I am having a hard time with the following problem:
In F(R), let f~g iff f(x)=g(x) for all x>c where c is some fixed real number.
I proved that it was a equivalence relation by the following:
f~f __ f(x)=f(x) so that is fine.
f~g implies g~f __ f(x)=g(x) and g(x)=f(x) f~g does imply g~f so that is fine.
f~g, g~h implies f~h __ f(x)=g(x) and g(x)=h(x) therefore you can substitute h(x) for g(x) thus f(x)=g(x).
The part that I am having trouble with is describing the partition associated with this equivalence relation. I know that the partition is equivalent to the equivalence class but I am unsure about how to find that since I'm dealing with functions. My assumption is that the partition is the collection of functions of f(x) where x>c.