Comment Comment by skulk > There is no infinity at the end of a number line. There is a process that says how to extend that number line ever further.Sure, but ordinal numbers exist and are useful. It's impossible to prove Goodstein's theorem without them.https://en.wikipedia.org/wiki/Ordinal_numberhttps://en.wikipedia.org/wiki/Goodstein%27s_theoremThe statement and proof of the theorem are quite accessible and eye-opening. I think the number line with ordinals is way cooler than the one without them. parent skulk 11 months ago
Sure, but ordinal numbers exist and are useful. It's impossible to prove Goodstein's theorem without them.
https://en.wikipedia.org/wiki/Ordinal_number
https://en.wikipedia.org/wiki/Goodstein%27s_theorem
The statement and proof of the theorem are quite accessible and eye-opening. I think the number line with ordinals is way cooler than the one without them.