Why can no one in sci.math understand my simple point?
in [Logic]
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From: |-|ercules on 15 Jun 2010 00:13 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) as pi is an infinite digit sequence, this means this list contains every digit of an infinite digit sequence (2) similarly, as computable digit sequences contain increasing lengths of ALL possible finite prefixes the list of computable reals contain every digit of ALL possible infinite sequences (3) OK does everyone get (1) (2) and (3). 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: jaimie on 15 Jun 2010 00:16 Again, nope hoint a tall. "|-|ercules" <radgray123(a)yahoo.com> wrote in message news:87ocucFrn3U1(a)mid.individual.net... > Consider the fact that I have learned to post both numeric and alphabetic > characters; no one nose Y.
From: Peter Webb on 15 Jun 2010 02:15 "|-|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. > 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. > > 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: |-|ercules on 15 Jun 2010 02:49 "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. Given the increasing finite prefixes of e 2 21 218 ... This list contains every digit of the infinite expansion of e. Given the increasing finite prefixes of ALL infinite expansions, that list contains every digit of every infinite expansion. So (3) is true. > the list of computable reals contain every digit of ALL possible infinite > sequences (3) Herc
From: fishfry on 15 Jun 2010 02:58
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." |