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Counting of Numbers
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‘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
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