TITLE: There is no infinite descending chain of ordinals
QUESTION [6 upvotes]: I'm currently reading a set theory book and it uses the fact that 

There is not infinite descending chain of ordinals.

But I can't find the proof. (And also I remember Topology by Munkres uses this fact somewhere) 
I don't know how to prove this. May I get a help?

REPLY [3 votes]: Well ordering means that a non-empty subset has a least element. Now if there were an infinite descending chain $... a_2 < a_1 < a_0$, then there would be a non-empty subset $\{ ...,a_2,a_1,a_0\}$ which doesn't have a least element. Contradiction.