what does equivalence class mean?
I am trying to understand I think that I am a little confused so let's take this example:
Suppose that we have the relation $2x+3y$ is a number less than or equal 20 on the set $\{1, 2, 3, 4\}$ this relation is equivalence relation because it is reflexive, symmetric and transitive, now let's get the equivalence class for each of the elements:
$[1]$ = $\{1, 2, 3, 4\}$, [2] = $\{2,1,3,4\}$, $[3]$ = $\{3, 1, 2, 4\}$, $[4]$ = $\{4, 1, 2, 3\}$.
have I calculated the equivalence relations correctly or I made some mistakes and if the answer is that you calculated them correctly this will push me to ask does the equivalence class of an element in a set is the set itself?