### AIMS Mathematics

2021, Issue 4: 4011-4024. doi: 10.3934/math.2021238
Research article

# Numerical computations for Operator axioms

• Received: 24 October 2020 Accepted: 27 January 2021 Published: 04 February 2021
• MSC : 11Y16, 65H05, 49M25, 11B85, 03D05

• The Operator axioms have produced new real numbers with new operators. New operators naturally produce new equations and thus extend the traditional mathematical models which are selected to describe various scientific rules. So new operators help to describe complex scientific rules which are difficult described by traditional equations and have an enormous application potential. As to the equations including new operators, engineering computation often need the approximate solutions reflecting an intuitive order relation and equivalence relation. However, the order relation and equivalence relation of real numbers are not as intuitive as those of base-b expansions. Thus, this paper introduces numerical computations to approximate all real numbers with base-b expansions.

Citation: Pith Peishu Xie. Numerical computations for Operator axioms[J]. AIMS Mathematics, 2021, 6(4): 4011-4024. doi: 10.3934/math.2021238

### Related Papers:

• The Operator axioms have produced new real numbers with new operators. New operators naturally produce new equations and thus extend the traditional mathematical models which are selected to describe various scientific rules. So new operators help to describe complex scientific rules which are difficult described by traditional equations and have an enormous application potential. As to the equations including new operators, engineering computation often need the approximate solutions reflecting an intuitive order relation and equivalence relation. However, the order relation and equivalence relation of real numbers are not as intuitive as those of base-b expansions. Thus, this paper introduces numerical computations to approximate all real numbers with base-b expansions.

 [1] P. Xie, A logical calculus to intuitively and logically denote number systems, Prog. Appl. Math., 1 (2011), 43-70. [2] P. Xie, Number systems based on logical calculus, Int. Math. Forum, 8 (2013), 1663-1689. doi: 10.12988/imf.2013.39167 [3] P. Xie, Improvement on operator axioms and fundamental operator functions, Int. J. Math. Appl., 5 (2017), 125-151. [4] C. A. Shaffer, Data structures and algorithm analysis in C++, Third Edition, Dover Publications, 2011. [5] B. Parhami, Computer arithmetic: algorithms and Hardware designs, Oxford University Press, 2000. [6] S. C. Chapra, R. P. Canale, Numerical methods for engineers, Sixth Edition, McGraw-Hill Companies, Inc., 2009.
• © 2021 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
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沈阳化工大学材料科学与工程学院 沈阳 110142

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