An Alternative Proof that the Real Numbers are Uncountable
Keywords:
real numbers, uncountabilityAbstract
Many students as well as educators find it difficult to accept Cantor’s Diagonalization argument that the real numbers are uncountable. In this paper, we provide an alternative proof that may be easier for students to accept. The proof could provide further insight into the reason that the real numbers are uncountable. That is, any statement that leads to anything being possible includes the fact that the statement is impossible.
References
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Cantor, G., Ueber eine elementare Frage der Mannigfaltigkeitslehre, Jahresbericht der Deutschen Mathematiker-Vereinigung (1891). 75–78.
Courant, R., Robbins, H., & Stewart, I. (1996). What Is Mathematics? : An Elementary Approach to Ideas and Methods. Oxford: Oxford University Press. 68.
Gascón, J. (2015) Another Proof That the Real Numbers R Are Uncountable, American Mathematical Monthly, 122(6), 596–597, DOI: 10.4169/amer.math.monthly.122.6.596.
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Weisstein, E. W. Russell’s Antimony. MathWorld [Website]. https://mathworld.wolfram.com/RussellsAntinomy.html
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