The Definition of Points
in [Math]
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From: Virgil on 31 Mar 2007 21:44 In article <460ef5d1(a)news2.lightlink.com>, Tony Orlow <tony(a)lightlink.com> wrote: > stephen(a)nomail.com wrote: > > Tony rejects all these options, and apparently has some fourth > > Elusive option. > > > > Stephen > > > > Oy. The "elusive" option is that there is no acceptable "size" for N. > That was really hard to figure out after all this time... There is in ZF and in NBG and in NF. In what system does TO not find a "size" that is suitable in that system?
From: Virgil on 31 Mar 2007 21:45 In article <460ef650(a)news2.lightlink.com>, Tony Orlow <tony(a)lightlink.com> wrote: > Bob Kolker wrote: > > Tony Orlow wrote:>> > >> > >> Measure makes physics possible. > > > > On compact sets which must have infinite cardinality. > > > > The measure of a dense countable set is zero. > > > > Bob Kolker > > Yes, some finite multiple of an infinitesimal. In any consistent system in which there are infinitesimals, none of those infinitesimals are zero.
From: Virgil on 31 Mar 2007 21:46 In article <460ef795(a)news2.lightlink.com>, Tony Orlow <tony(a)lightlink.com> wrote: > Virgil wrote: > > In article <460edc26(a)news2.lightlink.com>, > > Tony Orlow <tony(a)lightlink.com> wrote: > > > >> Bob Kolker wrote: > >>> Tony Orlow wrote: > >>>> As I said to Brian, it's provably the size of the set of finite > >>>> natural numbers greater than or equal to 1. No, there is no last > >>>> finite natural, and no, there is no "size" for N. Aleph_0 is a phantom. > >>> No. It is the cardinality of the set of integers. > >> No, Bob, that's a Muslim lie, perpetrated by the Jews as a joke on the > >> xtians. > > > > And does TO pretend to have a mathematically valid proof of that claim? > > Allah: I am the last prophet. > Jehovah: My last prophet is second only to me. > El: There is none close to Us. > Jesus: Come sit next to me. > > Therefore, according to obviously plain logic, I'm right, of course! > > QED. Looks purely Left to me.
From: Virgil on 31 Mar 2007 21:51 In article <460ef839(a)news2.lightlink.com>, Tony Orlow <tony(a)lightlink.com> wrote: > Virgil wrote: > > In article <460ee056(a)news2.lightlink.com>, > > Tony Orlow <tony(a)lightlink.com> wrote: > >> Please do expliculate what the contradiction is in an uncountable > >> sequence. What is true and false as a result of that concept? > > > > A mathematical sequence is a function with the naturals as domain. > > If TO wishes to refer to something which is not such a function, he > > should not refer to it as a sequence if he wishes to be understood in > > sci.math. > > > > > > Pray tell, what term shall I use???? TO is so inventive in so many useless ways that I cannot believe that his imagination will fail him in such a trivially useful way. > > >>> I know you are incapable of actually thinking about all the elements of > >>> N, > >>> but that is your problem. In any case, N is not an element of N. > >>> Citing Ross as support is practically an admission that you are wrong. > >>> > >>> Stephen > >>> > >> Sure, of course, agreeing with someone who disagrees with you makes me > >> wrong. I'll keep that in mind. Thanks.. > > > > It is not so much that Ross disagrees with one person, it is that he > > disagrees with everyone, frequently including himself. > > Ross has a vision, even if not axiomatically expressed. In fact, he's > entirely honest about that, expounding an axiom free system. I like > Ross. So do you. Admit it. :) > Like Russell? What is there about him to like?
From: Tony Orlow on 31 Mar 2007 21:51
Lester Zick wrote: > On Fri, 30 Mar 2007 12:33:00 -0500, Tony Orlow <tony(a)lightlink.com> > wrote: > >> Lester Zick wrote: >>> 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~~ >> Okay, fill in this table for me please, explaining whether (A B) is true >> or false in the following circumstances: > What question are you about to ask? > What table, Tony? What true false? > >> A B (A B) >> true true true or false? >> true false true or false? >> false true true or false? >> false false true or false? >> >> Now, we can see what 2-place operator you're talking about. > Okay, now it looks like you changed two of the "true or false?" entries. No, it's just bad tabbing... > What two place operator, Tony? Would you care to define any of these > terms before talking about them or should we try to talk about them > before defining them? I don't mind talking about tables, true, false, > two place operators, etc. before defining them but then I insist on my > definitions intead of yours. Of course I can't tell exactly what my > definitions might be until I define them in preference to yours. But > that doesn't really matter since they're my definitions to begin with. > > ~v~~ wahhhh.... sigh. Okely dokums. Here goes, again. A logical statement can be classified as true or false? True or false? A logical operator can be defined as one taking some number of arguments or parameters, and producing a statement that falls in one class or the other. True or false? A statement cannot have a negative number of variables, can it? So, the fewest parameters it can have is zero, and the only two operators that put out values of "true" and "false" given no inputs are true() and false(). There are 2^0=1 inputs, or no choice, and 2^1 outputs, two possible. Out of the 1-place operators, there are four. There are 2^1=2 possible input states, and 2^2=4 possible output mappings. One is always true and one always false, no matter what the input is, so those are redundant. Call the input x, either 0 or 1. One of the 1-place operators is the same as x. The only other of the four is not(x). That'd the only 1-place operator of any significance. When it comes to 2-place operators, there's A and B, A or B, A xor B, A implies B, A is implied by B, and their negations, pretty much. 01oo |