What is the theory for a number divided by zero?

The theory is simple: the answer for dividing by zero is NaN, "not a number". Zero cannot divide into any number, including itself. Conceptually, there is no correct finite answer because you can always take away more zeros from the numerator.To get this answer in mathematical terms, we instead look at what is called a limit as a function approaches a point that is NaN.

For example, take the function f(x)=1/(x^2). This function has no value at x=0. However, if we look at the value of the function at x values very, very, very (actually, infinitely) close to x=0, we can see a trend and use that to understand what happens at x=0.

In the case of 1/(x^2) the function approaches infinity at very small negative and very small positive values, so we conclude that the limit as x approaches 0 of 1/(x^2) is infinite, even though the function has no value at x=0 The above applies to many, but not all, algebraic structures. Specifically, because it models the world we live in, it's true for fields The axioms of a field require that any number multiplied by zero is equal to zero and that any number multiplied by its inverse is equal to one. Therefore, 0*0 1 equals both 1 and 0 according to these rules which is a contradiction, therefore making division by zero in general undefinable.

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