some notation about set-related discussion...

[ssibseya]

From "http://en.wikipedia.org/wiki/Strict_weak_ordering"

For a strict weak order "<" another associated reflexive relation is its reflexive closure, a (non-strict) partial order "≤". The two associated reflexive relations differ with regard to different a and b for which neither a < b nor b < a: in the total preorder we get a b and b a, while in the (non-strict) partial order we get neither a ≤ b nor b ≤ a. For strict total orders these two associated reflexive relations are the same: the corresponding (non-strict) total order.

I can't understand "For strict total orders these two associated reflexive relations are the same: the corresponding (non-strict) total order.".
Do this sentence mean following?
total preorder -> strict total orders
(non-strict) partial order -> strict total orders
but how derive "strict total orders" from "reflexive closure"?

And I am not so good at set-related notations...
Anyway I must know the some notations about such a things like preorder, strict weak order and so on...
Is there any book for freshman like me?