The Definition of Points
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From: Tomasso on 18 Apr 2007 07:33 "Alan Smaill" <smaill(a)SPAMinf.ed.ac.uk> wrote in message news:fwe8xcq3qza.fsf(a)collins.inf.ed.ac.uk... > Phil Carmody <thefatphil_demunged(a)yahoo.co.uk> writes: > >> Brian Chandler <imaginatorium(a)despammed.com> writes: >>> David R Tribble wrote: >>> > Tony Orlow writes: >>> > >> ala L'Hospital's theft from the Bernoullis, and >>> > >> the division by 0 proscription. >>> > > >>> > >>> > Alan Smaill wrote: >>> > > and Zick was the one who claimed that he would use l'Hospital to work >>> > > out the right answer for 0/0. such a japester, eh? >>> > >>> > Geez. How many posts before someone points >>> > out that it's l'H�pital's rule? L'Hospital is where >>> > you take someone after they get punched in the >>> > nose by a mathematician after saying "l'Hospital's rule". >>> >>> Well, given that "�" is only a French spelling for "o-with-the- >>> following-s-omitted", seems to me that l'Hospital is a pretty >>> reasonable asciification. >> >> But it seems to be missing the "omitted" part of that. > >> Can I have a coffee without milk? >> I'm sorry, we don't have any milk. >> Ah, OK, how about a coffee without cream? > > like the silent "k" in "frying pan" Brilliant guys! Now, what was the question? Tomasso. >> Phil >> -- >> "Home taping is killing big business profits. We left this side blank >> so you can help." -- Dead Kennedys, written upon the B-side of tapes of >> /In God We Trust, Inc./. > > -- > Alan Smaill
From: Lester Zick on 18 Apr 2007 12:18 On Tue, 17 Apr 2007 15:44:25 -0600, Virgil <virgil(a)comcast.net> wrote: >In article <46250ea8(a)news2.lightlink.com>, > Tony Orlow <tony(a)lightlink.com> wrote: > >> In all fairness to Lester > >Why bother to be fair to one who is so compulsively unfair? Aw poor baby. Have I ever been other than scrupulously fair in pointing out that you're too lazy or stupid to demonstrate the truth of what you claim but not too lazy or stupid to claim it anyway? Let me speak to your Mommy. I mean assuming you know who she is. ~v~~
From: Lester Zick on 18 Apr 2007 13:39 On 17 Apr 2007 15:25:41 -0700, Marcus <BezekMarcus(a)aol.com> wrote: >Can you answer Ivey's challenge? If not, then it seems that your so- >called "problem" may not be a problem after all. I thought I had explained the circumstances of my original post relating to circular definition of geometric figures with SOAP operas. I rarely have occasion to argue issues with textbooks college level or otherwise so might be more appropriate to ask mathematikers for citations justifying their use of circular definitions instead of me. As for whether it remains a problem just consider PD's reply to me this morning on the collateral thread "Zick's Postulate" to wit that "mathematics is what mathematicians say it is and science is what scientists say it is". ~v~~
From: Tony Orlow on 18 Apr 2007 13:55 Virgil wrote: > In article <4625a9df(a)news2.lightlink.com>, > Tony Orlow <tony(a)lightlink.com> wrote: > >> Mike Kelly wrote: >> < snippery > >>> You've lost me again. A bad analogy is like a diagonal frog. >>> >>> -- >>> mike. >>> >> Transfinite cardinality makes very nice equivalence classes based almost >> solely on 'e', but in my opinion doesn't produce believable results. > > What's not to believe? > > Cardinality defines an equivalence relation based on whether two sets > can be bijected, and a partial order based on injection of one set into > another. > > Both the equivalence relation and the partial order behave as > equivalence relatins and partial orders are expected to behave in > mathematics, so what's not to believe? > > > What I have trouble with is applying the results to infinite sets and considering it a workable definition of "size". Mike's right. If you don't insist it's the "size" of the set, you are free to do with transfinite cardinalities whatever your heart desires. What I object to are statements like, "there are AS MANY reals in [0,1] as in [0,2]", and, "the naturals are EQUINUMEROUS with the even naturals." If you say they are both members of an equivalence class defined by bijection, then I have absolutely no objection. If you say in the same breath, "there are infinitely many rationals for each natural and there are as many naturals overall as there are rationals", without feeling a twinge of inconsistency there, then that can only be the result of education which has overridden natural intuition. That's my feeling. I'd rather acknowledge that omega is a phantom quantity, and preserve basic notions like x>0 <-> x+y>y, and extend measure to the infinite scale. >> So, >> I'm working on a better theory, bit by bit. I think trying to base >> everything on 'e' is a mistake, since no infinite set can be defined >> without some form of '<'. I think the two need to be introduced together. > > Since any set theory definition of '<' is ultimately defined in terms of > 'e', why multiply root causes? It's based on the subset relation, which is a form of '<'.
From: Tony Orlow on 18 Apr 2007 14:03
stephen(a)nomail.com wrote: > In sci.math Tony Orlow <tony(a)lightlink.com> wrote: >> Mike Kelly wrote: >>> The point that it DOESN'T MATTER whther you take cardinality to mean >>> "size". It's ludicrous to respond to that point with "but I don't take >>> cardinality to mean 'size'"! >>> >>> -- >>> mike. >>> > >> You may laugh as you like, but numbers represent measure, and measure is >> built on "size" or "count". > > What "measure", "size" or "count" does the imaginary number i represent? Is i a number? > The word "number" is used to describe things that do not represent any sort of "size". > > Stephen Start with zero: E 0 Define the naturals: Ex -> Ex+1 Define the integers: Ex -> Ex-1 Define imaginary integers: Ex -> sqrt(x) i=sqrt(0-(0+1)), so it's built from 0 and 1, using three operators. It's compounded from the naturals. A nice picture of i is the length of the leg of a triangle with a hypotenuse of 1 and a leg of sqrt(2), if that makes any sense. It's kind of like the difference between a duck. :) Tony |