Sets, Multisets and Partial Orders

Set :- An unordered collection of different, well defined objects.
Multiset :- An unordered collection of well defined objects.

That is a Set is a Multiset with distinct objects only.

Touple :- A permutation of well defined objects.

Equivalence Class :- Its a set S, with respect to a relation '~', such that
& ∀ x,y,z ∈ S:-

1. Reflexive : x ~ x
2. Symmetric :x ~ y ⇒ y ~ x
3. Transitive : x ~ y and y ~ z ⇒ x ~ z

Partial Order :- Its a set S, with respect to a relation '≥', such that 
& ∀ x,y,z ∈ S:-

1. Reflexive : x ≥ x
2. Anti-symmetric :x ≥ y and y ≥ x ⇒ y = x
3. Transitive : x ≥ y and y ≥ z ⇒ x ≥ z

These above concepts are  very important.