Tag Archives: Zero

The Identity Crisis (Element) (Published)

Citation: James H. Hughes (2022) The Identity Crisis (Element), International Journal of Mathematics and Statistics Studies, Vol.10, No.1, pp.47-71

Abstract: To prove that addition and multiplication require different identity elements, this paper introduces the idea of a multiplicative union and the different symmetries and dimensions involved.

Keywords: Dimension., Symmetry, Zero, identity element, multiplicative union, set theory.

Division by Zero (Published)

There is an exception to the rule that division by zero is undefined or prohibited, which results in a well-defined number, and follows the rules of set theory and algebra.  This paper disproves the “proof by contradiction” by using a counterexample, an examination of its logic as a compound statement of two forms of statements that are not accepted as logically equivalent, an explanation of it as a sophism, and by examining some of its underlying assumptions. 

Keywords: Counting Function, Empty Set, Zero, division, set theory.