# Set theory

1. Sep 13, 2010

### imranq

1. The problem statement, all variables and given/known data

2. Relevant equations
An equivalence relation on a set A, is for a,b,c in A if:
a~a
a~b => b~a
a~b and b~c => a~c

3. The attempt at a solution
It seems uncomplicated, but I don't know how I would write down a proof. The book I'm using is Topics in Algebra, 1st Edition Herstein

2. Sep 13, 2010

### jgens

What if there were some element $a \in A$ which wasn't related to any other member of $A$?

3. Sep 13, 2010

### HallsofIvy

Staff Emeritus
In other words, consider A= {1, 2, 3} and the relation is {(1, 1), (1,2), (2,1), (2,2)},

4. Sep 13, 2010

### imranq

I don't understand this. I think equivalence classes are generalized equal signs for some property. So (1,1) I understand, but how so for (1,2)?