Document Type

Article

Author ORCID Identifier

Vladimir Kulyukin https://orcid.org/0000-0002-8778-5175

Journal/Book Title/Conference

Mathematics

Volume

12

Issue

18

Publisher

MDPI AG

Publication Date

9-15-2024

Journal Article Version

Version of Record

First Page

1

Last Page

17

Creative Commons License

Creative Commons Attribution 4.0 License
This work is licensed under a Creative Commons Attribution 4.0 License.

Abstract

Signifiable computability aims to separate what is theoretically computable from what is computable through performable processes on computers with finite amounts of memory. Real numbers and sequences thereof, data types, and instances are treated as finite texts, and memory limitations are made explicit through a requirement that the texts be stored in the available memory on the devices that manipulate them. In Part I of our investigation, we define the concepts of signification and reference of real numbers. We extend signification to number tuples, data types, and data instances and show that data structures representable as tuples of discretely finite numbers are signifiable. From the signification of real tuples, we proceed to the constructive signification of multidimensional matrices and show that any data structure representable as a multidimensional matrix of discretely finite numbers is signifiable.

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