Elementary hyperrational analysis includes defining and evaluating such notions as continuity, differentiability and integral calculus.
Yuri N. Lovyagin, Nikita Y. Lovyagin 2019, 'The Monotonic Sequence Theorem and Measurement of Lengths and Areas in Axiomatic Non-StandardHyperrational Analysis', Axiomshttps://www.mdpi.com/2075-1680/8/2/42. Retrieved from DOAJ CC BY 4.0 (https://creativecommons.org/licenses/by-sa/4.0/legalcode)
Also, we solve the task of line segment measurement using hyperrational numbers.
Yuri N. Lovyagin, Nikita Y. Lovyagin 2019, 'The Monotonic Sequence Theorem and Measurement of Lengths and Areas in Axiomatic Non-StandardHyperrational Analysis', Axiomshttps://www.mdpi.com/2075-1680/8/2/42. Retrieved from DOAJ CC BY 4.0 (https://creativecommons.org/licenses/by-sa/4.0/legalcode)
In the axiomatic theory of non-standard arithmetic, hyperrational numbers are defined as triplets of hypernatural numbers.
Yuri N. Lovyagin, Nikita Y. Lovyagin 2019, 'The Monotonic Sequence Theorem and Measurement of Lengths and Areas in Axiomatic Non-StandardHyperrational Analysis', Axiomshttps://www.mdpi.com/2075-1680/8/2/42. Retrieved from DOAJ CC BY 4.0 (https://creativecommons.org/licenses/by-sa/4.0/legalcode)