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Inequalities and equalities of means in Constructive Mathematics

  • Teruma Kawakubo
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Abstract

We study the inequalities and equalities of means of numbers in constructive mathematics. The parameters of such means are constructive real numbers. We show that it is impossible to have an algorithm that can always decide whether the two means are equal or not. Of course, this problem can always be solved if the parameters are rational numbers.

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Cite

BibTeXRIS
BibTeX
@misc{kawakubo2026inequalities,
  title = {{Inequalities and equalities of means in Constructive Mathematics}},
  author = {Teruma Kawakubo},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.10593},
  eprint = {2609.10593},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.10593},
}
RIS
TY  - UNPB
TI  - Inequalities and equalities of means in Constructive Mathematics
AU  - Teruma Kawakubo
PY  - 2026
DA  - 2026/09/06
PB  - arXiv
DO  - 10.48550/arxiv.2609.10593
UR  - https://arxiv.org/abs/2609.10593
AB  - We study the inequalities and equalities of means of numbers in constructive mathematics. The parameters of such means are constructive real numbers. We show that it is impossible to have an algorithm that can always decide whether the two means are equal or not. Of course, this problem can always be solved if the parameters are rational numbers.
ER  -