An equivalence relation is defined to be

1. Reflexive

IE given a relation, R, it is reflexive iff

2. Symmetric

IE, given a relation R, it is symmetric iff

3. Transitive

IE, given a relation R, it is transitive iff and

Make sure these 3 properties hold. If one does not, it's not an equivalence relation.

so, say, the first one, for example.

such that

So f is in relation with g so that if f(n) is less than or equal to g(n) for all n bigger than some natural number, say, k.

Well, is it reflexive?

such that

It holds because f(n) = f(n) for all n, no matter what k you choose.