User blog comment:Alejandro Magno/My Ordinal is Smaller!/@comment-1605058-20140922145716/@comment-1605058-20140922150507

It's trivial fact from order theory that if ordinal a is additively principal number, then for every b<a we have a-b=a. K is regular cardinal, and thus it follows that it's additively principal, so K-anything=K, thus the step is of size K provided we choose a smaller ordinal.