Division by Zero

''[http://powerlisting.wikia.com/wiki/User_blog:Thekingsman/Do_not_like_non-cannon_powers. Note] : This power is not specifically stated by official works or accredited from characters appearing in official/professional works of fiction. Any information given is speculated and may not hold any credibility.''

The power to divide by zero ie. make affected entities equivalent and collapse multiple entities into one. Sub-power of Mathematics Manipulation and Logic Manipulation. Can be interpreted as a generalised, more complicated version of Transmutation.

Also Called

 * N/0
 * Divided by Zero
 * Zero Divider

Capabilities
The user is able to utilize the effects of division by zero, which has an apparent property of collapsing the affected system in question. ''In a nutshell. It's most widely used effect is to turn many things into just one, irreversibly unless a more powerful power reverse it afterwards.''

Basically the major effect of this power is it can equalize entities and/or collapse them into one, so by making A=B users can achieve feats impossible using A and B together as distinct entities.

One typical way to use it is say you want to apply it on A (e.g. a tree), you then use this power via B (e.g. water). After that A=B (Tree and water now become one and the same) with A having the properties of B (e.g. there is no such thing as tree, there's only water.)

What you use to execute this power is important. Using water to divide tree by zero is not the same as using a tree to divide water by zero, because what you use to divide the target by zero will determine what the target will become or take traits on.

The user can also project an all absorbing energy sphere as a projectile or a expanding energy shield by performing a division by zero of nothingness against nothingness. 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. There sphere usually dissipates after a few seconds or longer if the user master this power.

Description of a few applications
Due to its collapsing property, it can be used to make two entities/concepts equivalent. For example, make fire and water equivalent so they inflict the same effects, or Space-Time Manipulation by making space and time equivalent so that you can freely travel in time and/or make others forced to travel in a certain direction in space.

For example, division by zero can create black holes since black holes warp space-time to such an extent that the law of physics as we know it collapses at the center of it.

A more concrete example is say you have a base and you defend it using a steel wall. Now a user of this power will divide the wall by zero using a wooden stick. What happens is that your steel wall will become a pile of sticks and any future steel walls you built will become sticks. Thus you lost your protection. In this case we make steel wall=wooden stick by dividing the steel wall by zero using a wooden stick.

Another application which also make use of this "collapse the system" property is say you are a evil and fire user trying to fight a good water user. Given in the universe where this battle takes place has a rule such that water wins over fire. In order to turn the tables, you divide the concept "opposites" by zero. The outcome of this is that the many different types of opposites (polar, elemental, moral etc.) all collapsed into one type decided by the user, say moral. Now the law of this universe is circumverted and you will be unharmed by the water attacks since the elemental opposite aspect of it is removed, leaving only the moral aspect which depends on the moral alighment of the water user, which is good. Thus you now effectly end up only with evil vs good, which is not specified by the rules of this universe thus the outcome that you win becomes possible.

Another even direct example is based on the pricinple of the previous example. Say you are fighting against a user who has the ability to be in many places at once, or make a lot of clones. By dividing by zero you force all copies to be gone regardless of the nature of the duplication (unless because of plot reasons or the user is at least Nigh Omnipotent). This is actually very powerful because you can effectively undo all teleportation or dimensional travel ability of the opponent (e.g. time travel, dimensional shifting, the ability to initiate a chronolock or omnilock etc. NB If the user is already omnilocked, then it does not owrk because of the properties of omnilock), provided that the opponent is less powerful than you and the story would not be affected resulting in plot control.

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.

(Please skip this section if you are not interested in maths, despite it has been laymennized to be easy to understand. This basically just provide the background on what this power is based on)

Division is the inverse of multiplication, that is if e.g. AXB=C then A=C/B where C/B is a unique number (Let's call it D for simplicity) such that DXB=C. For the case of zero in most number systems (reals, complex etc.) because of the axioms, or rules that build them result in a property that 0xn=0 for any number n in the number system, there is no unique number D such that Dx0=n (In the case of 0/0 theoretically all numbers will satisfy it's requirement since it basically means it is a number D such that Dx0=0 thus it is indeterminate and tells no useful information, hence it is undefined). Thus division by zero is undefined.

In more exotic number system such as the complex projective plane (Think the complex plane as a 2D sheet of paper. You then roll it up into a sphere and glue it at a point known as infinity) division by zero is possible and this will equal to infinity (note this infinity has no signs because -infinity and infinity are equivalent in this number system). However 0/0 is still undefined.

0/0 can be defined using a weird mathematic 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 uniary operation such that /a.b=b./b. The result is that 0/0+x=0/0 for any x and in general 0x=/=0. More info here.

Division by zero in the real number system is only possible if you relax one of its axioms such that 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 rxr=r and r+r=r, a very boring mathematical structure. (Skip ends here)

Applications

 * Black Hole Creation
 * Infinite Supply (If used on anything located on any spherical surface)
 * Space-Time Manipulation
 * Transmutation (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).

Associations

 * Logic Manipulation
 * Mathematics Manipulation
 * Nonexistence

Limitations

 * Tend to collapse entities, thus effects is usually one-sided. Can be destructive as other powers are required to reverse the operation.
 * Unskilled user will often found a black hole is left in its wake.
 * Although extremely capable, it cannot match the power of Omnipotence or Nigh Omnipotence