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.
The Anti-Existence Theorem (Published)
An element of a set that possesses the property of anti-existence may be described by a negative integer.
Keywords: Annihilation, Anti-Existence, Coordinate System, Counting Function, Element, Intersection, Mirror Image, Partition, Set, Subtraction, Symmetry, Union., addition, natural numbers