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Well Ordering the Real Numbers
2005 Dec 06
... Cantor was wrong
...
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"When one considers how to enumerate the points on the real number line, such that one can name a first one, and a next one for every one, perhaps what one might think of is starting with 0. This is the way the counting numbers work, but they count their way up from nothing. When we want to enumerate some infinite real interval, perhaps we should try to emulate what is normally considered such an enumeration for a finite real interval, the digital numbers being such an enumeration of the reals in [0,1]. Perhaps instead of trying to count, we should subdivide the interval in some consistent manner so as to achieve a dense emueration of the set, which somehow follows a linear order. It certainly seems that any digital system allows us to use one interpretation of the digit string to map bijectively to the real interval, and that any other set which is also in bijection with the digital system is, by transitivity of bijection, also in bijection with the reals. However, for some reason, this doesn?t seem to fly among the community. So, the hope is to subdivide the infinite expanse in a logical, stepwise manner, so that there is a first element, which by some sort of successor operation, generates a next element, which generates a next, etc."
An Editor Recalls Some Hopeless Papers
2004 Feb 26
... Cantor was wrong
. resources
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"I dedicate this essay to the two-dozen-odd people whose refutations of Cantor's diagonal argument have come to me either as referee or as editor in the last twenty years or so. Sadly these submissions were all quite unpublishable; I sent them back with what I hope were helpful comments. A few years ago it occurred to me to wonder why so many people devote so much energy to refuting this harmless little argument -- what had it done to make them angry with it? So I started to keep notes of these papers, in the hope that some pattern would emerge. These pages report the results. They might be useful for editors faced with similar problem papers, or even for the authors of the papers themselves. But the main message to reach me is that there are several points of basic elementary logic that we usually teach and explain very badly, or not at all."
In PostScript format.
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Dilworth v. Dudley
2001 Oct 09
... Cantor was wrong
. legal
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"The decision handed down by Judge Posner in the lawsuit brought by William Dilworth against Underwood Dudley, author of Mathematical cranks. The plaintiff was upset about being referenced in Dudley's book regarding his (cranky) refutation of Cantor's diagonal construction, and sued for defamation. The suit was dismissed 'for failure to state a claim.'"
Cantor Is Wrong!
2001 Jul 21
... Cantor was wrong
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"All infinite sets have the same number of members ... All 'infinities' are equal (i.e., there is only one infinity) ... The so-called transfinites? ... Aleph-not! ... Transfinite numbers, that is infinite quantities greater than oo, are a sham, a hoax, a fantasy, a delusion, a load of hoey, total crap, completely bogus, existing neither in the real world nor even in principle ... Cantor's Diagonal Theorem, which supposedly demonstrates there are more reals (R) than integers, is simply wrong ... it does not and cannot prove what it attempts to prove, because what it attempts to prove is false...initially, this page will be a series of ideas and observations ... numbered ..."
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