The "Numbers" are a special group of Xyz Monsters (with some exceptions) that are that debuted in Yu-Gi-Oh! ZEXAL. Supposedly pieces of the mysterious entity Astral, the protagonist of the show, Yuma Tsukumo, must acquire all 100 and solve the mysteries behind these powerful creatures.
Here is the information regarding the Numbers, in both the canon series, and in other stories in other universes.
When Yuma Tsukumo unlocked the Door with his Emperor's Key, he opened a portal between his own dimension and another, allowing the mysterious entity Astral to come into his world. Yuma found himself trapped within a sphere of blank cards, which shortly shattered away. By crossing into Yuma's world, Astral's memories got transformed into the hundred "Number" cards and scattered in unknown directions. In order to regain his lost memories, Astral teamed up with Yuma. These cards that take the form of what whoever finds them desires the most, design themselves to fit their original owner's Decks, and keep that form forever. Some Duelists may have more than one "Number" card that fit their Deck. Their card text is written in a strange alien language that only those who wield them can understand (in the dub, all "Numbers" appear normally like other cards seen with the exception of episode 2 which Number 39: Utopia is blurred). When they are Summoned, their respective numbers are printed on their users, appearing in such places as the forehead, neck, left and right hands (in Cameron Clix's case, it appeared under his right eye and in Number 56's Holder's case, it appeared in his left shoulder). When Summoned, they use a galaxy-like "Overlay Network" portal in contrast to regular Xyz Monsters, who use a red spiral portal. All Xyz Monsters are said to come from another dimension and are made of antimatter. This would include the "Numbers".
They have been shown to be very dangerous, as their users are easily possessed by their power (with the exception of Yuma due to his partnership with Astral and Kaito who has powers similar to those of Astral's). It is said that these "Number" monsters cannot be destroyed with cards in this world. "Number" monsters can only be defeated by other "Number" monsters. However, when two or more "Numbers" confront themselves in a Duel they'll fight each other to consume one another. When a "Number" is defeated in a Duel by Yuma, Yuma obtains it, and its power is absorbed into Astral. Also when Yuma defeats a "Number" monster Astral gains another part of his memory.
Astral mentions there are 99 Numbers, but according to Kaito Tenjo, there are 100 Numbers. As Astral already had 1 of the Numbers, "Number 39: Utopia", it is possible Astral was referring to the other 99 Numbers.
However, there are also alternate Numbers from other universes. In some realities, these Numbers have replaced other Numbers from the original Duel Monsters universe. For example, in one alternate reality, Kotori, Yuma's love interest, gains Number 13: Paradise to help out Number 39: Utopia. Plus, some duelists are able to control normal Numbers as well without having the Number take them over, such as Chris Muir, who has Number T: Chrono Star Jiffy. Since these Numbers are from different universes, some Numbers in one reality will be completely different Numbers in others, allowing for different cards to have the same Number.
In the anime, "Numbers" have a few "special" abilities that are unique. "Numbers" can only be destroyed by other "Numbers". The "Numbers" amplify the darkness and desires of humans, whether these cause good or bad. When a "Number" is defeated, they are absorbed into Astral, and can be used by any duelist whom Astral is currently with. Each "Number" contains a piece of Astral's memory, which he recovers each time he absorbs one.
They are also known to manipulate their user into summoning them as soon as possible, sometimes to the point of cheating as seen with Rikuo and Kaio. Numbers also manipulate their users into protecting them at any cost, as seen when "Number 83: Galaxy Queen" made Fuya Okudaira believe that she was his mother. Thus, he equipped her with "Cursed Seal of Dead Max" to protect her from being destroyed by battle, and changed the attack target to his "D.D. Esper Star Sparrow" via "Star Robin is Forever!", causing him to lose the Duel. A person possessed by a "Number" easily becomes addicted to their power and desires to obtain more "Numbers". It is, however, possible for some people to resist this effect, at least temporarily, as Tetsuo Takeda managed to do when he used Number 39: Utopia to save Yuma from "Number 96: Black Mist".
Interestingly, whenever a "Number" is Xyz Summoned, they initially appear as a strange object, what is possibly a sealed form, until they transform into the actual monster and gain their Number on their bodies.
In the Numbershots, blank Numbers are capable of fusing with existing Xyz Monsters, transferring their Number, battle immunity, and any other abilities they may have to that monster, as seen when Zaman's "Temporal Future King" monster fused with a blank Number and became "Number 44: Temporal Future King". When a Number such as this is removed from its owner, the original Xyz Monster returns to normal, but the Number retains that monster's identity, becoming a second copy of that monster.
Furthermore, there are several different subsets of the Numbers, which will be described below.
The "Chaos Numbers" are a new set of Xyz Monsters. They seem to be upgrades of Numbers, but how and why is not yet certain. All that is known is that they can use the previous Number as an Xyz Material, along with the previous Number's materials, have special support monsters called "Zexal Weapons", and have rather powerful effects that can only be activated at certain times of the duel.
A breed of Chaos Numbers can also be created from certain "Rank-Up-Magic" cards, among them being "Chaos Over-Hundred Numbers" used by the Barians.
Outside of cards that are designed to Summon "CXyz" monsters and Chaos Numbers, Numbers that are affected by "Rank-Up-Magic" cards become very distant from their roots, tending to associate more with the origin of their Rank-Up Magic.
The "Verz Numbers" are only used by Yamoto in Taylor Gorrell's fanfiction universe. Through the use of his "Rank-Up-Magic Infestation Evolution" card, Yamoto can corrupt the Numbers he has into "Neoverz" monsters. Although the TCG term for the Verz Archetype is Evilswarm, Taylor Gorrell prefers to use Verz, so in the TCG, Verz Numbers are denoted as "Number V##" on English cards. All Verz Numbers are "Neoverz" monsters.
Notably, all Verz Numbers retain the Numbers' invincibility by battle with non-Numbers (or some variation of it) in the TCG/OCG.
The "Aero Numbers" are only used by Commander Cincinnatus Foster, formed through his "Rank-Up-Magic Cross Into The Blue" card. "Aero Numbers" are used alongside the "AXyz" cards due to their shared "Rank-Up-Magic", and like the "AXyz"s, the "Aero Numbers" are all WIND. These cards are noted as "Number A##" on their card names. Like the "AXyz" cards, "Aero Numbers" are generally rather futuristic and mechanical in appearance, and have the ability to fly. Plus, they possess light-blue lines on their bodies, as opposed to the red lines of Barian-based "CXyz" and "[Chaos Numbers".
The "Imperial Numbers" are primarily used by Naoki Saotome and are formed through the card. "Rank-Up-Magic Royal Fire Formation - Kogumaza". "Imperial Numbers" are used alongside the "IXyz" cards due to their shared "Rank-Up-Magic", and like the "IXyz"s, the "Imperial Numbers" are all FIRE and/or Beast-Warrior-Types. These cards are noted as "Number I##" on their card names. "Imperial Numbers" are generally clad in ornate golden armor resembling that of a Japanese samurai, just like the "IXyz"s, and possess a royal stature. They also possess glowing gold lines, to contrast with the red accents of the "CXyz" and "Chaos Numbers".
The "Toon Numbers" are primarily used by Theodor Crawford, formed through his "Rank-Up-Magic Cartoon Transformation". "Toon Numbers" are used alongside the "TXyz" cards due to their shared "Rank-Up-Magic", and like the "TXyz"s, the "Toon Numbers" are, as their name suggests, all Toon Monsters. These cards are noted as "Number T##" on their card names. Like the "TXyz" cards and Toon Monsters in general, "Toon Numbers" are very colourful, cartoonish and childish in appearance. There Overlay Units are pink-coloured and are called "Animated Overlay Units".
"Number T: Chrono Star Jiffy" is not part of this subtype.
Zombie Numbers, or ZNumbers, are Zombie counterparts for Number monsters. They share the same attribute, slightly altered ATK/DEF than its preceders and they are Zombies. They are used by an amorphous ghoul that duels Richard in Yu-Gi-Oh! Chaos Returns. They are ranked-up via "Rank-Up-Magic Zombie Force" . Also, there is a thread on pojo that allows pojo accounts to enhance this idea. []
Chaos Zombie Numbers
Chaos Zombie Numbers or CZNumbers are Zombie counterparts that evolved from Zombie Numbers when they were infused with Chaos. Since they are both Chaos Numbers and Zombie Numbers, you can use either Rank-Up cards that lets you summon Chaos Numbers, or You can use Rank-Up Magic Zombie Force to do so. The only known Chaos Zombie Number so far is Number CZ101: Silent Horror Dark Wight.
Knight Numbers, or KNumbers, are Warrior-Type counterparts for non-Warrior-Type Number monsters. They have knight-looking appearance, hence their Warrior as a type, plus they are ranked-up via "Rank-Up-Magic Knights' Force".
Twilight Numbers are Twilight counterparts to Chaos Numbers. They have a brighter color scheme (sometimes) compared to some other Rank-Up monsters. They are Ranked-up via "Rank-Up-MagicTwilight Force" cards. They are commonly given temporary immunity from card effects alongside their own very powerful effects.
Twilight Fall Numbers
Twilight Fall Numbers are Ranked-Down versions of Twilight Numbers. Like Twilight Numbers, they sometimes gain temporary immunity from effects. So far, the only Twilight Fall Number monster is "Number TF90: Constellation Primal Scorpion".
Cross Numbers (ＸＮｏ．(クロスナンバーズ) Kurosu Nanbāzu) are an upgraded style of Ranked-Up Numbers introduced in various fanfics. The Xyz analogue of Fusion Monsters, Cross Numbers are formed by merging two or three Number monsters together, forming a new Number whose Rank is the combination of the originals' Ranks and whose Number is the product of the originals' Numbers. One such Number is "Number X663: Utopia Rider," which combines the offensive abilities of "Number 17: Leviathan Dragon" and the defensive abilities of "Number 39: Utopia".
Jiffy's Cross Numbers
Adding to the mix are the Cross Numbers created by adding in "Number T: Chrono Star Jiffy", a curious little Xyz Monster that contains a power similar to "Elemental HERO Neos". Jiffy can easily combine with other Numbers to increase her own power, and her Cross Numbers have slightly different effects. Like a regular Cross Number, each effect needs a specific Number to be utilized in the Xyz Summon to activate, but if a specific Xyz Material is detached to pay for the effect, an additional effect is usually triggered.
Arcadia's Cross Numbers
Not unlike Jiffy, there is another Number with power similar to "Neos": "Number 100: Arcadia", a 101st Emperor's Key Number created between the energies of Number 39 and 13, taking the form of what could be seen as their child. Arcadia is capable of Rank-Crossing with other Numbers without the need of a "Rank-Cross-Magic" card, making him the original "Rank-Cross" monster. His Cross forms enhance his power with their powers, the other Numbers becoming armor of sorts and influencing his weapons. Unlike other Cross Numbers, whose Numbers are read in normal Japanese fashion, Arcadia's Cross Numbers are literally read as "## Hundred"(## Hyaku).
Cross Master's Cross Numbers
There are also the Cross Numbers created with the power of Number X0: Cross Master, an artificially created Number, created by the time-travelling Nova X, with the ability take over and Rank Cross with other Numbers into Cross Numbers. These Cross Numbers have enhanced versions of the original abilities, along with the ability to reincarnate themselves by returning to them Extra Deck and Summoning their counterparts from the grave. Cross Master also has a Chaos Number called "Number CX0: Cross Overlord Ultra," which gives up Cross Master's abilities for the power to banish Numbers to gain their strength.
The "Half Numbers" are a set of 100 Numbers that will appear in future fanfic of ZEXAL, identified by the ".5" that follows the number. In this yet unknown alternate reality of this fanfic, the original Numbers have split to form themselves and these Half Numbers, obtaining one shows bits and pieces of the memory it holds, while obtaining both the original and the half will show the whole memory. Some of them follow the same theme as their original half, i.e. Number 33: Chronomaly Machu Mech and Number 33.5: Chronomaly Pyramid Golem, and others take on their own form, i.e. Number 50: Blackship of Corn and Number 50.5: Patriot's Firestorm.
The United Numbers are a form of evolution used by Simon Notroson, Yuma, and a few of their friends in Rocket Knight 777's Zexal universe. They are created when two Numbers are overlayed together, or "fused", creating a form that seems to embody elements of both monsters. These cards have a "U" preceding the Number, like the Chaos Numbers, have a C preceding the Number. The Number itself is the sum of the two combined Numbers. The Numbers of the cards used in the unification appear in the relative spot they appeared on their original forms, or are placed in a spot appropriate to the new monster. More info to come.
True Numbers, or TNumbers, are a variation of United Numbers, where a Number and its corresponding Half Number are overlayed together, or "fused", to unlock their full and true power. More information coming soon.
The "Minus Numbers" (AKA Negative Numbers, "negative" effectively translates to "minus" in Japanese) are an alternate set of Numbers created by the Barians of the above-mentioned future of ZEXAL. They are denoted (both in English and Kanji) as having a negative number in both their names and artwork.Most Minus Numbers themselves are not actual cards, but they are formed from the card "Rank-Slide-Magic Minus Operation" by converting existing Xyz Monsters (except Numbers). The focus of the Minus Numbers is to gather the original Numbers, as Minus Operation successfully pulls 45 of them from Astral. Each Minus Number, pre-determined depending on the copy of Minus Operation held, is capable of locating the original with the same Number.Some Minus Numbers have no visual relation to the positive counterparts, while others have a much more visible link (Ex. Number 39: Utopia and Number -39: Purgatory).
Minus Cross Numbers do exist, able to be Rank-Crossed with positive Numbers. Minus Numbers cannot be Rank-Crossed with each other, however.
Notably, the Over-Hundred Numbers of the main ZEXAL canon are retconned to be Minus Numbers, having the same Number as in canon, but being Minus, to reflect the Legendary Numbers also being retconned to being positive Over-Hundred Numbers.
The Order Numbers are a counterpart of the Chaos Numbers. They are created through the power of Order harnessed by the Astral World denizens. More information to come.
Galaxy Numbers (Number G)
A variation of the normal Number C (Chaos Numbers). They are Summoned by "Rank-Up-Magic Galaxion Force".Most of these are Number monsters that originate from the Time World. They are tens to hundred times bigger than their normal size. Awakening these Numbers is similar to awakening Chaos Numbers, but a bit different. More information coming soon.
Finally, there are the "Lost Numbers", a very small group of Xynchro Monsters. All of them are "00", and they all have more specific requirements than "Multinetwork God Yotta Byte". However, they are very few and very far between, though their power is quite impressive. The only one known, "Lost Number 00: Biobeast Zonoid", is virtually unstoppable with an unnegatable negation ability.
In Trey Arclight's works, they were formed after Astral used the Numeron Code to rewrite the dimensional history. After all 100 "Numbers" were gathered, they were supposed to remain contained within the new Astral World, but an abnormality caused not only those cards, but blank cards filled with energy, to scatter across different dimensions. The Fusion Numbers were born when these blank cards absorbed the summoning energy of the Fusion Dimension. Since then, Academia has dedicated resources to gathering all 100 of these new Numbers, creating anti-Number Fusion Cards to hinder opponents who use them, and utilizing "Level-Up-Magic" cards to Chaosify the ones they have.
Creation Numbers are one of two types of numbers introduced in Yu-Gi-Oh! Celestial. They are versions of numbers used by the denizens and allies of Astral World. However, even though some Creation Numbers are similar to their non-Creation counterpart, (I.E. “Number 39: Utopia” and “NumberCR39: Utopia Lio”) some of them are different. (I.E. “Number 17: Leviathan Dragon” and “Number CR17: Infinite Legion”).
Void Numbers are one of two types of numbers introduced in Yu-Gi-Oh! Celestial. They are versions of numbers used by the antagonists, the Void Kings. Mostly, Void Numbers are extremely dark, and the often have lime green energy around their bodies.
"Normal Numbers" are some of the only "Numbers" that are not Xyz Monsters. As their name suggests, they are Normal Monster cards, and as such, they got no effect. While they have no card effects, they got a lot of support cards that supports Normal Monsters. They are the weakest type of "Number" monsters, as none of them can reach beyond 3000 ATK by themselves.
Chaos Normal Numbers
A different group of "N. Numbers" that evolved with the power of chaos. They level-up through Level-Up-Magic" cards, and unlike their base numbers, they are Fusion Monsters, with effects, similar to Transformation Summon. They were able to reach beyond 3000 ATK, but they were still weaker, as many of them were level 9, since most of the time, the highest level that a Normal Monster can be is level 8.