Why can no one in sci.math understand my simple point?
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From: |-|ercules on 15 Jun 2010 03:28 "fishfry" <BLOCKSPAMfishfry(a)your-mailbox.com> wrote > In article <87ocucFrn3U1(a)mid.individual.net>, > "|-|ercules" <radgray123(a)yahoo.com> wrote: > >> Consider the list of increasing lengths of finite prefixes of pi >> >> 3 >> 31 >> 314 >> 3141 >> .... >> >> Everyone agrees that: >> this list contains every digit of pi (1) >> > > No, I don't agree, so "Everyone agrees that ..." is false. > > The list consists of a collection of integers. Item n on the list are > the first n digits of pi, starting from 3 and ignoring the decimal > point. So the 1000th item on the list is 31... pi to 1000 places. > > There is no one element of the list that contains pi in its entirety. > And the reason is because each 'n' represents a FINITE NUMBER. Like 6, > or 100043, or a zillion eleven. And on that line we find a zillion > eleven digits of pi. But no more! > > No one item on the list contains pi in its entirety. > > Do you understand that? > > What is true is that: if you ask me for, say, pi to a trillion digits, > I'll say, "No problem, here it is, it's the trillionth item on the > list." > > But if you ask me for ALL the digits of pi, I have to say, "Sorry, > that's not on the list." How many digits of pi do all the list's members contain? Herc
From: Derek Holt on 15 Jun 2010 04:03 On 15 June, 07:15, "Peter Webb" <webbfam...(a)DIESPAMDIEoptusnet.com.au> wrote: > "|-|ercules" <radgray...(a)yahoo.com> wrote in message > > news:87ocucFrn3U1(a)mid.individual.net... > > > Consider the list of increasing lengths of finite prefixes of pi > > > 3 > > 31 > > 314 > > 3141 > > .... > > > Everyone agrees that: > > this list contains every digit of pi (1) > > Sloppy terminology, but I agree with what I think you are trying to say. > > > as pi is an infinite digit sequence, this means > > > this list contains every digit of an infinite digit sequence (2) > > Again sloppy, but basically true. > > > similarly, as computable digit sequences contain increasing lengths of ALL > > possible finite prefixes > > Not "similarly", but if you are claiming that all Reals which have finite > decimal expansions can be listed, this is correct. > > > the list of computable reals contain every digit of ALL possible infinite > > sequences (3) > > No. You cannot form a list of all computable Reals. If you could do this, > then you could use a diagonal argument to construct a computable Real not in > the list. A little more precisely, there does not exist a computable bijection from the natural numbers to the set of all computable reals. But the set of computable reals is of course countable so there does exist a list of all computable reals - but not a computable list. Derek Holt. > > OK does everyone get (1) (2) and (3). > > No. (3) is not true, as it is based on a false premise (that the computable > Reals can be listed). > > > There's no need for bullying (George), it's just a maths theory. Address > > the statements and questions and add your own. > > > Herc > > -- > > If you ever rob someone, even to get your own stuff back, don't use the > > phrase > > "Nobody leave the room!" ~ OJ Simpson > >
From: Peter Webb on 15 Jun 2010 04:28 "|-|ercules" <radgray123(a)yahoo.com> wrote in message news:87oodjFn51U1(a)mid.individual.net... > "fishfry" <BLOCKSPAMfishfry(a)your-mailbox.com> wrote >> In article <87ocucFrn3U1(a)mid.individual.net>, >> "|-|ercules" <radgray123(a)yahoo.com> wrote: >> >>> Consider the list of increasing lengths of finite prefixes of pi >>> >>> 3 >>> 31 >>> 314 >>> 3141 >>> .... >>> >>> Everyone agrees that: >>> this list contains every digit of pi (1) >>> >> >> No, I don't agree, so "Everyone agrees that ..." is false. >> >> The list consists of a collection of integers. Item n on the list are the >> first n digits of pi, starting from 3 and ignoring the decimal point. So >> the 1000th item on the list is 31... pi to 1000 places. >> >> There is no one element of the list that contains pi in its entirety. And >> the reason is because each 'n' represents a FINITE NUMBER. Like 6, or >> 100043, or a zillion eleven. And on that line we find a zillion eleven >> digits of pi. But no more! No one item on the list contains pi in its >> entirety. >> >> Do you understand that? >> >> What is true is that: if you ask me for, say, pi to a trillion digits, >> I'll say, "No problem, here it is, it's the trillionth item on the list." >> But if you ask me for ALL the digits of pi, I have to say, "Sorry, that's >> not on the list." > > > How many digits of pi do all the list's members contain? > > Herc > All of them. But no single member of the list contains all digits of pi. Pi doesn't appear anywhere on the list.
From: Peter Webb on 15 Jun 2010 04:29 "|-|ercules" <radgray123(a)yahoo.com> wrote in message news:87om34FahrU1(a)mid.individual.net... > "Peter Webb" <webbfamily(a)DIESPAMDIEoptusnet.com.au> wrote >> "|-|ercules" <radgray123(a)yahoo.com> wrote in message >> news:87ocucFrn3U1(a)mid.individual.net... >>> Consider the list of increasing lengths of finite prefixes of pi >>> >>> 3 >>> 31 >>> 314 >>> 3141 >>> .... >>> >>> Everyone agrees that: >>> this list contains every digit of pi (1) >>> >> >> Sloppy terminology, but I agree with what I think you are trying to say. >> >>> as pi is an infinite digit sequence, this means >>> >>> this list contains every digit of an infinite digit sequence (2) >>> >> >> Again sloppy, but basically true. >> >>> similarly, as computable digit sequences contain increasing lengths of >>> ALL possible finite prefixes >>> >> >> Not "similarly", but if you are claiming that all Reals which have finite >> decimal expansions can be listed, this is correct. > > You didn't follow the similarity. > > Given the increasing finite prefixes of pi > > 3 > 31 > 314 > .. > > This list contains every digit of the infinite expansion of pi. > But pi doesn't appear on the list. So?
From: |-|ercules on 15 Jun 2010 05:21
"Peter Webb" <webbfamily(a)DIESPAMDIEoptusnet.com.au> wrote > "|-|ercules" <radgray123(a)yahoo.com> wrote in message > news:87om34FahrU1(a)mid.individual.net... >> "Peter Webb" <webbfamily(a)DIESPAMDIEoptusnet.com.au> wrote >>> "|-|ercules" <radgray123(a)yahoo.com> wrote in message >>> news:87ocucFrn3U1(a)mid.individual.net... >>>> Consider the list of increasing lengths of finite prefixes of pi >>>> >>>> 3 >>>> 31 >>>> 314 >>>> 3141 >>>> .... >>>> >>>> Everyone agrees that: >>>> this list contains every digit of pi (1) >>>> >>> >>> Sloppy terminology, but I agree with what I think you are trying to say. >>> >>>> as pi is an infinite digit sequence, this means >>>> >>>> this list contains every digit of an infinite digit sequence (2) >>>> >>> >>> Again sloppy, but basically true. >>> >>>> similarly, as computable digit sequences contain increasing lengths of >>>> ALL possible finite prefixes >>>> >>> >>> Not "similarly", but if you are claiming that all Reals which have finite >>> decimal expansions can be listed, this is correct. >> >> You didn't follow the similarity. >> >> Given the increasing finite prefixes of pi >> >> 3 >> 31 >> 314 >> .. >> >> This list contains every digit of the infinite expansion of pi. >> > > But pi doesn't appear on the list. > > So? that doesn't matter, because that's a convergent sequence. This is what matters. > the list of computable reals contain every digit of ALL possible infinite > sequences (3) Do you now agree with (3) ? Herc |