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\(\log 0 = \log \infty = 0\) and Applications

  • Hiroshi Michiwaki
  • Tsutomu Matuura
  • Saburou Saitoh
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 230)

Abstract

In this paper, we will show that \(\log 0 = \log \infty =0\) by the division by zero \(z/0=0\) and its fundamental applications. In particular, we will know that the division by zero is our elementary and fundamental mathematics.

Keywords

Division by zero \(1/0=0/0=0 \) \(\log 0 =0\) \(\log \infty =0\) \(0^0=1.0\) \({e^0= 1, 0}\) \(\cos 0 = 1, 0\) Y-field Point at infinity Infinity Green function Robin constant Capacity Riemann mapping function Laurent expansion 

Notes

Acknowledgements

The authors wish to express their deep thanks Professor Haydar Akca for his kind invitation of the papers [9, 10] based on recent results for the division by zero. Saitoh wishes to express his sincere thanks Professors James .A.D.W. Anderson, J. A. Bergstra, Lukasz T. Stepien and Dr. Masako Takagi for their valuable information and suggestions.

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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • Hiroshi Michiwaki
    • 1
  • Tsutomu Matuura
    • 2
  • Saburou Saitoh
    • 3
  1. 1.NejiLaw Inc.TokyoJapan
  2. 2.Gunma UniversityKiryuJapan
  3. 3.Institute of Reproducing KernelsKiryuJapan

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