An Editor Recalls Some Hopeless Papers (1998)
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author = {Wilfrid Hodges},
title = {An Editor Recalls Some Hopeless Papers},
year = {1998}
}
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Abstract:
set theory' [12] as his source, and another refers to Barrow `Theories of everything' [2]. One contents himself with references to two earlier unpublished papers of his own. Others give no source. For definiteness let me write down a proof, not in Cantor's words, which contains all the points we shall need to comment on. (1) We claim first that for every map f from the set {1, 2, . . . } of positive integers to the open unit interval (0, 1) of the real numbers, there is some real number which is in (0, 1) but not in the image of f. (2) Assume that f is a map from the set of positive integers to (0, 1). (3) Write 0 . a n1 a n2 a n3 . . . for the decimal expansion of f(n), where each a ni is a numeral between 0 and 9. (Where it applies, we choose the expansion which is eventually 0, not that which is eventually 9.) (4) For each positive integer n, let b n be 5 if a nn #= 5, and 4 otherwise. (5) Let b be the real number whose decimal expansion is 0 . b 1 b 2 b 3 . . . . (6...
