Corpus ID: 204931378

The Axiomatic Construction Of A New Algebraic Structure In Order To Extend A Field And Define Division By Zero

@inproceedings{Santangelo2016TheAC,
  title={The Axiomatic Construction Of A New Algebraic Structure In Order To Extend A Field And Define Division By Zero},
  author={B. Santangelo},
  year={2016}
}
In order to define the operation of Division By Zero, a new algebraic structure will be created as an extension to a Field in such a way that for every non-zero $x$ which is an element of a Field, the equation $0\cdot s=x$ will have exactly one, unique solution. However, the equation $0\cdot s=0$ will have two or more possible solutions with no preference towards any one particular solution, making $s$ indeterminate. This will allow us to uniquely define $x$ divided by $0$ for any $x$ which is… Expand
Division by Zero : A Survey of Options
TLDR
A survey of some options for defining an outcome for the application of division in case the second argument equals zero is provided. Expand