Beyond Infinity

Eli Maor
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Eli Maor: Oakland University, Department of Mathematical Sciences

Chapter 10 in To Infinity and Beyond, 1987, pp 60-65 from Springer

Abstract: Abstract To show that the real numbers cannot be counted, Cantor first established a fact which, if anything, seems to be almost beyond belief: There are as many points along an infinite straight line as there are on a finite segment of it. The proof, shown in Fig. 10.1, is so simple that one wonders why no one before him had made the discovery. It shows that our conception of a line as being made up of many dots of ink is fundamentally wrong: the physical dot and the mathematical point have absolutely nothing in common!

Keywords: Number Line; Irrational Number; Continuum Hypothesis; Finite Segment; Actual Infinite (search for similar items in EconPapers)
Date: 1987
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DOI: 10.1007/978-1-4612-5394-5_10

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