Galileo's Paradox
in [Math]
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From: David Marcus on 6 Dec 2006 00:35 Virgil wrote: > In article <45706F34.1070809(a)et.uni-magdeburg.de>, > Eckard Blumschein <blumschein(a)et.uni-magdeburg.de> wrote: > > The word completeness is misleading. > > "Complete" for an ordered set has a precise mathematical definition. > That mathematical meaning is the only relevant meaning in any > mathematical discussion of ordered sets. Most words used in technical > senses in mathematics mean something quite different from their common > meanings, and those who conflate the common with the technical meanings > demonstrate their mathematical incompetence in so doing. It is interesting that most cranks seem unable to deal with the fact that common words have technical meanings. They also seem to have trouble divorcing a word from its meanings. -- David Marcus
From: David Marcus on 6 Dec 2006 00:38 Virgil wrote: > In order to discuss anything, there must be agreement on the meaning of > the terms to be used in that discussion. Thousands of mathematicians > have agreed on the meanings of certain mathematical terms, so that those > who wish to discuss things mathematical cast themselves into outer > darkness by insisting on using those terms to mean things at variance > with their standard meanings. > > If EB wants to express different meanings he must come up with unused > word or phrases to carry those meanings. Mathematics will not allow EB > to rewrite mathematical dictionaries to suit his whims. Or, clearly state what meaning he is giving to words. -- David Marcus
From: David Marcus on 6 Dec 2006 00:40 Virgil wrote: > In article <456f34bc(a)news2.lightlink.com>, > Tony Orlow <tony(a)lightlink.com> wrote: > > Virgil wrote: > > > In article <456e475e(a)news2.lightlink.com>, > > > Tony Orlow <tony(a)lightlink.com> wrote: > > >> Given a > > >> set density, value range determines count. > > > > > > Compare the "set densities" of the set of naturals, the set of > > > rationals, the set of algebraics, the set of transcendentals, the set of > > > constructibles, and the set of reals. > > > > Rather difficultt o formulate relations between those in standard > > theory. In the name of IST, I'll avoid any criteria including the notion > > of "standard" and state the following. The size of the set of > > hypernaturals is the square root of the size of the set of hyperreals. > > The set of hyperrationals corresponds to the square of the set of > > hypernaturals, minus all those pairs that are redundant, such as 2/4 or > > 6/18. That number of the hyperreals are the hyperirrationals. I am not > > sure how to relatively quantify transcendentals, constrictibles, or > > algebraics. Those are probably considered all "countable" by you, which > > doesn't say much about their relative sizes. > > When challenged to support his fool theories, TO resorts to nonsense. At least he admitted that his fool theory has no relevance to any of the number systems commonly used in Mathematics. -- David Marcus
From: David Marcus on 6 Dec 2006 00:55 Eckard Blumschein wrote: > On 11/29/2006 6:12 PM, stephen(a)nomail.com wrote: > > Again, your problem is insisting that cardinality match some vague notion of 'how many' > > that you have not defined. > > The basic problem is: He lacks the insight that cardinality is a > cardinal mistake, Ah, mathematical argument via pun. > something that has proven unfounded as well as useless. Define "unfounded". -- David Marcus
From: David Marcus on 6 Dec 2006 00:58
Tonico wrote: > Ps Have you, and anyone else, noted how all the anticantorian cranks > are NEVER mathematicians? Kind of hard to survive graduate school if you can't think mathematically. -- David Marcus |