Q.E.D.
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From: Sylvia Else on 7 Jul 2010 21:04 On 8/07/2010 10:53 AM, |-|ercules wrote: > "Sylvia Else" <sylvia(a)not.here.invalid> wrote >> On 8/07/2010 10:41 AM, |-|ercules wrote: >>> "Sylvia Else" <sylvia(a)not.here.invalid> wrote >>>> On 8/07/2010 5:11 AM, |-|ercules wrote: >>>>> "Marshall" <marshall.spight(a)gmail.com> wrote >>>>>> On Jul 6, 10:10 pm, "|-|ercules" <radgray...(a)yahoo.com> wrote: >>>>>>> <porky_pig...(a)my-deja.com> wrote ... >>>>>>> >>>>>>> > Reading Stark, Number Theory. The first time he used Q.E.D., >>>>>>> there's a >>>>>>> > footnote: "In English: Quite Easy Done". :-) >>>>>>> >>>>>>> I was just checking sci.math subjects to see if there was a reaction >>>>>>> to my breakthrough infinity proof! >>>>>> >>>>>> http://www.soundboard.com/sb/laugh_track.aspx >>>>> >>>>> At which step are you lost? >>>>> >>>>> >>>>> C10 = 0.12345678910111213141516... >>>>> >>>>> 1/ there's no infinite sequence of pi's digits within C10 (every >>>>> finite >>>>> starting point has a finite ending point) >>>>> 2/ as the length of C10 digit expansion -> oo, the consecutive >>>>> number of >>>>> digits of pi -> oo >>>>> 3/ the length of C10 digit expansion is oo >>>>> 4/ the consecutive number of digits of pi = oo (3) -> (2) >>>>> 5/ CONTRADICTION (1) & (4) >>>>> 6/ THEREFORE no limit exists as the length of digit expansions (of any >>>>> real) -> oo >>>>> 7/ GENERALIZATION no limit exists as the length of sequences (of any >>>>> type) -> oo >>>>> 8/ INFERENCE there is no oo >>>>> >>>>> Quite Easily Done! >>>>> >>>>> Herc >>>>> >>>> >>>> You go from the situation where something tends to infinity to the >>>> situation where something equals infinity, without any justification. >>>> >>>> Sylvia. >>> >>> >>> >>>>> 4/ the consecutive number of digits of pi = oo (3) -> (2) >>> >>> Put variable 3 into equation 2. >>> >> >> Why? There's no justification for doing that. There's no reason to >> think 2 holds for the inifinte case. >> >> Sylvia. > > You could reorganise the proof, > > As x->oo, y->oo > x = oo > > Assume the limit exists. > y=oo > Contradiction > Limit doesn't exist. > Same result, same conclusion. > > y cannot reach infinity > therefore x cannot reach infinity > > Herc I'm at a complete loss to see why you think that proves anything. Anyway, I'm not going to get suckered into this again. I've said my piece. Sylvia.
From: |-|ercules on 7 Jul 2010 21:08 "Sylvia Else" <sylvia(a)not.here.invalid> wrote... > On 8/07/2010 10:53 AM, |-|ercules wrote: >> "Sylvia Else" <sylvia(a)not.here.invalid> wrote >>> On 8/07/2010 10:41 AM, |-|ercules wrote: >>>> "Sylvia Else" <sylvia(a)not.here.invalid> wrote >>>>> On 8/07/2010 5:11 AM, |-|ercules wrote: >>>>>> "Marshall" <marshall.spight(a)gmail.com> wrote >>>>>>> On Jul 6, 10:10 pm, "|-|ercules" <radgray...(a)yahoo.com> wrote: >>>>>>>> <porky_pig...(a)my-deja.com> wrote ... >>>>>>>> >>>>>>>> > Reading Stark, Number Theory. The first time he used Q.E.D., >>>>>>>> there's a >>>>>>>> > footnote: "In English: Quite Easy Done". :-) >>>>>>>> >>>>>>>> I was just checking sci.math subjects to see if there was a reaction >>>>>>>> to my breakthrough infinity proof! >>>>>>> >>>>>>> http://www.soundboard.com/sb/laugh_track.aspx >>>>>> >>>>>> At which step are you lost? >>>>>> >>>>>> >>>>>> C10 = 0.12345678910111213141516... >>>>>> >>>>>> 1/ there's no infinite sequence of pi's digits within C10 (every >>>>>> finite >>>>>> starting point has a finite ending point) >>>>>> 2/ as the length of C10 digit expansion -> oo, the consecutive >>>>>> number of >>>>>> digits of pi -> oo >>>>>> 3/ the length of C10 digit expansion is oo >>>>>> 4/ the consecutive number of digits of pi = oo (3) -> (2) >>>>>> 5/ CONTRADICTION (1) & (4) >>>>>> 6/ THEREFORE no limit exists as the length of digit expansions (of any >>>>>> real) -> oo >>>>>> 7/ GENERALIZATION no limit exists as the length of sequences (of any >>>>>> type) -> oo >>>>>> 8/ INFERENCE there is no oo >>>>>> >>>>>> Quite Easily Done! >>>>>> >>>>>> Herc >>>>>> >>>>> >>>>> You go from the situation where something tends to infinity to the >>>>> situation where something equals infinity, without any justification. >>>>> >>>>> Sylvia. >>>> >>>> >>>> >>>>>> 4/ the consecutive number of digits of pi = oo (3) -> (2) >>>> >>>> Put variable 3 into equation 2. >>>> >>> >>> Why? There's no justification for doing that. There's no reason to >>> think 2 holds for the inifinte case. >>> >>> Sylvia. >> >> You could reorganise the proof, >> >> As x->oo, y->oo >> x = oo >> >> Assume the limit exists. >> y=oo >> Contradiction >> Limit doesn't exist. >> Same result, same conclusion. >> >> y cannot reach infinity >> therefore x cannot reach infinity >> >> Herc > > I'm at a complete loss to see why you think that proves anything. You are ignoring the bit above the QED again! 8/ INFERENCE there is no oo > > Anyway, I'm not going to get suckered into this again. I've said my piece. > > Sylvia. Just say which step you disagree with. Herc
From: Marshall on 8 Jul 2010 00:07 On Jul 7, 12:11 pm, "|-|ercules" <radgray...(a)yahoo.com> wrote: > "Marshall" <marshall.spi...(a)gmail.com> wrote > > > On Jul 6, 10:10 pm, "|-|ercules" <radgray...(a)yahoo.com> wrote: > >> <porky_pig...(a)my-deja.com> wrote ... > > >> > Reading Stark, Number Theory. The first time he used Q.E.D., there's a > >> > footnote: "In English: Quite Easy Done". :-) > > >> I was just checking sci.math subjects to see if there was a reaction to my breakthrough infinity proof! > > >http://www.soundboard.com/sb/laugh_track.aspx > > At which step are you lost? At no point am I lost. However after step 1 you're just tacking words together in an attempt to sound like you know some math. It's not something that's particularly amenable to refutation, because it's not coherent enough to mean anything specific. > C10 = 0.12345678910111213141516... > > 1/ there's no infinite sequence of pi's digits within C10 (every finite starting point has a finite ending point) > 2/ as the length of C10 digit expansion -> oo, the consecutive number of digits of pi -> oo > 3/ the length of C10 digit expansion is oo > 4/ the consecutive number of digits of pi = oo (3) -> (2) > 5/ CONTRADICTION (1) & (4) > 6/ THEREFORE no limit exists as the length of digit expansions (of any real) -> oo > 7/ GENERALIZATION no limit exists as the length of sequences (of any type) -> oo > 8/ INFERENCE there is no oo
From: Transfer Principle on 8 Jul 2010 00:08 On Jul 7, 6:08 pm, "|-|ercules" <radgray...(a)yahoo.com> wrote: > "Sylvia Else" <syl...(a)not.here.invalid> wrote... > > Anyway, I'm not going to get suckered into this again. I've said my piece. > Just say which step you disagree with. In standard theory, step (4) is invalid. In standard theory, it's possible that Chapernowne's constant contains every finite prefix of pi, yet not contain pi itself, just as it is possible for a list to contain every finite prefix of pi and not contain pi itself. This appears to be another case of Herc's induction schema, though I can't be sure since I still don't know what the difference between the angle and square brackets are. It might also be a case of the schema: (Ax (x finite -> phi(x))) -> Ax (phi(x)) Of course, these schemata are invalid in standard theory. Also, strictly speaking, step (1) is invalid as well. It is theoretically possible (though highly unlikely) that the Chapernowne's constant _does_ contain infinitely many digits of pi after all! Note that as of now, about 10^12 digits of pi are known, approximately one trillion. (Actually, since Herc is an Aussie, let me hereby use the international term "billion" instead of "trillion.") And so it's possible that the second billion digits are equal to the first billion digits plus 1, the third billion digits are equal to the first billion digits plus 2, the fourth billion digits are equal to the first billion digits plus 3, and so on. Then Chapernowne's constant will contain all the digits of pi, starting from about the 10^24-th (Aussie "quadrillionth," Yankee "septillionth") digit. This is highly unlikely, but theoretically possible (just as it's possible, though unlikely, that pi contains only finitely many digits other than 0 or 1, an oft-mentioned example of this). As unlikely as its negation may be, it's still not the sort of thing that should be mentioned in any formal _proof_. Notice that the first five digits of pi, "31415," appear unusually early in Chapernowne's constant: C_10 = 0.1234567891011121_31415_16... but we have to go far just to find one more digit, "314159." But of course, Herc is now a finitist, which means that he doesn't work in ZFC at all. In a theory in which every set is finite, the schema: (Ax (x finite -> phi(x))) -> Ax (phi(x)) trivially holds. But Herc wanted to know with which step someone like Else (who does work in ZFC or some other standard theory) would disagree with, and so I answer.
From: |-|ercules on 8 Jul 2010 02:30 "Marshall" <marshall.spight(a)gmail.com> wrote > On Jul 7, 12:11 pm, "|-|ercules" <radgray...(a)yahoo.com> wrote: >> "Marshall" <marshall.spi...(a)gmail.com> wrote >> >> > On Jul 6, 10:10 pm, "|-|ercules" <radgray...(a)yahoo.com> wrote: >> >> <porky_pig...(a)my-deja.com> wrote ... >> >> >> > Reading Stark, Number Theory. The first time he used Q.E.D., there's a >> >> > footnote: "In English: Quite Easy Done". :-) >> >> >> I was just checking sci.math subjects to see if there was a reaction to my breakthrough infinity proof! >> >> >http://www.soundboard.com/sb/laugh_track.aspx >> >> At which step are you lost? > > At no point am I lost. However after step 1 you're just tacking words > together in an attempt to sound like you know some math. It's not > something that's particularly amenable to refutation, because it's > not coherent enough to mean anything specific. > > >> C10 = 0.12345678910111213141516... >> >> 1/ there's no infinite sequence of pi's digits within C10 (every finite starting point has a finite ending point) >> 2/ as the length of C10 digit expansion -> oo, the consecutive number of digits of pi -> oo >> 3/ the length of C10 digit expansion is oo >> 4/ the consecutive number of digits of pi = oo (3) -> (2) >> 5/ CONTRADICTION (1) & (4) >> 6/ THEREFORE no limit exists as the length of digit expansions (of any real) -> oo >> 7/ GENERALIZATION no limit exists as the length of sequences (of any type) -> oo >> 8/ INFERENCE there is no oo Step 2 then? >> 2/ as the length of C10 digit expansion -> oo, the consecutive number of digits of pi -> oo Seems trivial to me. Herc
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