User blog comment:Bubby3/FGH on ordinals/@comment-32876686-20171105152536/@comment-30754445-20171105154658

Both of you are correct.

In ordinal arithmetics, 2ω is actually equal to ω:

2ω = lim (21, 22, 23, 24, ...) = lim(2, 4, 8, 16...) = ω.

So ω×2ω = ω×ω = ω2.