'When Are Relations Neither True Nor False?
in [Math]
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From: Jesse F. Hughes on 21 Mar 2010 11:25 Marshall <marshall.spight(a)gmail.com> writes: > On Mar 19, 7:18 pm, "Jesse F. Hughes" <je...(a)phiwumbda.org> wrote: >> Transfer Principle <lwal...(a)lausd.net> writes: >> > On Mar 17, 5:27 am, Alan Smaill <sma...(a)SPAMinf.ed.ac.uk> wrote: >> >> Transfer Principle <lwal...(a)lausd.net> writes: >> >> > (even though almost 40% of >> >> > physicists believe that 0.999...<1) >> >> Do I get labelled as a bully if I ask for some evidence for your claim? >> >> [...] >> >> > We notice at the top of the Metamath page, it reads: >> >> > "Interestingly, about 40% of the people responding to a poll at >> >http://forum.physorg.com/index.php?showtopic=13177disagree." >> >> An online poll at physorg.com and you concluded that 40% of physicists >> believe 0.999... < 1? >> >> That is just incredibly lame evidence. All one can conclude is that >> 40% of the visitors to physorg.com *who chose to answer* the question >> said that 0.999... < 1. You have no idea how many of those folks were >> physicists, whether the percentage who chose to answer are >> representative of physicists as a whole (or even physorg.com visitors) >> and so on. It's a voluntary poll, indicative of nothing much at all. > > > You know, I mostly think TP is a nut, and folks like Moe and Jesse > are top-drawer, but I have to point something out here. Yes, the > evidence that TP has provided is weak, and we can poke all manner > of holes in it and so forth. But crappy as it is, it still counts as > evidence. > > What has been offered against it opinion. No one has offered a counterclaim, though we all find the claim doubtful. We've only asked for Walker's evidence, and what he offered was perfectly laughable, so pathetically weak that it counts as negligible. > And the best opinions in the world do not, IMHO, rise to the level > of the worst evidence. I'm calling round 1 for TP here. What nonsense, as has already been pointed out here. -- Jesse F. Hughes "Everybody has a heart, except some people." -- All About Eve
From: Nam Nguyen on 21 Mar 2010 11:31 J. Clarke wrote: > > However, if the definition of a "relation" is "a set of n-tuples", then > by definition the empty set is not a "relation" and so your statement > that "a false relation is an empty set" violates the definition. If you > want to say that the empty set is not a relation that's fine, > but if you > want to say that it is a "false relation" please demonstrate that it is > a relation at all. As long as you understand the empty set is a set, then you'd understand a demonstration. Here is one. A predicate formula P(x1,x2,...,xn) is defined to be true in the relation set R iff the n-tuple (x1,x2,...,xn) is in R, and *_defined_ to be _false_ iff the n-tuple (x1,x2,...,xn) _is not_ in R*. But since the empty set is defined so that it has no element, (x1,x2,...,xn) is not in R is true, no matter what n-tuple one would happen to have.
From: Nam Nguyen on 21 Mar 2010 11:33 J. Clarke wrote: > > However, if the definition of a "relation" is "a set of n-tuples", then > by definition the empty set is not a "relation" and so your statement > that "a false relation is an empty set" violates the definition. If you > want to say that the empty set is not a relation that's fine, > but if you > want to say that it is a "false relation" please demonstrate that it is > a relation at all. As long as you understand the empty set is a set, then you'd understand a demonstration. Here is one. A predicate formula P(x1,x2,...,xn) is defined to be true in the relation set R iff the n-tuple (x1,x2,...,xn) is in R, and *_defined_ to be _false_ iff the n-tuple (x1,x2,...,xn) _is not_ in R*. But since the empty set is defined so that it has no element, (x1,x2,...,xn) is not in R is true, no matter what n-tuple you'd happen to have.
From: Nam Nguyen on 21 Mar 2010 11:40 J. Clarke wrote: > On 3/21/2010 10:13 AM, Jesse F. Hughes wrote: >> "J. Clarke"<jclarke.usenet(a)cox.net> writes: >> >>> However, if the definition of a "relation" is "a set of n-tuples", then >>> by definition the empty set is not a "relation" [...] >> >> Nonsense! The empty set is a set of n-tuples for *every* n. Every >> element of the empty set is an n-tuple (no matter the value of n). >> >> The empty set is a relation. > > I thought I had you killfiled. > > Well, back you go. Whatever the reason for the killfile, do you understand that he was correct and you weren't?
From: Jesse F. Hughes on 21 Mar 2010 11:46
"J. Clarke" <jclarke.usenet(a)cox.net> writes: > On 3/21/2010 10:13 AM, Jesse F. Hughes wrote: >> "J. Clarke"<jclarke.usenet(a)cox.net> writes: >> >>> However, if the definition of a "relation" is "a set of n-tuples", then >>> by definition the empty set is not a "relation" [...] >> >> Nonsense! The empty set is a set of n-tuples for *every* n. Every >> element of the empty set is an n-tuple (no matter the value of n). >> >> The empty set is a relation. > > I thought I had you killfiled. > > Well, back you go. Yes, well, darned shame and all, but as it happens, what I wrote is plainly correct. -- Jesse F. Hughes "If anything is true in general about Usenet, it's that people can go on and on about just about anything." -- James Harris speaks the truth. |