Have rephrased as “So, does 1+ω make sense as something different from ω?”.
1+ω = ω, for the usual ordering convention for ordinal addition.
Edit: I can’t figure out how to delete my comment, but ricraz already said this. https://www.lesserwrong.com/posts/GhCbpw6uTzsmtsWoG/the-different-types-not-sizes-of-infinity/xDfSmdiQATFF4sLPt
Have rephrased as “So, does 1+ω make sense as something different from ω?”.
1+ω = ω, for the usual ordering convention for ordinal addition.
Edit: I can’t figure out how to delete my comment, but ricraz already said this.
https://www.lesserwrong.com/posts/GhCbpw6uTzsmtsWoG/the-different-types-not-sizes-of-infinity/xDfSmdiQATFF4sLPt