Galileo's Paradox
in [Math]
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From: David Marcus on 5 Dec 2006 02:15 Eckard Blumschein wrote: > On 11/30/2006 1:32 PM, Bob Kolker wrote: > > Eckard Blumschein wrote: > > > >> Uncountable means: Counting is impossible. This property obviously > >> belongs to fictitious elements of continuum. There is simply too much of > >> them. So counting is not feasible. As long as one looks at a finite, > >> just potentially infinite heap of single integers, one has to do with > >> individuals. The set of all integers is something else. It is a fiction. > >> It is to be thought constituted of an uncountable amount of > >> non-elementary elements. Well this looks nonsensical. There is indeed a > >> selfcontradiction within the notion of an infinite set. > >> Non-elementary means not having a distinct numerical address. Element > >> means "exactly defined by an impossible task". > > > > Have you forgotten to take your meds again? > > Element should read "element of IR" Is that a "yes"? -- David Marcus
From: David Marcus on 5 Dec 2006 02:18 Lester Zick wrote: > On Fri, 01 Dec 2006 11:39:57 -0500, Tony Orlow <tony(a)lightlink.com> > wrote: > > >Lester Zick wrote: > >> On Thu, 30 Nov 2006 12:08:03 +0100, Eckard Blumschein > >> <blumschein(a)et.uni-magdeburg.de> wrote: > >> > >>> On 11/29/2006 8:13 PM, Bob Kolker wrote: > >>>> Tony Orlow wrote: > >>>>> Uncountable simply means requiring infinite strings to index the > >>>>> elements of the set. That doesn't mean the set is not linearly ordered, > >>>>> or that there exist any such strings which do not have a successor. > >>>> Uncountable means infinite but not of the same cardinality as the > >>>> integers. For example the set of real numbers. It is an infinite set, > >>>> but it cannot be put into one to one correspondence with the set of > >>>> integers. > >>> Uncountable means: Counting is impossible. This property obviously > >>> belongs to fictitious elements of continuum. There is simply too much of > >>> them. So counting is not feasible. As long as one looks at a finite, > >>> just potentially infinite heap of single integers, one has to do with > >>> individuals. The set of all integers is something else. It is a fiction. > >>> It is to be thought constituted of an uncountable amount of > >>> non-elementary elements. Well this looks nonsensical. There is indeed a > >>> selfcontradiction within the notion of an infinite set. > >>> Non-elementary means not having a distinct numerical address. Element > >>> means "exactly defined by an impossible task". > >> > >> You make the same mistake of assuming "infinite" means "larger than" > >> when it only means numerically undefined. Infinites are neither large > >> nor small; they're only undefined. Consequently there are no numerical > >> relations or operations possible between them and finites. The reason > >> counting is not possible is not because infinites are huge or because > >> they form a continuum but because there is no numeric metric defined > >> for them and counting as well as every other arithmetic relation and > >> operation requires some kind of numeric definitional metric. > >> > >> ~v~~ > > > >Huh! So, what happens if I declare a number, Big'un, and say that that > >is the number of reals in (0,1]? What if I say the real line is > >homogeneous, so every unit interval contains the same number of points? > > If you do, Tony, then what you've defined as "points" are in point of > fact infinitesimals not points. > > >And then, what if I say the positive number line is going to include > >Big'un such unit intervals, so it has Big'un^2 reals up to Big'un? Does > >the universe collapse, or all tautologies suddenly become false? > > You could do this but the result wouldn't be finite in numerical terms > and anything you might try to do between them and finites would cause > the universe to collapse because they just aren't there on the same > line and have different properties because they are finitely infinite. > > This is the price to be paid for absurdities like the real number line > and putting infinities on them. "Infinite" means "not finite" and you > just can't do finite arithmetic with "not finites". You wrote above that "infinite" means "numerically undefined". Does "numerically undefined" mean "not finite"? -- David Marcus
From: David Marcus on 5 Dec 2006 02:20 Tony Orlow wrote: > Virgil wrote: > > In article <45705ad3(a)news2.lightlink.com>, > > Tony Orlow <tony(a)lightlink.com> wrote: > > > >> Huh! So, what happens if I declare a number, Big'un, and say that that > >> is the number of reals in (0,1]? What if I say the real line is > >> homogeneous, so every unit interval contains the same number of points? > >> And then, what if I say the positive number line is going to include > >> Big'un such unit intervals, so it has Big'un^2 reals up to Big'un? Does > >> the universe collapse, or all tautologies suddenly become false? > > > > As long as it is only TO playing his silly games, nobody much cares. > > > > If TO were ever to produce anything like a coherent system with actual > > proofs, we might actually have to pay some attention. > > Of course, that would be nice, to get some attention around here, > especially from Virgil. But, he never pays me no mind. He hardly > responds to anything I say. Virgil obviously meant mathematical attention as opposed to crank attention. -- David Marcus
From: David Marcus on 5 Dec 2006 02:24 Eckard Blumschein wrote: > Reals, as indirectly defined with DA2, Why do you think that the diagonal argument defines the reals? I mean, you say lots of nonsense, but I don't see where you got this particular nonsense from. Did you read it in a book? -- David Marcus
From: Ross A. Finlayson on 5 Dec 2006 02:47
Virgil wrote: > > It is the quality of being a subset. It is one, but not the only, > measure of set "size". Why, that's certainly not your stated, repeated, and derogatorily upheld in the face of denial opinion. Consider, for example, last week, when you said anybody who said such a thing as you just said was a variety of bad things, and the trouble I went through to explain that. About empiricism and transfinite cardinals: there's the universe, it's an example of the powerset result seen to not hold. There is no universe in ZF, and no class of classes in ZF with classes. So, where is it? There is no universe in ZF. There is, to quantify, there isn't. Sizehood is a quibble of transitive plain language definition, where's your universe? Ross |