Algebra

   

Lattice Rationals

Authors: Nathaniel S. K. Hellerstein

This paper redefines the addition of rational numbers, in a way that allows division by zero. This requires defining a "compensator" on the integers, plus extending least-common-multiple (LCM) to zero and negative numbers. "Compensated addition" defines ordinary addition on all ratios, including the 'infinities' n/0, and also 'zeroids' 0/n. The infinities and the zeroids form two 'double ringlets'. The lattice rationals modulo the zeroids yields the infinities plus the 'wheel numbers'. Due to the presence of the 'alternator' @ = 0/-1, double-distribution does not apply, but triple-distribution still does.

Comments: 17 pages

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Submission history

[v1] 14 Nov 2010

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