Open Access
Subscription Access
Open Access
Subscription Access
Counting of Numbers
Subscribe/Renew Journal
‘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.
Keywords
Natural numbers, Transfinite numbers, Order of irrational numbers, Degree of infinity
User
Subscription
Login to verify subscription
Font Size
Information
- 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.
Abstract Views: 124
PDF Views: 0