The chief object of this work is to create an exact and consistent arithmetic of zero, denoted 0, and infinity (zero divisor), written as 1/0 and denoted ∞  , based on the conventional division by zero $$ \dfrac{{0}}{{0}}=1. $$ Manifold and undeniable applications of this arithmetic are given in this work in order to show its usefulness.

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This article is concerned mainly with Bhaskara's arithmetic operation of division by zero. This is the simplest of all for teaching analysis and is the most consistent and philosophical. Some mathematicians have attempted to impugn it, but when I examined their reasonings, I observed that they have done so because they have failed to comprehend the true behavior of zero. In this article I have aimed to clarify and justify Bhaskara's law of impending operations involving zero and furnish hints at the foundations upon which the arithmetic operation of division by zero rests its claims to be preferred to its fashionable rivals, the methods of innitesimals and limits.

The ultimate goal of this work is to provide in a concise manner old and new results relating to the simplicial polytopic numbers.

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