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More Than Infinite

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The scenario is thus: you are facing down a god-like being whose powers are impossible for you to match. They are infinite in their potential. Thus, the only way to overpower it is with something beyond that.
This counterattack is usually reserved for a character that is omnipotent because this is the only kind of character who could believably have 'infinite power'.
When done poorly it feels like a Deus ex Machina, Ass Pull, or Only the Author Can Save Them Now.
Not to be confused with There Is No Kill like Overkill, or Readings Are Off the Scale. Tentatively related to My Kung Fu Is Stronger, but only applies if the being your kung fu is stronger against is an omnipotent being. See also Even More Omnipotent. Might overlap with Eleventy Zillion.
note Minor footnote type thing: It should be noted that there are degrees of infinity. For instance there are strictly more points on a line (real numbers) than integers (whole numbers). However this rather abstract fact isn't usually what is meant by "more infinite than infinite" in fiction. Alternative number systems, studied in the field of nonstandard analysis, sometimes do include notions of values beyond infinity defined in a formal way. The ordinal numbers extend beyond infinity with the first values being 0, 1, 2, 3, and so on. Then after all of the integers is omega which is the first infinite ordinal. Then is omega plus 1, omega plus 2, omega plus 3, and so on eventually there is omega plus omega and it is possible to continue in this way forever with values like omega squared showing up. Another, this time less formal, use of "infinite" is to mean "can grow without bound". Something like this can go on forever, eventually surpassing every finite number, but it will not technically ever reach an infinite value.
The Infinity +1 Sword does not (usually) work this way.
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In Digimon V-Tamer 01, Taichi and Zeromaru discover a level of Digivolution beyond Ultimate, appropriately named Super Ultimate. (Note that the "Ultimate" level is called "Mega" in earlier translations). This makes one conversation in the English dub of the first series Hilarious in Hindsight. When Miyotismon becomes VenomMiyotismon, a Mega-level Digimon, The Team had up until that point, only seen Digimon as high as Ultimate (or what was called "Ultimate" in the dub) and were incredulous that there would be a level beyond Ultimate, saying something to the effect of "What is he, then? Super-Mega-Ultimate!?"
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This comes up in some of the more extreme matches in DEATH BATTLE!: the combatants' powers are in some sense infinite, but the show comes up with an argument to decide whose are more so.
"Goku vs. Superman" (original): Though both have measurable feats, the argument for who wins is also backed up by this argument: Superman has no real physical limits, whereas Goku can increase his physical limits indefinitely by training, but they're not infinite as long as he can do that — only potentially infinite — so Superman wins.
The Flash (Wally West) vs. Archie Comics' Sonic the Hedgehog: Both have incalculable, massively cosmic speed with no limits. The Flash can drain speed from his opponent to increase his own speed, though, so if they start out at the same speed, he can get faster.
"Saitama vs. Popeye": A perhaps infinitely strong Invincible Hero who finds no challenge in fighting godlike beings against someone who can do anything with Toon Physics. Again, though the analysis gives some arguments that Saitama allegedly has some limits (in fact, it's a bit like with Goku having infinite potential that hasn't all been realised), it also has a backup argument that even if not, his infinite strength still loses to Toon Physics.
"Chuck Norris vs. Segata Sanchiro": Averted. They're just both infinitely Memetic Badass. It's a draw.
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Crisis on Infinite Earths is a story about a really powerful bad guy destroying an infinite number of universes one at a time. Because he's just that powerful!
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A Certain Magical Index: Touma Kamijou does battle with Fiamma of the Right. Fiamma possesses the Holy Right, which grants him complete omnipotence and infinite power. Touma possesses the Imagine Breaker, which can negate anything Touma sees as not normal, including attacks with infinite power. Fiamma assimilates the Imagine Breaker into the Holy Right and succeeds in going past infinite power twice over, becoming "He Who Is Above God". However, this unleashes The Invisible Thing, an entity so powerful and destructive that even the now-exponentially-infinite Fiamma is reduced to cowering in fear of being devoured by a presence that is beyond even that. Then the Invisible Thing is itself outdone by yet another power within Touma, which dwarfs the power of The Holy Right, the Imagine Breaker, and the Invisible Thing combined.
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This was bound to happen eventually on Tengen Toppa Gurren Lagann, the Trope Namer of Beyond the Impossible. In the final showdown, the effectively omnipotent Big Bad throws a Big Bang at the good guys. One of them then absorbs the attack (via Heroic Sacrifice) and channels its power into the good guys' Indescribably Humongous Mecha, making its power More Than Infinite and allowing them to finish off the enemy.
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Irregular Webcomic! has the Infinity Plus One Razor.
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In the comic Superman: Red Son, Superman is trapped by the Green Lanterns who construct a box made out of infinite layers of other boxes. Superman still breaks out though, with just one punch.
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The cosmic hierarchy of the Marvel universe runs on this trope. Cosmic Cubes (and the beings created from them), for example, have explicitly infinite power, but Celestials are multiple levels of infinity beyond them. The Celestials themselves are several rungs below the cosmic abstracts like Death and Eternity, who are powerless against a wielder of the Infinity Gauntlet, which is itself weaker than the Living Tribunal. Of course, the Living Tribunal is merely a creation and servant of the One-Above-All.
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Kamen Rider OOO explains that OOO's name is an infinity symbol plus an extra loop; OOO is powered by Greed, the ability to have everything there could possibly be and still want more. Despite this, his actual power at any given moment is finite, limited by how many Core Medals and Cell Medals he has.
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Magic: The Gathering has many infinite loops that can allow a player to, say, gain infinite life or deal infinite damage, and lots of rule space is devoted to making sure the game doesn't blow up when two of those loops collide. Essentially, "infinity" translates into "whatever really big but still finite number you want", so if your opponent comes along with another infinite loop later on, they can choose a number bigger than the one you chose.
Infinite damage loops tend to end when the thing they're damaging runs out of whatever it is that damage depletes (life for players, loyalty for planeswalkers, or toughness for creatures), or when someone renders the damage irrelevant.
Infinite loops that perpetuate themselves without any input from players (such as three Faceless Butcher creatures without any other creatures in play, which will repeatedly exile each other and return each other to the battlefield) which don't incrementally progress toward a win condition instead result in a draw if no player can interrupt them.
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Three examples of this are shown in the Yu-Gi-Oh! anime:
First, Yugi Mutou, to defeat a monster with an infinite attack, brings out all three Egyptian God Cards, then sacrifices two of them to make the third one — whose power would've already gone to infinite by the two sacrifices — even infiniter.
At the end of the Doma arc the Big Bad, Dartz somehow managed to summon a monster with infinite attack points. Yugi responds by having two of his monsters attack, bouncing the attack between them until it reached infinity and then having a third monster attack to exceed infinity and destroy Dartz' monster.
During the show's Memory World arc, to defeat the Big Bad Zorc Necrophades, one of Atem's priests (who resembled Yugi's grandfather) summoned Exodia, a monster who was apparently so powerful (in the anime, his total ATK was infinite), he needed to be split up into five pieces. Even so, Zorc exploited the fact that Exodia needed the priest's life energy to remain manifest, draining that energy in the fight while he remained more than infinite thanks to his power being sustained by the darkness. Zorc's Power truly would have surpassed infinite if he tried to send the universe into shadows.
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 plus 100. This is put to the test when it's used in the 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. The game physics for the manga actually follow real-world mathematics and consider "∞ + 1" to still be equal to "∞", meaning both monsters are considered to have equal ATK and, thus, do each other in.
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In the DarkMatter2525 video "God's God", Yahweh and Jeffry get into an argument that leads to both of them killing each other. They both wind up in The After Afterlife and meet a being claiming to be the god that created Yahweh in the first place. When Yahweh points out that he was eternal, God's God gets around this by claiming that he is "beyond eternity."
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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 plus 100. This is put to the test when it's used in the 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. The game physics for the manga actually follow real-world mathematics and consider "∞ + 1" to still be equal to "∞", meaning both monsters are considered to have equal ATK and, thus, do each other in.
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The author's notes for Chapter 34 of Harry Potter and the Methods of Rationality discusses the Gambit Pileups in the chapter using transfinite ordinals. He concludes that Quirrel's plot is at least 2w+1 (that is two times infinity plus one)note Which should be ω2 + 1; ordinal multiplication is non-commutative and 2ω is equal to ω.
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At the end of the Star Trek: The Next Generation novel trilogy The Q Continuum, based on the history of the already-omnipotent being Q, he is forced to absorb the equally-powerful Calamarain to become a more-than-infinite 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, as he's now capable of ignoring certain fundamental rules of reality that such beings must acknowledge to prevent total chaos. By merging with the Calamarain, Q was able to share their power so that the two could stop their insane more-than-omnipotent opponent.
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