My FINAL Cantor thread!
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From: |-|ercules on 29 Jun 2010 18:36 "George Greene" <greeneg(a)email.unc.edu> wrote .. > On Jun 29, 2:04 am, "|-|ercules" <radgray...(a)yahoo.com> wrote: >> The proof is not induction on finite sequences, it is induction on finite prefixes. >> Learn the difference! > > You DON'T KNOW jack about induction. > Proving something for all finite prefixes IS EXACTLY THE SAME > as proving it for all finite sequences: EVERY finite prefix IS a > finite sequence, > and EVERY finite sequence IS a finite prefix (of the string > consisting of itself > concatenated with ANOTHER 0). Let's call that a default_finite_prefix. Then every finite sequence being a default_finite_prefix does not make them equivalent. You prove a property for increasing different objects. I sample larger and larger sizes of the one object. Different style of proof! I prove, by induction, the (anti-transfiniteness) property holds for all digit widths (all digits) You prove, by induction, that all (finite) sizes of prefixes the (pro-transfiniteness) property holds. Herc
From: |-|ercules on 29 Jun 2010 19:53 "George Greene" <greeneg(a)email.unc.edu> wrote > On Jun 27, 7:16 am, "Mike Terry" > <news.dead.person.sto...(a)darjeeling.plus.com> wrote: >> That's not the way you defined w at the start of the thread. > > THAT is NOT the issue! Correct! > The issue IS that this definition IS > INCOHERENT! Wrong on both counts This definition is entirely clear, and the issue is whether Mike and others can review the proof with the clearer definition. > Was the one at the start any better???? No. That's the issue. > > And I still insist you can't tolerate "w" as the letter for this, Like I said, use another letter. A million variable declarations using w are written by mathematicians and students every day, none of them are referring to infinity, 99% don't even realize the connotation of the letter. w is for width. You said yourself it's a good coincidence. I was being clever since the proof shows w IS infinity. A double meaning lost on you. > because w IS ACTUALLY THE RIGHT width ("w" is ascii for > lower-case-greek omega, WHICH IS RIGHT). But w as he is trying to > define > it is too meaningless to be wrong -- you cannot define "w" OR ANYTHING > ELSE > as the maximum of a series THAT DOES NOT HAVE a maximum! So you can't define a list of all reals, a function that determines if a program halts.. For each subset of computable reals, there exists a maximum digit length that that subset doesn't miss a possible sequence of digits. w is the maximum of those maximums. GOT IT! Herc
From: Dingo on 29 Jun 2010 22:37 On Tue, 29 Jun 2010 12:28:38 -0700 (PDT), George Greene <greeneg(a)email.unc.edu> wrote: >On Jun 27, 7:16�am, "Mike Terry" ><news.dead.person.sto...(a)darjeeling.plus.com> wrote: >> That's not the way you defined w at the start of the thread. > >THAT is NOT the issue! The issue IS that this definition IS >INCOHERENT! >Was the one at the start any better???? > >And I still insist you can't tolerate "w" as the letter for this, >because w IS ACTUALLY THE RIGHT width ("w" is ascii for >lower-case-greek omega, WHICH IS RIGHT). But w as he is trying to >define >it is too meaningless to be wrong -- you cannot define "w" OR ANYTHING >ELSE >as the maximum of a series THAT DOES NOT HAVE a maximum! You're never going to convince Herc he's mistaken or imagining things - that is one of the indicators of his mental illness.
From: |-|ercules on 29 Jun 2010 22:49 "Dingo" <dingo(a)gmail.com> wrote ... > On Tue, 29 Jun 2010 12:28:38 -0700 (PDT), George Greene > <greeneg(a)email.unc.edu> wrote: > >>On Jun 27, 7:16 am, "Mike Terry" >><news.dead.person.sto...(a)darjeeling.plus.com> wrote: >>> That's not the way you defined w at the start of the thread. >> >>THAT is NOT the issue! The issue IS that this definition IS >>INCOHERENT! >>Was the one at the start any better???? >> >>And I still insist you can't tolerate "w" as the letter for this, >>because w IS ACTUALLY THE RIGHT width ("w" is ascii for >>lower-case-greek omega, WHICH IS RIGHT). But w as he is trying to >>define >>it is too meaningless to be wrong -- you cannot define "w" OR ANYTHING >>ELSE >>as the maximum of a series THAT DOES NOT HAVE a maximum! > > You're never going to convince Herc he's mistaken or imagining things > - that is one of the indicators of his mental illness. Dingo agrees with George Greene that definitions must only be of real possible entities. There you go George, strength in numbers, a drunkard yobbo troll agrees with you. Herc -- > There IS NOT a computer program that lists the outputs of all computer programs! WRONG! > The LIST of computable reals exists, but howEVER you got it, you DIDN'T get it from a computer. GEORGE GREENE DEFIES LOGIC YET AGAIN!
From: Dingo on 29 Jun 2010 23:53
On Wed, 30 Jun 2010 12:49:17 +1000, "|-|ercules" <radgray123(a)yahoo.com> wrote: >Dingo agrees with George Greene that definitions must only be of real possible entities. I said no such thing, fool. >There you go George, strength in numbers, a drunkard yobbo troll agrees with you. My lawyers have been notified - I may be a drunkard but I'm no yobbo! |