00:01
In this problem, we define an equivalence relation, t, on the set of real numbers are by the ordered pair x, y, of real numbers, is in t if and only if x squared equals y squared.
00:11
So we are saying x is related to y in t if and only if their squares are the same.
00:16
The question we have to address is, given a real number in, what is the equivalence class of n? so to start the solution, we're going to rewrite the equivalence relation in this way.
00:29
T is actually a set of ordered pairs of real numbers.
00:35
So using the definition of t, we see that t is the set of all order pairs of real numbers, which have the following property.
00:48
X squared has to equal y squared.
00:51
That's another way of expressing t.
00:55
So we are given a real number in, and we want to know what its equivalence class is.
01:03
So we will write down that definition.
01:10
The equivalence class of n under t is, and we're going to use some notation here...