In Magic the Gathering there are both infinite life combos and infinite damage combos and if the rules committee weren't such cowards figuring out what happens when both things are on the board should be done by having to prove that the cardinality of one infinity is greater than the other's
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in reply to @bruno's post:
you know, there may be situations where the cardinality is relevant but it feels like in many cases the operative question is how fast
anyway, mathematicians have already come up with a robust solution to this incredibly niche problem: ultrafinitism
under ultrafinitist axioms, the only natural numbers that exist are the numbers that somebody has specifically mentioned by name, or specifically constructed in terms of something they've mentioned. and also all the natural numbers that are less than those ones.
so under ultrafinist MtG you could not say "I am invoking this combo infinity times". you would have to say "I am invoking this combo 500 million billion times".
your opponent could then respond by saying "I am invoking my own combo 500 million billion times plus one".
this has a close resemblance to a playground argument that many people have had at least once in their lives, and in this respect it could be said to be a good fit for the game's core themes.
now we want to know what the tournament rules actually do :D
Good news, this is in fact exactly what the tournament rules say. You're allowed to choose any finite number of times to loop the combo, and in the case of multiple players each pulling off their own infinite combo, the player going second will always be able to "a googol plus one" the first player
their cardinalities are necessarily countable. unfortunately the way it happens right now (say an arbitrarily large postive integer) is the only sane way for it to work
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