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.
Beginning Arithmetic Proposition: The Arithmetic Operator Requires Three Elements (Published)
For those not fully satisfied with abstract algebra’s presentation of group and ring theory, the proposition that the arithmetic operator requires three elements is offered as a part of a new approach to algebra.
Keywords: addition, arithmetic, division, elements, identity element, multiplication, operator, set theory.