y'all need a math lesson..

Infinite and infinite plus 1 are the same size - you would need to play infinite + infinite delay orders to outdelay the OD card - ie a second order delay card.

+1 for getting infinity + 1 right, but infinity + infinity will just be the size of the bigger of the two infinites. As we are talking about moves here, it is reasonable to assume all infinities mentioned are countably infinite, and infinite + infinite will just be again the same infinity. Also infinity * infinty is still the same thing, not any bigger.

As a curiosity, in maths there is a concept of "infinity plus one", in the ordinal numbers.

Cardinals and ordinals are not the same, cardinals are about size, ordinals about order.

You can define w + 1 as the number that comes after all countable infinity, but that doesnt change that the size (or cardinality of the set of all those numbers) is unchanged by adding another.

If you want to know if two sets are of equal size, the definition is very intuitive:

They are if and only if there exists a bijection between the two sets

or in other words, find a 1-to-1 paring of the sets members.

It should immediatly make sense how this lines up with our understanding of being same size.

With that definition, you can also easily convince yourself that all those infinites are the same thing.

If you want the next bigger thing, you ll have to leave the countable realms, for example looks at real numbers.

However, back to outdelaying the infinite moves, it is about order, so w+1 is the way to go indeed.

Anything +1, is 1 bigger. If it was a finite amount of dummy moves, there should be a number where 1 more is enough, like the wiki would suggest. Infinity doesn’t mean endless, correct? Just means unquantifiable, by our standards

nonononono

Edited 10/13/2024 14:21:17