The Definition of Points
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From: Virgil on 18 Apr 2007 02:56 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? > 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?
From: Phil Carmody on 18 Apr 2007 05:53 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? 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./.
From: Mike Kelly on 18 Apr 2007 06:31 On 18 Apr, 06:17, Tony Orlow <t...(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', Why "almost solely"? > but in my opinion doesn't produce believable results. Which "results" of cardinality are not believable? You don't think the evens and the naturals and the rationals are mutually bijectible? Or you do think the reals and the naturals are bijectible? Or did you mean you have a problem not with what cardinality actually is but with what you hallucinate cardinality to be? > I'm working on a better theory, bit by bit. You have never managed to articulate a problem with what cardinality actually says (all it says is which sets are bijectbile). You've never managed to explain the motivation behind your "better theory". I don't even know whether your ideas are supposed to be formulated in ZF or in something else, possibly a new foundation of your own devising(or, perhaps, never formalised at all?). FWIW I don't think it would be very hard to define, say, "density in the naturals" in ZF. I just don't see the motivation behind doing so. > 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. But you are, in fact, completely mistaken here. Several people have told you this. You have some inability to acknowledge this. Oh well. PS you snipped a lot of my post; maybe you found it boring. I find your evasiveness quite interesting, though. What does cardinality claim to tell that it can't? -- mike.
From: Alan Smaill on 18 Apr 2007 06:40 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" > 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: Phil Carmody on 18 Apr 2007 07:15
Alan Smaill <smaill(a)SPAMinf.ed.ac.uk> writes: > 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" There ain't no "f" in "honest politicians". There's a silent "c" in "rap" though. 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./. |