Wow way to kill the enjoyment of a nonsense verse
Nah the verse was wonderful, I thoroughly enjoyed it.
Re:Endless Horse
by thaumasiotes on Friday December 30, 2022 @06:28AM
(#34184078)
In the ordinal-numbers model that your notation leans toward, 2+2+2+... and 2+1+2+1+... are definitely the same infinity, both ω.
On the other hand, you reminded me that conditionally convergent series may converge to different sums depending on how you choose to group their terms, which is fun. (That is, [(s_1 + s_2) + s_3 + (s_4 + s_5) + s_6 + ...] may have a different sum than [(s_1 + s_2) + (s_3 + s_4) + (s_5 + s_6) + ...] does.)†
† I hope this is true; I can't find a cite for it. The more famous theorem is that you can get any sum you want by reordering the terms, but I think regrouping is good enough to get you different sums, if not arbitrary sums.
2+2+2+… is a different infinity than 2+1+2+1+…
You can construct infinite sets of numbers that do not overlap. Odd vs. Even infinity is the example our professor used in class to show the concept. I don’t remember enough to replicate here.