My FINAL Cantor thread!
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From: George Greene on 1 Jul 2010 01:22 On Jun 30, 6:11 pm, "|-|ercules" <radgray...(a)yahoo.com> wrote: > HAHAHA. > Are you really that stupid to assume induction on both forms is the same too? I don't NEED to ASSUME! I KNOW what induction is! YOU DON'T! > > Does the list > 0.0 > 0.1 > 0.2 > ... > 0.9 > 0.10 > 0.11 > ... > 0.99 > 0.101 > ... > > use this induction schema too? A LIST *CANNOT*USE* "an induction schema" !! WHY DON'T YOU SIMPLY STATE which induction schema YOU are using??? THE STANDARD induction schema requires you to START with a ONE-place predicate that takes A NUMBER as a parameter. You can change that from a number to something else as LONG as you have a clear notion of what THE SUCCESSOR, THE NEXT element, of something, would be. And in any case, you have THE WRONG list. The ACTUAL list is ..0 ..1 ..2 ..3 ..4 ..5 ..6 ..7 ..8 ..9 ..01 ..11 ..21 etc. It does NOT have .10 after .9 ! The reason for this is that you need LOTS OF LEADING ZEROS as prefixes! You have to spell 10, 100, 1000 etc. FROM RIGHT TO LEFT. > > phi( <[1] 2 3 4...> ) & An ((phi ( <[1 2 ... n] n+1 n+2 ...>) -> phi( <[1 2 ... n n+1] n+2 n+3 ...> )) > -> > phi( <[1 2 3 4...]> ) THIS IS NOT an induction schema, DUMBASS. The induction schema JUST has phi(0), NOT phi (<[1] 2 3 4>). Moreover, the conclusion of an induction schema IS NOT phi(<[1 2 3 4...]>). IT IS, rather and INSTEAD, An[phi(n)]. THIS MATTERS because there MIGHT be MORE things in the domain THAN JUST natural numbers. The point is, you CANNOT conclude -- not by induction, anyway -- that something that is true for [1] AND [1 2] AND [1 2 3 ] AND [1 2 3 ] AND [1 2 3 4 ], .etc. IS ALSO true for [1 2 3 4 5 ...] TO INFINITY. THAT IS NOT WHAT INDUCTION *SAYS*, DUMBASS. What it DOES say is that something is true for 1 AND for 2 AND for 3 AND for 4 AND for 5 AND for 6 AND for 7 AND for 8 ... etc., BUT NOT *TO*INFINITY* -- RATHER, IT ONLY says this for infinitely MANY DIFFERENT *FINITE* things, DUMBASS! It does NOT say it for EVEN ONE INFINITE thing!
From: |-|ercules on 1 Jul 2010 04:42 "George Greene" <greeneg(a)email.unc.edu> wrote > On Jun 30, 6:11 pm, "|-|ercules" <radgray...(a)yahoo.com> wrote: >> HAHAHA. >> Are you really that stupid to assume ...? > > I don't NEED to ASSUME! You're right there! Stupid is as stupid does. > > I KNOW what induction is! > > YOU DON'T! > >> >> Does the list >> 0.0 >> 0.1 >> 0.2 >> ... >> 0.9 >> 0.10 >> 0.11 >> ... >> 0.99 >> 0.101 >> ... >> >> use this induction schema too? > > A LIST *CANNOT*USE* "an induction schema" !! > WHY DON'T YOU SIMPLY STATE which induction schema YOU are using??? > > THE STANDARD induction schema requires you to START with a ONE-place > predicate > that takes A NUMBER as a parameter. You can change that from a number > to something > else as LONG as you have a clear notion of what THE SUCCESSOR, THE > NEXT element, > of something, would be. > And in any case, you have THE WRONG list. > The ACTUAL list is > .0 > .1 > .2 > .3 > .4 > .5 > .6 > .7 > .8 > .9 > .01 > .11 > .21 etc. > > It does NOT have .10 after .9 ! > The reason for this is that you need LOTS OF LEADING ZEROS as > prefixes! > You have to spell 10, 100, 1000 etc. FROM RIGHT TO LEFT. >> >> phi( <[1] 2 3 4...> ) & An ((phi ( <[1 2 ... n] n+1 n+2 ...>) -> phi( <[1 2 ... n n+1] n+2 n+3 ...> )) >> -> >> phi( <[1 2 3 4...]> ) > > THIS IS NOT an induction schema, DUMBASS. > The induction schema JUST has phi(0), NOT phi (<[1] 2 3 4>). > Moreover, the conclusion of an induction schema IS NOT > phi(<[1 2 3 4...]>). IT IS, rather and INSTEAD, > An[phi(n)]. > THIS MATTERS because there MIGHT be MORE things in the domain THAN > JUST > natural numbers. > > The point is, you CANNOT conclude -- not by induction, anyway -- that > something that is true for > [1] AND > [1 2] AND > [1 2 3 ] AND > [1 2 3 ] AND > [1 2 3 4 ], .etc. IS ALSO true for > [1 2 3 4 5 ...] TO INFINITY. > THAT IS NOT WHAT INDUCTION *SAYS*, DUMBASS. > What it DOES say is that something is true for > 1 AND > for 2 AND > for 3 AND for > 4 AND for 5 AND for 6 AND for > 7 AND for > 8 ... etc., BUT NOT *TO*INFINITY* -- RATHER, IT ONLY says this for > infinitely MANY DIFFERENT *FINITE* things, DUMBASS! > It does NOT say it for EVEN ONE INFINITE thing! In the words of the commander in the starting scene of Gladiators, "You'd think the savage would know when he is beaten." phi(1) & An (phi(n) -> phi(n +1)) -> An phi(n) Let phi(n) = property-all-sequences holds for n. phi(1) & phi(2) & phi(3) = property-all-sequences holds for 1, 2 & 3. <=> < [1 2 3] 4 5 6...> An phi(n) = property-all-sequences holds for all digits <=> <[1 2 3 4...]> That is impossible to dispute, your argument could now become that property-all-sequences is merely equivalent to property-all-sequences-up-to In the words of Buzz Aldrin, UP TO INFINITY AND BEYOND! Herc
From: |-|ercules on 1 Jul 2010 04:47 "|-|ercules" <radgray123(a)yahoo.com> wrote > In the words of Buzz Aldrin, > > UP TO INFINITY AND BEYOND! > Buzz LIGHTYEAR! Buzz LIGHTYEAR! Herc
From: Don Stockbauer on 1 Jul 2010 07:06 On Jul 1, 3:47 am, "|-|ercules" <radgray...(a)yahoo.com> wrote: > "|-|ercules" <radgray...(a)yahoo.com> wrote > > > In the words of Buzz Aldrin, > > > UP TO INFINITY AND BEYOND! > > Buzz LIGHTYEAR! Buzz LIGHTYEAR! > > Herc Just 2 infinities: 1. Potential. 2. Actualized.
From: Marshall on 1 Jul 2010 11:51
On Jul 1, 4:06 am, Don Stockbauer <donstockba...(a)hotmail.com> wrote: > On Jul 1, 3:47 am, "|-|ercules" <radgray...(a)yahoo.com> wrote: > > > "|-|ercules" <radgray...(a)yahoo.com> wrote > > > > In the words of Buzz Aldrin, > > > > UP TO INFINITY AND BEYOND! > > > Buzz LIGHTYEAR! Buzz LIGHTYEAR! > > > Herc > > Just 2 infinities: > > 1. Potential. > > 2. Actualized. Wow, the cranks are really coming out in force now. Maybe Herc is the crank messiah! Marshall |