Gilreath, William Fletcher
Mathematics and Applied Mathematics
March 26, 2018
absolute value, absolute value function, cogent function, cogent value function, ceiling function, continuous function, derivative, derivative of function, differentiability, differential of function, greatest integer function, floor function
The absolute value function is a fundamental mathematical concept taught in elementary algebra. In differential calculus, the absolute value function has certain well-known mathematical properties that are often used to illustrate such concepts of—a continuous function, differentiability or the existence of a derivative, the limit, and etcetera.
An alternative to the classical definition of absolute value is given to define a new function that is mathematically equivalent to the absolute value, yet the different mathematically. This new mathematical formalism, the cogent value function, does not have the same mathematical properties of the absolute value function. Two other new mathematical functions are used in the definition of the cogent value function—the parabolin function, and the magnum function.
The cogent value function and the absolute value function have the same domain and range, but both are mathematically very different. The cogent value function demonstrates that the same mathematical concept when formally defined by an alternative method has different mathematical properties. The functions by operation are mathematically similar, but in mathematical formalism each is unique.