Counting of Numbers

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Authors

  • Nirendra Mohan Ganguli
     Suryatoran, Flat No. 2B, 234A, N. S. C. Bose Road, Kolkata 700040 ,IN

DOI:

https://doi.org/10.24906/isc/2023/v37/i1/222818

Keywords:

Natural numbers, Transfinite numbers, Order of irrational numbers, Degree of infinity

Abstract

‘χ0’ and ‘c’, termed as transfinite numbers, signify the number of elements in the infinite set of positive integers and that of real numbers respectively. Cantor proved that c > χ0 using the diagonal argument; but the infinitude of ‘c’ is on two counts i.e. magnitude and type of the element while that of χ0 is on single count i.e. magnitude. ‘c’ is not numerically greater than ‘χ0’, but denotes a higher degree of infinity. Hence the continuum hypothesis is rather irrelevant.

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Published

2023-08-09

How to Cite

Ganguli, N. M. (2023). Counting of Numbers. Indian Science Cruiser, 37(1), 33–38. https://doi.org/10.24906/isc/2023/v37/i1/222818

Issue

Vol 37, No 1 (2023)

Section

Search & Survey
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References

S Hawking, God Created the Integers, Penguin Books, UK, 2006.

W C Salmon, Zeno’s Paradoxes, 2nd Edition, Indianapolis: Hackett Publishing Co. Inc., 2001.

G F Simmons, Introduction to Topology and Modern Analysis, Tata McGrew-Hill, 2004.

R Courant, H Robbins and I Stewart, What is Mathematics? An Elementary Approach to Ideas and Methods, 1996, 2nd Edition, New York/Oxford: Oxford University Press.

N M Ganguli, Classification of Irrational Numbers, Indian Science Cruiser, Vol 33, No 1, page 57-62, 2019, Institute of Science, Education and Culture, Kolkata.