Math Is Fun Forum

entity

Member

Registered: 2010-05-04

Posts: 2

Proofs involving equivalence classes and relations

The question is asking me to find/describe the set of equivalence classes of the following equivalence relations.

a) let S: R^2 --> R^2 where (x1,y1)S(x2,y2) if and only if x1=x2

I don't understand equivalence classes or relations really and I don't even know what they are asking... I have a rough idea of what they are but the book isn't really making it clear... can anyone help?

entity

Member

Registered: 2010-05-04

Posts: 2

Re: Proofs involving equivalence classes and relations

bump

Ricky

Moderator

Registered: 2005-12-04

Posts: 3,791

Re: Proofs involving equivalence classes and relations

Look at the elements (1,0) and (1, 1).  Since the first coordinate in each of these elements are the same, (1,0)S(1,1).  The same goes for (1,0)S(1,5).  So we consider them to all be the same, which we call a "class".  Your task is to find a way to represent exactly one element from each class.  So (1,0) is a representative of the class {(1,0), (1, 1), (1, 5), ...}.

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"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."