James Anderson (computer Scientist) - Transreal Arithmetic

Transreal Arithmetic

Zero divided by zero
In mathematical analysis, the following limits can be found:

is also an indeterminate form. See exponentiation.
In IEEE floating-point arithmetic:
by definition

In several computer programming languages, including C's pow function, is defined to be, as that is the most convenient value for numerical analysis programs, since it makes (and many other functions) continuous at zero, with the notable exception of .
In transreal arithmetic:
by definition
by Anderson's proof, reported on by the BBC, that:

Anderson's transreal numbers were first mentioned in a 1997 publication, and made well-known on the Internet in 2006, but not accepted as useful by the mathematics community. These numbers are used in his concept of transreal arithmetic and the Perspex machine. According to Anderson, transreal numbers include all of the real numbers, plus three others: infinity, negative infinity and "nullity", a numerical representation of a non-number that lies outside of the affinely extended real number line. (Nullity, confusingly, has an existing mathematical meaning.)

Anderson intends the axioms of transreal arithmetic to complement the axioms of standard arithmetic; they are supposed to produce the same result as standard arithmetic for all calculations where standard arithmetic defines a result. In addition, they are intended to define a consistent numeric result for the calculations which are undefined in standard arithmetic, such as division by zero.

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