everyday847

Originally Posted By: Khoth You don't need the axiom of choice to well-order the rationals. Any ordering you come up with to show they're countable will do (eg the one you get by writing them all down in an infinite plane and spiralling out from 0). Right: I'm saying that the axiom of choice is equivalent to something that's called something like the well-ordering principle that states that you can well-order any (nonempty?) set. Originally Posted By: Khoth I think the lexicographical ordering works if you extend it to negative numbers (just shove in -x after every positive x). No. What, by the lexicographical ordering, is the smallest negative rational number? If you can't answer that question, it's not a well-ordering. Ohh, are you proposing that you do something like 1, 1/2, 1/3, 1/4, ..., -1, -1/2, ... Yeah, I guess that works.

Originally Posted By: Celtic Minstrel Originally Posted By: Micawber Induction works on well-ordered sets. Being well-ordered is completely different from being countable, although the natural numbers happen to be both. But uncountable well-ordered sets are much studied. The rational numbers in the usual ordering are not well-ordered. But if I'm not mistaken, it's possible to well-order the rationals, isn't it? Perhaps using a lexicographical ordering? (ie 1, 1/2, 1/3, ..., 2, 2/3, 2/5, ..., 3, 3/5, 3/7, 3/8, ..., etc) Every set can be well-ordered if you're down with the axiom of choice, so yes--but the "lexicographical" ordering doesn't really work. For a well-ordering, every nonempty subset of the set you want to well-order has to have a least element. What's the smallest negative rational?

Originally Posted By: Like Mana from the Pacific Comparisons are by definition not equations. Equations require that equals sign. But your point is otherwise correct. —Alorael, who wouldn't be too sure about horses. He's fairly sure that's how dogs' brains work. His point is that the notion of comparing less than/ greater than (in the way that seems most obvious for real numbers) comes from mathematics, rather than from our external experience of real numbers. I don't find this to be accurate (though I'll readily admit that the reals look nice under that ordering--but I could well just be biased about it!).

Originally Posted By: Jadan Reguardless, Eating more or less is still a generic terminology involving mathematics. No, comparisons aren't defined in terms of mathematical relations. Quite the opposite; you can't define a field and hope that its structure will just tell you how to order its elements. (Though because of external intuition because we have concepts of eating more and less or whatever, some orderings seem more natural than others.)

Originally Posted By: Celtic Minstrel Originally Posted By: No_More_PLL_Ever some non-rational numbers, such as pi or the squared root of any prime number, have "names" and so any multiplication of them with a rational number has a "name" (maybe even addition can be dragged in this way). Not just the square root of prime numbers; the square root of any non-square number, the cube root of any non-cube, the nth root of any non-nth-power... and that's not the only set of functions that generates irrationals from rationals in a systematic way. There's the log functions, the trigonometric functions... even regular operations such as addition, subtraction, multiplication, division, and exponentiation. You're slightly misinterpreting, I imagine: he's not saying that "only the square roots of primes are irrational"; he's saying that "the square roots of primes can be said to have 'names' and then you can start generating the names of other irrationals from there." Nonetheless, you'd need the nth roots of all primes, plus a bunch more, and you'd still never accomplish the task because there are uncomputable numbers and as long as a number can't be computed, you can't meaningfully give it a name (since you can't call it 'log of pete' or 'cosine of mike' or much of anything else, as it can't be given as a function evaluated on some argument that can be computed by a finite, terminating algorithm.)

You're totally right, Slarty. Though, for what it's worth, a lot of qualities of written language can be interpreted in terms of features of spoken language. (Italics, perhaps, or, on the Internet, the use of <sarcasm> tags or something, could be effectively prosodic features. They certainly are as analogous to spoken prosody as certain qualities of signs in ASL can be said to be.)

Yeah, there's really no way to answer this question. There aren't objects with which we can interact that could interact with spirits or demons or whatever (unless you have a really strange construction of what a spirit or demon would be, were one to exist). The natural bridge is that you have to assume that magic (of some form; doesn't matter if it's FMA's alchemy, So You Want To Be a Wizard style, Robert Jordan style, D&D style, Spiderweb Software style, whatever) exists. That magic could be directed against the demon or spirit or it could be used to enchant a weapon. But since magic doesn't exist, this isn't real life; since neither demons nor spirits exist, I'm not too worried.

Originally Posted By: CRISIS on INFINITE SLARTIES Originally Posted By: Celtic Minstrel and the meaning of a word has nothing to do with grammar. Originally Posted By: everyday847 Well, from a linguistic standpoint Celtic Minstrel is right on the second point: the lexicographic representation of a language doesn't have anything to do with its grammar. 1) "The meaning of a word" and "the lexicographic representation of a language" (AKA, the lexicon) are not the same thing. 2) Even if you divorce "meaning" from all utterance-specific context and instead say "the imaginary, perfect dictionary definition of a word has nothing to do with grammar" you are still incorrect. We can perhaps pretend in our heads that we are thinking of the essential concept behind a given word, but the reality is that, when a concept is given representation in a word, that word has phonological, morphological, and of course, syntactic features that depend on the grammar and which, in addition to influencing the lexical form of the word, impact its meaning. To illustrate this point, show me how the intransitive lexical entry for "kill" can have the same meaning in a nominative-accusative and an ergative-absolutive language. It can't, even though the concept of killing is the same in both cases. Yeah, you're right.

Well, from a linguistic standpoint Celtic Minstrel is right on the second point: the lexicographic representation of a language doesn't have anything to do with its grammar. But that's the sort of boring point you can only make if you're okay with people who interject "2+2=4? who says I'm not working mod 3? pfaugh!" when you're clearly just adding numbers together not being strangled.

I'm skeptical.

Well, it's the name of Ahriman. There's plenty of analogy to the Christian devil if you are a Christian, I guess, but "the devil" came second.

Saraph observes "with his senses:" dynamite prose right there. Also, he hugs his sister for a straight hour? Impressive.

I'd sooner attribute Ahriman to Zoroastrianism, wouldn't you?

I'm holding my breath.

Steven Crane's collected poetry: the volume has Black Riders, War is Kind, and a few freestanding poems.