Mathematics and Applied Mathematics
June 1, 2020
Division by zero, Real numbers, Rational numbers, Ratio, Fraction, Fixing mathematics
This paper solves the problem of division by zero. Starting with a deep analysis of multiplication and division, it is presented that they are one in the same, as an operation. Together with the operation of selection, they are different forms of the transformation operation, that changes one pair of numbers into another pair of numbers. It is presented that the numbers are always in reference to some other numbers. Therefore, the only correct form of the number, is when it is a ratio between the certain value and the base measure, which this value is related to. It is clearly proven that the problem of division by zero is the result of unauthorized simplification, which was done by bringing all the rational numbers (which are represented by the ratio of the value to the measure) to the fractions, with a denominator of 1. This paper shows why we should not make fractions with different numerators and denominators equal, even so they seem to be in the same proportion. Finally, there are two graphs with the functions presented 1/x and tg(x) with their discontinuity points, which are visible only on the real numbers graph. This result is from projecting points of the rational numbers graph onto the real numbers graph with a denominator of 1. These discontinuity points disappear when we present our graphs in rational numbers. This paper fixes one of the foundations of mathematics and shows us how to divide by zero.../...