The Definition of Points
in [Math]
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From: Lester Zick on 29 Mar 2007 18:12 On Thu, 29 Mar 2007 09:37:21 -0500, Tony Orlow <tony(a)lightlink.com> wrote: >> Just ask yourself, Tony, at what magic point do intervals become >> infinitesimal instead of finite? Your answer should be magnitudes >> become infintesimal when subdivision becomes infinite. > >Yes. Yes but that doesn't happen until intervals actually become zero. >But the term >> "infinite" just means undefined and in point of fact doesn't become >> infinite until intervals become zero in magnitude. But that never >> happens. > >But, but, but. No, "infinite" means "greater than any finite number" and >infinitesimal means "less than any finite number", where "less" means >"closer to 0" and "more" means "farther from 0". Problem is you can't say when that is in terms of infinite bisection. ~v~~
From: Lester Zick on 29 Mar 2007 18:18 On Thu, 29 Mar 2007 09:37:21 -0500, Tony Orlow <tony(a)lightlink.com> wrote: >>And until it does the magnitude of subdivisions remains >> finite. The fact that there is a limit to the process doesn't mean the >> process itself ever reaches that limit or ever can reach that limit. >> > >There is a definable limit, but that limit is not reached. Because you >cannot convey a point in every language with a finite alphabet in a >finite string, this means that point doesn't exist? Then, no points >exist, since there is always a number system which requires an infinite >number of bits to specify that point. What bits? Do limits exist only because there are bits? Why don't you stop beating around the bush and just come right out and say "points are bits and as long as we restrict ourselves to binary logic bits everything'll be just honky dorry and we can play mathematics on a Nintendo GameCube instead of having to demonstrate truth logically"? ~v~~
From: Lester Zick on 29 Mar 2007 18:21 On Thu, 29 Mar 2007 09:37:21 -0500, Tony Orlow <tony(a)lightlink.com> wrote: >>> Bijections have their applications. I just don't think bijection alone >>> is all that significant for infinite sets. The actual mapping function >>> describes the relationship between infinite sets. >> >> Well if you mean "matching" don't say "bijection". I don't have any >> use for people whose only purpose in math is terminological regression >> and the creation of buzzwords instead of mechanical reduction. First >> they say they can't use generic language because it isn't sufficiently >> precise then they turn right around and corrupt the usage of perfectly >> acceptable generic words such as "cardinality" on the same basis. Such >> "mathematikers" are just speaking in tongues. They don't understand >> what truth is so they just proclaim whatever they say is mathematical >> truth because the domain of their discussion is supposed to be truth. >> > >It's the proper and commonly used term. "Matching" is more colloquial >and not well defined. A bijection between sets is a relation where each >element of each set corresponds to a unique element of the other set. >The mapping function is this relation, and a function from x to y can be >inverted to form a function from y to x. Where the function is expressed >as a formula, that formula characterizes the relative sizes of the sets. >The only restriction with this approach is that the bijection must be in >quantitative order for both sets. That's nice, Tony. Doesn't have much to do with my observation but I'm quite confident it'll get you a few rungs higher in mathematical hell. ~v~~
From: Lester Zick on 29 Mar 2007 18:28 On Thu, 29 Mar 2007 09:37:21 -0500, Tony Orlow <tony(a)lightlink.com> wrote: >>> You don't really seem interested in demonstrations of truth, are you? >> >> What demonstrations of truth did you have in mind exactly, Tony? All >> I've seen so far are your ideas of truth per say and not per se.When I >> demonstrate truth the demonstration is per se by exhaustive mechanical >> reduction and not simply per say according to what seems plausible to >> me or anyone else just because I say so. What I don't seem interested >> in at the moment are more philosophical tracts when I've already shown >> the demonstration of universal truth by finite tautological reduction >> to self contradictory alternatives whereas all you've demonstrated is >> philosophical preferences for some variety of ideas apart form others. >> > >It would help if you could define a predicate, or mechanically >demonstrate how "not" is universally true, instead of just axiomatically >assuming it and subsequently deriving the fact through circular logic, Gee. You coulda fooled me. Thought I'd done exactly that. Perhaps you could show me where I just axiomatically assumed the universal truth of "not" in E201 and E401 without any kind of demonstration? >without even defining what "truth" means to begin with. If you want to >deal mathematically with logic, why don't you start by listing all the >possible states a statement can have with respect to "truth"? Can it be >true? Can it be false? Is there something in between? Well when you axiomatically assume assumptions of truth I guess there can be true, false, and everywhere in between, maybe truer and falser would be appropriate. But when you have to demonstrate truth without just assuming it the problem gets a little difficulter. ~v~~
From: Lester Zick on 29 Mar 2007 18:33
On Thu, 29 Mar 2007 09:37:21 -0500, Tony Orlow <tony(a)lightlink.com> wrote: >> If I don't seem particularly interested in demonstrations of universal >> truth it's partly because you aren't doing any and I've already done >> the only ones which can matter. It's rather like the problem of 1+1=2 >> or the rac trisection of general angles. Once demonstrated in reduced >> mechanically exhaustive terms the problem if not its explication and >> implications loses interest. If you want to argue the problem itself >> go ahead. Just don't expect me to be interested in whether 1+1=2 or >> whether you can trisect general angles. > >You assume OR in defining AND, and then derive OR from AND, all the >while claiming all you've done is NOT. Of course I do. That's specifically why I chose to specify (A B) so I could get around the presence of conjunctions like "or" which I didn't know were there but I'll take your word for it since you seem to know and say what's there and what's not without having to demonstrate it whereas I'm forced to demonstrate what I say even though you don't. So I suppose we can just assume (A B) means there's a conjunction involved on your per say without having to demonstrate its presence. ~v~~ |