# Thread: Quick question on equivalence class theory

1. ## Quick question on equivalence class theory

Say I have a relationship on integers defined by given a, b in integers, a is related to b iff a^2 = b^2

Then the equivalence class of [271] would be what?

Is it [271] = {-271} or is [271] = {271, -271}?

What I mean is, [271] is the set of all things related to 271, but would you list 271 in there as well? My guess is yes, but I just want to make sure.

2. Originally Posted by swtdelicaterose
Say I have a relationship on integers defined by given a, b in integers, a is related to b iff a^2 = b^2

Then the equivalence class of [271] would be what?

Is it [271] = {-271} or is [271] = {271, -271}?

What I mean is, [271] is the set of all things related to 271, but would you list 271 in there as well? My guess is yes, but I just want to make sure.

If the relation is reflexive, as this one is, you must count each element in its class, so $[271]=\{-271,\,271\}$

Tonio