User blog comment:Nedherman1/Is it possible something like omega^...(n)...^omega?/@comment-27516045-20191214190657/@comment-39541634-20191214210653

Interesting question.

Subtraction isn't always well-defined for ordinals.

More to the point:

If there were an ordinal α which is equal to ω-1, then we would have:

α+1 = ω.

But it is easy to see that no such ordinal exists:

If α were finite, then α+1 would have been finite too. And if α were infinite, then α would have to be at least ω and therefore α+1 would have to be at least ω+1. Either way α+1 could not be ω.

To summarize: ω-1 does not exist as an ordinal.

(this also makes intuitive sense, because there is no number which is "just before" infinity).