In magic it is quite posisble to set up a countably infinite sequence - that is a sequence that can be perpetuated for as long as you care to, but which technically must be stepped through.
Most people tend to just end the game when one of these happens - but it is posisble for two such sequences to occur. For example, one gaining infinite life and one doing infinite damage. This locks the game into a draw, since neither player is willing to prematurely end their sequence.
So some means needs to be developed for the infinite sequences to be folded into a single event; as well as being able to know whether given sequences interact with one another, or can be used as being 'larger'
Well, actually, that's not quite it. The MtG Comprehensive Rules contain the following section on "Infinity":
There's no such thing as "infinity" in Magic rules. Occasionally the game can get into a state where a set of actions could be repeated forever. The "infinity rule" governs how to break such loops. See rule 421, "Handling 'Infinite' Loops."
421. Handling "Infinite" Loops
421.1. Occasionally the game can get into a state in which a set of actions could be repeated forever. The "infinity rule" governs how to break such loops.
421.2. If the loop contains one or more optional actions and one player controls them all, that player chooses a number. The loop is treated as repeating that many times or until the other player intervenes, whichever comes first.
421.3. If the loop contains at least one optional action controlled by each player and actions by both players are required to continue the loop, the active player chooses a number. The nonactive player then has two choices. He or she can choose a lower number, in which case the loop continues that number of times plus whatever fraction is necessary for the active player to "have the last word." Or he or she can agree to the number the active player chose, in which case the loop continues that number of times plus whatever fraction is necessary for the nonactive player to "have the last word." (Note that either fraction may be zero.)
Example: One player controls a creature with the ability "0: [This creature] gains flying." Another player controls a permanent with the ability "0: Target creature loses flying." The "infinity rule" ensures that regardless of which player initiated the gain/lose flying ability, the nonactive player will always have the final choice and therefore be able to determine whether the creature has flying. (Note that this assumes that the first player attempted to give the creature flying at least once.)
421.4. If the loop contains only mandatory actions, the game ends in a draw. (See rule 102.6.)
421.5. If the loop contains at least one optional action controlled by each player and these actions don't depend on one another, the active player chooses a number. The nonactive player can either agree to that number or choose a higher number. Note that this rule applies even if the actions could exist in separate loops rather than in a single loop.
However, that wasn't what we were discussion when the need for true /TransfiniteRules was suggested. We were wondering, if a player creates an infinite amount of green squirrel tokens for example, and then another player plays MTG: Hibernation, does the first player's hand size become infinitely large for a moment, before state-based effects kick in and the tokens are removed from the game? Ignore the inconvenient "fact" that there's no such thing as infinity in Magic for the moment... --AC
Sure - this would be an extension to do away with kludges like that. Instead of allowing the player to only pick a number that they can actually say (And I note that the rules do not specify 'aleph-zero' as being an invalid number) allow all actions to go to any number up to the highest infinity that they cover. And then deal with them.
(PeterTaylor) Isn't there another rule elsewhere which defines "number" as meaning "non-negative integer"?
Doesn't aleph-zero count as an integer? I can believe that they deliberately define it away - but that's still a gross hack. --Vitenka
(AlexChurchill) Well, "natural number", but close enough. (And yes, the judges' list has seen arguments about whether "natural numbers" includes zero. From context, it blatantly does.) Again from the CompRules glossary:
Magic uses only natural numbers. You may not choose a fractional number, deal fractional damage, and so on. When a spell or ability could generate a fractional number, the spell or ability will tell you whether to round up or down. If a creature's power or toughness, a mana cost, a player's life total, an amount of damage, or an amount of life loss would be less than zero, it's treated as zero for all purposes except adding to or subtracting from that total. :Example: A 0/2 creature gets -1/-1 until end of turn. It is now a -1/1 creature, which acts exactly like a 0/1 creature except for things that would change its power further. If it is later given +2/+0, then it becomes a 1/1 creature, not a 2/1 creature.
Because at the moment, the nasty situation is that a player may choose 'seventy million' intending this to be, basically, infinite - and then later discover that his opponent can actually do that much damage using non-infinite means. Which, really, should be impossible.
Hmmm. If people go for "a thousand", then that can be achieved without "arbitrarily large" combos. "Seventy million" would be pretty tough to achieve in Magic without being able to hit seventy gazillion just as easily. (Maybe something along the lines of using 50-odd tokens generated by normal doubling means, each of which is a copy of an animated MTG: Furnace of Rath - and with a few copies each of MTG: Coat of Arms and MTG: Repercussion. Then sacrifice one with MTG: Rupture or MTG: Bloodfire Infusion.)
Let's leave the x's in there! :) (Or, better by far in my opinion, play a game which cannot have such broken situations)
You're talking to the wrong people here, Vitenka :) The origin of this page was us deliberately trying to *extend* the rules of Magic (and invent new cards and such, probably) to handle ordinals or infinities of some form... I think the fact that Magic can come so close to this is precisely *why* we're setting this silly intellectual discussion in the context of Magic :) --AC
Well, true - but in order to get such rules that arne't a major kludge you'll need to root out quite a lot of almost-broken stuff I think. How about treating all numbers in magic as being transfinites of order zero - don't bother with what they are below that. --Vitenka