User blog comment:Ubersketch/Ordinals with transfinite FS expansions/@comment-35470197-20190701222433/@comment-32213734-20190702080815

Ordinals are well-founded, that is any set of ordinals has minimal element. That is there are infinite strictly increasing sequences of ordinals:
 * α0 > α1 > α2 > α3 > α4 > ... > αω > ...

but there are no infinite strictly decreasing sequences of ordinals (infinite descending chains):
 * α0 < α1 < α2 < α3 < α4 < ... < αω < ...

So, any strictly decreasing sequences of ordinals terminates, that is has finite number of elements. For example, let's start from ω2 and try to make an infinite strictly decreasing sequences, beginning from it. We'll can make only something like
 * ω2, ω + 5, ω + 4, ω + 3, ω + 2, ω + 1, ω, 5, 4, 3, 2, 1, 0

that is finite sequence. And it is the same for ω2, ωω, ε0, Ω, Ωω and any other ordinal (descending chain condition).