In this paper, there are 5 sections of tables represented by 5 linear sequence functions. There are two one-variable sequence functions that they are able to represent all prime numbers. The first one helps the last o...In this paper, there are 5 sections of tables represented by 5 linear sequence functions. There are two one-variable sequence functions that they are able to represent all prime numbers. The first one helps the last one to produce another three two-variable linear sequence functions. With the help of these three two-variable sequence functions, the last one, one-variable sequence function, is able to set apart all prime numbers from composite numbers. The formula shows that there are infinitely many prime numbers by applying limit to infinity. The three two-variable sequence functions help us to find the factor of all composite numbers.展开更多
New operators are presented to introduce “arithmetic calculus”, where 1) the operators are just obvious mathematical facts, and 2) arithmetic calculus refers to summing and subtracting operations without solving equ...New operators are presented to introduce “arithmetic calculus”, where 1) the operators are just obvious mathematical facts, and 2) arithmetic calculus refers to summing and subtracting operations without solving equations. The sole aim of this paper is to make a case for arithmetic calculus, which is lurking in conventional mathematics and science but has no identity of its own. The underlying thinking is: 1) to shift the focus from the whole sequence to any of its single elements;and 2) to factorise each element to building blocks and rules. One outcome of this emerging calculus is to understand the interconnectivity in a family of sequences, without which they are seen as discrete entities with no interconnectivity. Arithmetic calculus is a step closer towards deriving a “Tree of Numbers” reminiscent of the Tree of Life. Another windfall outcome is to show that the deconvolution problem is explicitly well-posed but at the same time implicitly ill-conditioned;and this challenges a misconception that this problem is ill-posed. If the thinking in this paper is not new, this paper forges it through a mathematical spin by presenting new terms, definitions, notations and operators. The return for these out of the blue new aspects is far reaching.展开更多
文摘In this paper, there are 5 sections of tables represented by 5 linear sequence functions. There are two one-variable sequence functions that they are able to represent all prime numbers. The first one helps the last one to produce another three two-variable linear sequence functions. With the help of these three two-variable sequence functions, the last one, one-variable sequence function, is able to set apart all prime numbers from composite numbers. The formula shows that there are infinitely many prime numbers by applying limit to infinity. The three two-variable sequence functions help us to find the factor of all composite numbers.
文摘New operators are presented to introduce “arithmetic calculus”, where 1) the operators are just obvious mathematical facts, and 2) arithmetic calculus refers to summing and subtracting operations without solving equations. The sole aim of this paper is to make a case for arithmetic calculus, which is lurking in conventional mathematics and science but has no identity of its own. The underlying thinking is: 1) to shift the focus from the whole sequence to any of its single elements;and 2) to factorise each element to building blocks and rules. One outcome of this emerging calculus is to understand the interconnectivity in a family of sequences, without which they are seen as discrete entities with no interconnectivity. Arithmetic calculus is a step closer towards deriving a “Tree of Numbers” reminiscent of the Tree of Life. Another windfall outcome is to show that the deconvolution problem is explicitly well-posed but at the same time implicitly ill-conditioned;and this challenges a misconception that this problem is ill-posed. If the thinking in this paper is not new, this paper forges it through a mathematical spin by presenting new terms, definitions, notations and operators. The return for these out of the blue new aspects is far reaching.
