On infinity and the infinitesimal

Author information

Author: Charles Ewan Milner

Author email address: charles.milner@outlook.com

Author ORCID iD link: https://orcid.org/0009-0001-5580-1345

Abstract

This paper explores true, logical meanings meanings in mathematics of infinity and the infinitesimal.

Main Paper

Infinity ( $\infty$ ) is the concept of an endlessly large value while the infinitesimal is the concept of an infinitely small value greater than zero. While these ideas are difficult to deal with mathematically and are commonly misunderstood, they do have reasonable meanings and can somewhat be used mathematically.

There are multiple numbers which are infinitely large and which are infinities. They can be described by using set theory or with other methods.

There are multiple infinitesimals which can always be mathematically expressed as ${\frac {p}{\infty }}$ , where $p$ is any finite, positive number, or which can be described by using set theory or with other methods.

The true meanings of infinity and the infinitesimal in logic and mathematics are covered with these facts.

Additional information

Acknowledgements

This paper was authored by Charles Ewan Milner.

Competing interests

There are no competing interests relating to this paper held by its authors.