Abstract
The division by zero has been a challenge over years, which is in two forms: one involves a non-zero numerator while the other involves a zero numerator. This work deals with the second form of division, with the aim of finding a solution to the equation obtained when the expression is equated to, say x, where x is not a quantity but the ‘number of times of one whole’. In this work, zero divided by itself has been exhausted using different approaches and methods to come to a conclusion; that this division has a unique solution, 1. Some of the methods employed include geometric series, logarithm, indices, reciprocals, factorials, self-operations, Euler’s number, binomial expansions, graphical method among others. The conclusion has been made that zero divided by zero is 1. The reverse of division by multiplication is not applicable because zero has been associated with two ‘abnormal’ properties or behaviour that’s not with other numbers.
Highlights
This work is an attempt to solve the division of zero by itself (0 / 0)
It is an attempt to prove that there is a unique solution to the equation 0/ 0 = x
The research done so far shows that previous attempts and mathematicians have concluded the solution as all numbers/any real number: 0, 1, 3
Summary
This work is an attempt to solve the division of zero by itself (0 / 0). It is an attempt to prove that there is a unique solution to the equation 0/ 0 = x. The work has used different approaches to find what x could be (the number of times of one whole that zero can go into itself x isn’t a quantity). One of the things that should be known and must be accepted is that zero has unique properties and this makes it not follow the already laid procedures and rules in fields and rings in totality. There are exceptions and zero is one of them. This does not qualify it to be an exception in all cases
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