History Main / MoreThanInfinite

In the world of mathematics, this is somewhat TruthInTelevision as there are degrees of infinity, albeit in terms of ordering than counting. For instance, you can list every natural number, integer, and rational number[[note]]These respectively mean: numbers you can count (like 1, 256, or Graham's number), whole numbers (like the previous plus to numbers like 0, -1, or -10[[superscript:100]]), and whole numbers plus fractions (like the previous plus numbers like 0.5, -1/12, or 0.3333...)[[/note]] and assign them a specific value, which means they are all the same size (usually denoted as aleph-0 or ℵ[[subscript:0]], the smallest infinite cardinal number). Meanwhile, you can't do the same thing with real numbers or complex numbers,[[note]]Respectively: any number that can be measured (like the previous notes plus numbers like e, √2, and π), and any real number plus any value associated with √-1 (like the previous ones plus i, 3+2i or √i)[[/note]] which means there are strictly more of them than rational numbers (it's usually denoted as 2[[superscript:ℵ[[subscript:0]]]]). 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 (ω) which is the first infinite ordinal. Then is ω + 1, ω + 2, ω + 3, and so on eventually there is ω + ω (or 2ω) and it is possible to continue in this way forever with values like ω[[superscript:2]] and ω[[superscript:ω]] 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.

In the world of mathematics, this is somewhat TruthInTelevision as there are degrees of infinity, albeit in terms of ordering than counting. For instance, you can list every natural number, integer, and rational number[[note]]These respectively mean: numbers you can count (like 1, 256, or Graham's number), whole numbers (like the previous plus to numbers like 0, -1, or -10[[superscript:100]]), and whole numbers plus fractions (like the previous plus numbers like 0.5, -1/12, or 0.3333...)[[/note]] and assign them a specific value, which means they are all the same size (usually denoted as aleph-0 or ℵ[[subscript:0]], the smallest infinite cardinal number). Meanwhile, you can't do the same thing with real numbers or complex numbers,[[note]]Respectively: any number that can be measured (like the previous notes plus numbers like e, √2, and π), and any real number plus any value associated with √-1 (like i, 3+2i or √i)[[/note]] which means there are strictly more of them than rational numbers (it's usually denoted as 2[[superscript:ℵ[[subscript:0]]]]). 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 (ω) which is the first infinite ordinal. Then is ω + 1, ω + 2, ω + 3, and so on eventually there is ω + ω (or 2ω) and it is possible to continue in this way forever with values like ω[[superscript:2]] and ω[[superscript:ω]] 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.

In the world of mathematics, this is somewhat TruthInTelevision as there are degrees of infinity, albeit in terms of ordering than counting. For instance, you can list every natural number, integer, and rational number[[note]]These respectively mean: numbers you can count (like 1, 256, or Graham's number), whole numbers (like the previous plus to numbers like 0, -1, or -10[[superscript:100]]), and whole numbers plus fractions (like the previous plus numbers like 0.5, -1/12, or 0.3333...)[[/note]] and assign them a specific value, which means they are all the same size (usually denoted as aleph-0 or ℵ[[subscript:0]], the smallest infinite cardinal number). Meanwhile, you can't do the same thing with real numbers or complex numbers,[[note]]Respectively: any number that can be measured (like the previous notes plus numbers like e, √2, and π), and any real number plus any value associated with √-1 (like i or 3+2i)[[/note]] which means there are strictly more of them than rational numbers (it's usually denoted as 2[[superscript:ℵ[[subscript:0]]]]). 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 (ω) which is the first infinite ordinal. Then is ω + 1, ω + 2, ω + 3, and so on eventually there is ω + ω (or 2ω) and it is possible to continue in this way forever with values like ω[[superscript:2]] and ω[[superscript:ω]] 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.

[[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.[[/note]]

* ''LightNovel/ACertainMagicalIndex'': Touma Kamijou does battle with Fiamma of the Right. Fiamma possesses the Holy Right, which grants him [[TheOmnipotent complete omnipotence and infinite power]]. Touma possesses the Imagine Breaker, which can [[AntiMagic 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 [[BeyondTheImpossible past infinite power twice over]], [[AbstractApotheosis becoming "He Who Is Above God"]]. However, this unleashes [[EldritchAbomination The Invisible Thing]], an entity so powerful and destructive that [[AlwaysABiggerFish 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 ''[[SerialEscalation yet another]]'' power within Touma, which ''dwarfs the power of The Holy Right, the Imagine Breaker, and the Invisible Thing '''combined'''''.

** "Saitama vs. Popeye": A perhaps infinitely strong InvincibleHero who finds no challenge in fighting godlike beings against someone who can do anything with ToonPhysics. [[spoiler: Again, though the analysis gives some arguments that Saitama allegedly has some limits, it also has a backup argument that even if not, his infinite strength still loses to Toon Physics.]]

* An [[UpToEleven absolutely extreme example]] occurs in ''LightNovel/ACertainMagicalIndex'', when Touma Kamijou does battle with Fiamma of the Right. Fiamma possesses the Holy Right, which grants him [[TheOmnipotent complete omnipotence and infinite power]]. Touma possesses the Imagine Breaker, which can [[AntiMagic 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 [[BeyondTheImpossible past infinite power twice over]], [[AbstractApotheosis becoming "He Who Is Above God"]]. However, this unleashes [[EldritchAbomination The Invisible Thing]], an entity so powerful and destructive that [[AlwaysABiggerFish 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 ''[[SerialEscalation yet another]]'' power within Touma, which ''dwarfs the power of The Holy Right, the Imagine Breaker, and the Invisible Thing '''combined'''''.

''Not'' to be confused with UpToEleven, ThereIsNoKillLikeOverkill, or ReadingsAreOffTheScale. Tentatively related to MyKungFuIsStronger, but ''only'' applies if the being your kung fu is stronger against is an [[TheOmnipotent omnipotent]] being. See also EvenMoreOmnipotent. Might overlap with EleventyZillion.

** "Goku vs. Superman" (original): Though both have measurable feats, the argument for who wins is also backed up by this argument: [[spoiler: 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, so Superman wins.]]