History Main / MoreThanInfinite

* In RealLife math, there's many different kinds of infinity.
** The lowest infinite ordinal number is ω. You can keep adding one, or ω, or ω^2, and so on.
** The lowest infinite cardinal number is ℵ₀. Adding one to it leaves it the same, as does doubling it, or even squaring it. You can get a higher one by essentially raising 2 to its power, getting ℵ₁. You can do this again to get ℵ₂, etc.
** With Hyperreal numbers, you can add an infinitesimal to an infinite and make it slightly bigger. You can also put it through some quickly increasing function to make it just ridiculous.
*** This troper likes "infinity to the infinite power" (∞^∞), whether or not this is mathematically correct.
**** Depends. In cardinal numbers, ℵ₀^ℵ₀ is no larger than 2^ℵ₀, which is equal to ℵ₁. In ordinal numbers and hyperreal numbers, ω^ω is much bigger than 2^ω or ω^2, and it is a number in its own right. So it is probably correct, but its exact value depends on the context.
** A fun little mind-bender this troper learned from his CS professor: the set of integers is infinite, but the set of real numbers is not only ''more'' infinite, but ''infinitely'' more infinite.
*** You can't be finitely more infinite: the integers and the even integers are the same size, even though only half the integers are even. There are ω of each of them.

** Pushed higher in the movie where [[spoiler:the good guys summon a HumongousMecha the size of a galactic supercluster and launch a FinishingMove at the BigBad... who copies said move and retaliates. ]].

* In ''Digimon V-Tamer'', Taichi and Zeromaru discover a level of Digimon evolution ''beyond'' Ultimate appropriately named Super Ultimate (Note that this "Ultimate" level is referred to as "Mega" in earlier translations).
* ''IrregularWebcomic!'' has the [[http://irregularwebcomic.net/1186.html Infinity Plus One Razor.]]

* At the end of a ''StarTrekTheNextGeneration'' novel trilogy based on the history of the already-omnipotent being Q, he is forced to absorb the equally-powerful Calamarain to become a MoreThanInfinite composite being to fight off another omnipotent, yet insane, being; the explanation given was that depriving an omnipotent being of his grasp of reality makes him even ''more'' omnipotent, essentially meaning Q had to become MoreThanInfinite to stop a being that's ''already'' gone MoreThanInfinite.
** A more plausible explanation is offered in the series. In spite of Q's boasting, the Q are merely so insanely powerful as to seem omnipotent to mere mortals but are not actually omnipotent.

* And in the real ''{{Yu-Gi-Oh}}'' trading card game all of the examples above would lose to 'The Wicked Avatar', whose ATK is equal to the ATK of the strongest monster on the field [[AlwaysSomeoneBetter plus 100]].
** This is actually put to the test when it's used in the ''[[{{Yu-Gi-Oh R}} Yu-Gi-Oh! R]]'' manga; it's able to dominate virtually ''everything'' used against it, including Kaiba's Blue-Eyes and Yugi's Slifer the Sky Dragon (an ''Egyptian God'' whose power level is variable depending on the number of cards in its controller's hand, ''and'' who can reduce an opponent's monster's ATK and DEF by 2000, when that monster's summoned, an ability that, of course, did ''nothing'' to The Wicked Avatar). It was only taken down by Yugi's Obelisk the Tormentor, after it uses its effect to power up its ATK to infinite. However, in this case, it's a ''subversion'', as the game physics for the manga consider "∞ + 1" to still be equal to "∞", meaning both monsters are considered to have equal ATK and, thus, [[DoubleKnockout do each other in]].
* This was bound to happen eventually on ''TengenToppaGurrenLagann'', the TropeNamer of BeyondTheImpossible. In the final showdown, [[spoiler:the effectively omnipotent BigBad ''throws a Big Bang'' at the good guys. One of them then ''absorbs the attack'' (via HeroicSacrifice) and channels its power into the good guys' Indescribably HumongousMecha, making its power More Than Infinite and allowing them to finish off the enemy]].
** Pushed even higher in the movie where [[spoiler:the good guys summon an [[BeyondTheImpossible ABSOLUTELY FUCKING]] HumongousMecha the size of a galactic supercluster and launch a FinishingMove at the BigBad... who copies said move and retaliates. [[CrowningMomentOfAwesome The universe simply can't take this much awesome and collapses into an infinity sign]]]].
* RealLife example: Tired of making sequels, Bungie decided to cut off speculation about ''[[{{Halo}} Marathon 4]]'' by naming the third ''{{Marathon}}'' game ''Marathon ∞'' (noting that it was the first to ship with [[GameMod modding tools]]). When an open source enhancement project later started up using the recently released public domain engine code, some wag decided to name it ℵ₁(Aleph One, the mathematical symbol for the smallest ''uncountable'' infinity).

[[quoteright:323:[[YuGiOh http://static.tvtropes.org/pmwiki/pub/images/infiniteatk_8275.png]]]]
[[caption-width-right:323: That's a lot of power. Too bad [[AssPull Yugi has something stronger]].]]

* ENDER'S GAME.

* ''KamenRiderOOO'' explains that OOO's name is actually an infinity symbol plus another O, thus his true power is litterally MoreThanInfinite. However, he hasn't yet reached this level so far.

* The Great Wheel cosmology of ''{{Planescape}}'' and pre-4E D&D often ran into this quandary, in that its various planes were considered infinite, with infinite numbers of beings living there. Yet for some reason, the infinite demons of the Abyss still ''outnumbered'' the infinite devils of Hell, and the Lower Planes in general still had a ''bigger'' infinite horde than did the infinite hosts of the Upper Planes.
** Hardly, the plane is infinite not the population. Demons are truly infinite because they arise spontaneously out of the Abyss while all other outsiders are transformed souls or specific ancient beings from the dawn of time.

* IrregularWebcomic! has the [[http://irregularwebcomic.net/1186.html Infinity Plus One Razor.]]

* RealLife example: Tired of making sequels, Bungie decided to cut off speculation about ?[[{{Halo}} Marathon 4]]? by naming the third ''{{Marathon}}'' game ''Marathon ∞'' (noting that it was the first to ship with [[GameMod modding tools]]). When an open source enhancement project later started up using the recently released public domain engine code, some wag decided to name it ℵ₁(Aleph One, the mathematical symbol for the smallest ''uncountable'' infinity).

The InfinitePlusOneSword does not work this way.

-->'''Yami Yugi''' to '''Dartz''', ''[[YuGiOh Yu-Gi-Oh!]]

-->'''Yami Yugi''', to '''Dartz'''

*** Just to make things even more confusing, a 2D plane with only integers along each axis is the same size as the normal, 1D set of integers. A 2D plane of the ''real'' numbers, however, is size 2^ℵ₁, or infinitely larger again than the reals.

*** Incredibly, ∞^∞ is just equal to 2^∞ or aleph-one. To get a greater infinity you have to raise 2 (or another number) to the aleph-one power.

* Two examples of this are shown in the ''{{Yu-Gi-Oh}}'' anime:

* The Great Wheel cosmology of ''{{Planescape}}'' and pre-4E D&D often ran into this quandary, in that its various planes were considered infinite, with infinite numbers of beings living there. Yet for some reason, the infinite demons of the Abyss still ''outnumbered'' the infinite devils of Hell, and the Lower Planes in general still had a ''bigger'' infinite horde than did the infinite hosts of the Upper Planes. SoYeah.

* And in the real ''{{Yu-Gi-Oh}}'' trading card game all of the examples above would lose to 'The Wicked Avatar', whose ATK is equal to the ATK of the strongest monster on the field [[AlwaysSomeoneBetter plus 100]]. SoYeah.

The scenario is thus: you are facing down a [[SufficientlyAdvancedAlien god-like being]] whose powers really are impossible for you to match. They are infinite in their potential, going way OverNineThousand into googleplex-in-base 13 levels. There is absolutely no way you can defeat it, until...