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.
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