  #4 
Newbie Joined: Jan 2014 Posts: 16 Thanks: 0  Re: Equivalence relation
Thanks! I think I know what to do now with the equivalence relation. But how do I do the second part dealing with equivalence classes?


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