*"Wait, what are you going to do? Divide me by zero?"*- ― Gumball, The Amazing World of Gumball

*"You can't divide tape with tape! You created a paradox."**"No, you did!*"- ― Cyborg and Robin (DC Nation)

The power to **divide by zero i.e. blend affected entities, collapse multiple entities into one or generate uncertainty**. Sub-power of Mathematics Manipulation, Pseudomathematics Manipulation and Logic Manipulation. Can be interpreted as a generalized, more complicated version of Transmutation and Amalgamation.

## Contents

## Also Called

- N/0
- Divided by Zero
- Zero Divider

## Capabilities

The user is able to utilize the effects of division by zero, which has the property of collapsing the affected entity in question. *In a nutshell. It's most widely used effect is to blend things, irreversibly unless a more powerful power reverses it afterwards.*

This power generally needs two entities. Let's take fire and water for example:

- Blending: The order matters (A/0)B =/= A(/0B)

Divide fire by zero with water will result in outcomes like fire that is cold to the touch, you can swim in it, or you can put out fires by tossing something burning into the fire.

Divide water by zero with fire will result in outcomes like you can light up a campfire by splashing water into a pile of wood.

- Sphere of nihilation: When the two entities are both nothingness or nonexistence 0/0 = Erase

Projects an all absorbing energy sphere as a projectile or an expanding energy field. The sphere is capable of eliminate anything in its path (save for objects with at least Nigh Omnipotent natures) by simply deleting them from existence. The sphere usually dissipates after a few seconds or longer if the user master this power.

- Scrambing: When there is only one entity A/0 = Scramble

The power will scramble the physical and metaphysical identity of the entity. Using on computer information or human (or similar) memory, the information will become unreadable gibberish. Using on physical objects such as fire, the object become a physical version of a wildcard, allow it to interact with other things with many properties all at once (e.g. can dissolve salt, can burn trees, can be molded etc.).

Perhaps most importantly, using it on the location of anything will result in irreversible Nigh Omnipresence of said thing. This scrambling ability can be used to rapidly spread something over a vast region in the blink of an eye, such as a virus or a wildfire.

- Eliminate duplicates: When there are duplicates and evasions (AAAAAA...)/0 = A

The power erases all notion of duplicates and erases all evasion countermeasures, making it very effective at fighting clones and mirages. Teleportation, dimensional shifting, time travel, initiation of any lock powers such as omnilock etc. are examples of things that can be affected. If the user is already "locked", then the power has no effect due to the properties of the lock powers.

- Null infusion (A/0)(B/0)(C/0)... = 0

The power also has the powerful property of imbuing a "null" property to its targets, such that when two or more null infused targets interact with each other, they will be erased from existence. Therefore users who teamed up in battle with another user who can arbitrary set the targets to be opposites to each other can quickly eradicate a large army in the blink of an eye.

- Interaction with nothingness and nonexistence based powers A0+A=A0, 0A+0B=0AB, 0/0+A=0/0

When erasure based powers collide with division by zero, the erasure powers usually loses its erasing ability, instead, they do weird things such as entities being impacted by erasure powers (the "erased" ones) will fuse together or being absorbed by another, while still retains the property of being "erased". Two similar entities, one being "erased" and one does not, the "erased" one will consume the unerased one. When a nigh omnipotent power or otherwise removed the division by zero, the "erased" ones will be erased from existence as erasure powers regain their ability to erase entities.

- Dividing itself by zero /0/0=/0/0

Dividing division by zero, or entities being infused with division by zero, does not do anything

## In English

Divide fire by zero with water will result in outcomes like fire that is cold to the touch, you can swim in it, or you can put out fires by tossing something burning into the fire.

Divide water by zero with fire will result in outcomes like you can light up a campfire by splashing water into a pile of wood.

Divide nothingness or noexistence by zero generate an expanding sphere that erase things

Divide information and memory by zero will scramble it into gibberish

Divide physical objects by zero alone will scramble their physics

Divide location by zero results in Nigh Omnipresence

Divide duplicates and evasive strategies by zero will erase them

Two entities being divided by zero can be inbued with null, and any null infused entities interacting with each other will be erased from existence

Division by zero has amalgamating effect to the act of erasure itself, result in targets to be frozen in the state of "being erased", allowing them to fuse and split in various impossible ways. Once the division by zero is reversed, said entities will then be erased from existence.

## Definition

The power basically utilize the metaphorical effects when one tries to introduce division by zero into number system and suggested by the memes of the same name in order to achieve its purpose.

**Click here to skip this section if you are not interested in maths. This basically just provide the background on what this power is based on.**

Division is the inverse of multiplication. For the case of zero in most algebraic structures, most axioms result in a theorem that 0 × n = 0 for any number n in the number system, there is no unique number D such that D × 0 = n. Thus division by zero is undefined.

In a sense division by zero is the most pathological example of a relation, where a single element is mapped to all elements in a mathematical space. (This inspires the scrambling ability, the duplication delete ability)

In the complex projective plane, division by zero is possible and this will equal to unsigned infinity. However 0/0 is still undefined. (This property is not included in the power anymore to keep it simple and not to confuse anymore future readers)

0/0 can be defined in a structure known as a wheel, by abandoning the notion that / is a binary operation (i.e. requires two inputs and output one result) but treated as a unitary operation such that /a.b=a./b. The result is that in general 0x ≠ 0, x - x ≠ 0 and terms with 0 will linger behind and can be group together e.g. 0x + 0y = 0xy. 0/0 however will turn any expressions that contains it into itself. (Inspires its interaction with erasure based powers)

Division by zero in the real number system is only possible if you relax one of its axioms (with some hints suggesting that associativity has to break, that's where the order matters idea is inspired from) else you end up having all numbers equal to each other, thus collapsing the entire real number line into just a single entity (Usually quoted as the trivial ring which means it is a set [r] such that r × r = r and r + r = r, a very boring mathematical structure. (This is the origin of the black hole meme which is also inspired from the faux proof that 2=1 which breaks logic, thus division by zero exists in both mathematics and pseudomathematics disciplines)

Suppose some axioms of the real numbers were relaxed, terms of the form 0x can do interesting stuff as they are no longer zero. For example 0x+x=0x

**Definition ends here.**

## Applications

- Black Hole Creation (Most common side effect for unskilled users)
- Amalgamation (Main application, more general, not just limited to physical entities, and its scale is always the entire reality. This is limited to avoid conflicting with Omnipotent beings).
- Nonexistence (As a projectile or energy field that removes anything upon contact)
- Nigh Omnipresence (Whenever the location of the entity is divided by zero)
- Nothingness Manipulation (Affected target gained a property that can allow them to be erased from existence once a certain condition is met)
- Anything else limited by imagination

## Associations

## Limitations

- Tend to blend entities, thus effects is usually one-sided. Can be destructive as other powers are often required to reverse the operation.
- Unskilled user will often found a black hole is left in its wake.
- Requires an extensive understand of the concepts involved in the blending to decided accurately what to blend, as due to the ambiguous nature of concepts, many unintended side effects can occur when the blending is brought out carelessly (e.g. "damage suffered" divided by zero with "healing himself", a person will be impervious to all kinds of damage, this include beneficial things such as blood transfusion (unless it can be done without a needle)
- Although extremely capable, it cannot match the power of Omnipotence or Nigh Omnipotence
- Entities who form the sole example of a given category are immune to collapse with regard to that category; If the entity is a duplicate in another category, it can be resistant to this power depending on the Verse requirements
- The scrambling ability of this power on physical target (instead of just one aspect of it such as its location) will make the target susceptible to Uncertainty Manipulation, since its original identity or nature has been lost and can be anything possible, including its original self, thus uncertain.

## Known Users

- Anne Poole (
*Fine Structure*) - Thoma Avenir (
*Magical Record Lyrical Nanoha Force*) - 01 - The Magician (
*Pharos of the End*) - SCP-2599 - Not Good Enough (
*SCP Foundation*)

## Known Objects

- Null Driver (
*Iji*)