Maximum run of one digit in decimal expansion of pi?
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From: spudnik on 24 May 2010 14:03 that's really beautiful, even if it's completely useless ... could you make it into a Turing machine that proves P in/equal NP? the subject of irrationality, and transcendentality, is interesting without these constructions, also. also see, Benson's law (sp.?). > (This doesn't even require the number to be irrational to create a Real with > a maximum run of a single digit being one, but that was the original > question in the context of pi being irrational) thusNso: I was taking monsieur Webb to task, for saying that *any* irrational number has a limited run of digits in *any* integral base ... unless it might be one that was (some how) specifically "constructed" to do that, with no other use for it. if you can't take the heat, get out of the frying-pan, or cut-across the bed of coals. the problem of "0.999.... not equal to one" is, almost always, stated by the math-newbie in those terms; whereas, what is really meant, is if there is a non-infinitessimal difference between the two real numbers, cf. 1.000.... (and, this was all covered in Simon Stevin's booklet, _The Decimals_, way back in when ever .-) after that, comes the wonderful world of p-adics! thusNso: what consistency or species of feces would you like? I clikced on your webpage with the shrine to Hope or Athens, and your "Prime Gaps" page seems to be nothing, but a crude attempt at the sieve of Eristosthenes; congradulations -- you get every turd of that, tossed playfully back at you! are you literate in any language? (this is a big problem on the web, folks .-) > thus: > well, that is where the problem with assigning a particle > to a wave, a la de Broglie et al, comes. the assumption, > that causes folks to say "particle," is that because a quantum > of light is absorbed by one atom of siver dioxide (say, > in the photographic emulsion; or, other detector) --some how-- > that it must be that a rock of light hit the electronic orbital > (although > this is never specified, as to how it could be, and the whole problem > of EM is also hard to describe, and variously is). > > this is really all of a confusion from Newton's "geometrical optics," > that is, the "ray" of light, which is just one "normal" > to the wave (or Huyghens wavelet). > thus: > about your five "cloture" events, the real problem is that > "the Fed" was never properly ratified (and is unconstitutional > for that reason, if not directly; it is modeled > upon the Federal Reserve System > of England). of coursel the 527 cmtes. have essentially taken > over the TV advertizing on all national issues & candidates, > through an Act that was passed unaanimously in both houses. > > "Senate rules don't trump the Constitution" --http://GreaterVoice.org/60 > > thus: > I've been saying, for a while, that if "green" gasoline can > be made, and gasoline fuel cells, what is the problem > with Fossilized Fuels (TM), which ain't fossilized? ... anyway, > see "Green Freedom" in the article, > which is not quite what I was refering to! thusNso: Young's two-pinhole experiment was the thing that killed the corpuscle o'light, so that anomalous & highly particular (sik) set-ups with giant molecules are only of pecuniary interest ... er, what ever "pecuniary" means, you have to actually look at the "particulars" of the write-up with the fullerenes, to be able to say any thing of interest -- to make a hypothesis, beyond regurgtiating their delciious resultage. see, you did not even bother to deal with the whole idea of duality, that Pascal essntially created in projective geometry (cf., "two-column proofs" .-) another way to "check" your theory -- iff it is one -- would be to explain Snell's law, electromagnetically and/or with aether ... even if it is an "undefined element" of your axioms. > The 'particle' associated with the photon wave enters and exits a > single slit. The 'particle' occupies a very small region of the wave. thusNso: yeah, but you don't need the particle, at all; your theory says nothing, at all, either, at least til you attempt to make it do some thing. one way to "check" it, would be to explain permitivity & permeability with the theory, if it is a theory & not just typing & macro-ing practice. > The associated wave exits the both slits and creates interference > which alters the direction the particle travels. thusNso: being legally enjoined from using the googolplex, what's YUV? thusNso: complainant: there's a series of his books from Cambridge U. Press, paperback, very nice, but they want $45 for the one that I was peruzing at the bookstore! (I think, I'd bought one of these, before, for about $25, although I lost it.) the titles of these seem generally to be a list of three subjects, _This, That and Another Thing_, although also the usual format of several independent essays/chapters. r.i.p., MG. --Pi, the surfer's canonical value -- accept no other! http://wlym.com
From: spudnik on 24 May 2010 14:18 OK, I'll simply conjecture that pi has no limited runs of any digit in any digital base, possibly excepting base-infinity, but including base-one (well, it probably isn't readily digestable in either format). the only "reason" for this is that of Liebniz, that nothing is proven til both neccesity & sufficiency is proven, although in this case, I'd settle for neccesity. certainly, it is neccesary that such constructions as you have all given, be possible -- a-men!... I mean, how about the number 1.6363636363....? thusNso: that's really beautiful, even if it's completely useless ... could you make it into a Turing machine that proves P in/equal NP? the subject of irrationality, and transcendentality, is interesting without these constructions, also. also see, Benson's law (sp.?). thusNso: if you can't take the heat, get out of the frying-pan, or cut-across the bed of coals. the problem of "0.999.... not equal to one" is, almost always, stated by the math-newbie in those terms; whereas, what is really meant, is if there is a non-infinitessimal difference between the two real numbers, cf. 1.000.... (and, this was all covered in Simon Stevin's booklet, _The Decimals_, way back in when ever .-) after that, comes the wonderful world of p-adics! thusNso: what consistency or species of feces would you like? I clikced on your webpage with the shrine to Hope or Athens, and your "Prime Gaps" page seems to be nothing, but a crude attempt at the sieve of Eristosthenes; congradulations -- you get every turd of that, tossed playfully back at you! are you literate in any language? (this is a big problem on the web, folks .-) > thus: > well, that is where the problem with assigning a particle > to a wave, a la de Broglie et al, comes. the assumption, > that causes folks to say "particle," is that because a quantum > of light is absorbed by one atom of siver dioxide (say, > in the photographic emulsion; or, other detector) --some how-- > that it must be that a rock of light hit the electronic orbital > (although > this is never specified, as to how it could be, and the whole problem > of EM is also hard to describe, and variously is). > > this is really all of a confusion from Newton's "geometrical optics," > that is, the "ray" of light, which is just one "normal" > to the wave (or Huyghens wavelet). > thus: > about your five "cloture" events, the real problem is that > "the Fed" was never properly ratified (and is unconstitutional > for that reason, if not directly; it is modeled > upon the Federal Reserve System > of England). of coursel the 527 cmtes. have essentially taken > over the TV advertizing on all national issues & candidates, > through an Act that was passed unaanimously in both houses. > > "Senate rules don't trump the Constitution" --http://GreaterVoice.org/60 > > thus: > I've been saying, for a while, that if "green" gasoline can > be made, and gasoline fuel cells, what is the problem > with Fossilized Fuels (TM), which ain't fossilized? ... anyway, > see "Green Freedom" in the article, > which is not quite what I was refering to! thusNso: Young's two-pinhole experiment was the thing that killed the corpuscle o'light, so that anomalous & highly particular (sik) set-ups with giant molecules are only of pecuniary interest ... er, what ever "pecuniary" means, you have to actually look at the "particulars" of the write-up with the fullerenes, to be able to say any thing of interest -- to make a hypothesis, beyond regurgtiating their delciious resultage. see, you did not even bother to deal with the whole idea of duality, that Pascal essntially created in projective geometry (cf., "two-column proofs" .-) another way to "check" your theory -- iff it is one -- would be to explain Snell's law, electromagnetically and/or with aether ... even if it is an "undefined element" of your axioms. > The 'particle' associated with the photon wave enters and exits a > single slit. The 'particle' occupies a very small region of the wave. thusNso: yeah, but you don't need the particle, at all; your theory says nothing, at all, either, at least til you attempt to make it do some thing. one way to "check" it, would be to explain permitivity & permeability with the theory, if it is a theory & not just typing & macro-ing practice. > The associated wave exits the both slits and creates interference > which alters the direction the particle travels. thusNso: being legally enjoined from using the googolplex, what's YUV? thusNso: complainant: there's a series of his books from Cambridge U. Press, paperback, very nice, but they want $45 for the one that I was peruzing at the bookstore! (I think, I'd bought one of these, before, for about $25, although I lost it.) the titles of these seem generally to be a list of three subjects, _This, That and Another Thing_, although also the usual format of several independent essays/chapters. r.i.p., MG. --Pi, the surfer's canonical value -- accept no other! http://wlym.com
From: Transfer Principle on 24 May 2010 14:50 On May 24, 10:51 am, Aatu Koskensilta <aatu.koskensi...(a)uta.fi> wrote: > Transfer Principle <lwal...(a)lausd.net> writes: > > So spudnik correctly points out that in both computer science and set > > theory, the real object 0.999... is not literally equal to the integer > > object 1. It definitely puts a new twist on the long-running debate > > about 0.999... and 1. > No it doesn't. I was careful to avoid grouping posters, yet Aatu implies that I'm still misinterpreting. To fix my error, I notice that spudnik does clarify what he is discussing: > > > the problem of "0.999.... not equal to one" is, > > > almost always, stated by the math-newbie in those terms; > > > whereas, what is really meant, is if there is a non-infinitessimal > > > between the two real numbers, cf. 1.000.... (and, > > > this was all covered in Simon Stevin's booklet, > > > _The Decimals_, way back in when ever .-) So Aatu and spudnik do point out that the poster who asks about 0.999... and 1 is asking whether the two numbers, considered as _reals_, are equal to each other. I was only pointing out that by a _loophole_ in the definition, one could argue that 0.999... and 1 really are different. I will accept Aatu and spudnik's explanation that mentioning the real 0.999... and the integer 1 in a thread started by a newbie is counterproductive hence a bad idea. > The "debate" has nothing to do with the tedious technical > details you mention. What tedious technical details? Does Aatu mean the construction of the reals from D-cuts and C-sequences, or something similar? If so, then maybe the next time there's a 0.999... thread, and someone tells the OP that he's wrong and mentions D-cuts or C-sequences, perhaps I'll quote Aatu that these are merely "tedious technical details" ...
From: Peter Webb on 24 May 2010 22:34 "spudnik" <Space998(a)hotmail.com> wrote in message news:81708225-06eb-4bfa-b8e1-b0bc9ff196d3(a)q23g2000vba.googlegroups.com... >I was taking monsieur Webb to task, for saying that > *any* irrational number has a limited run of digits > in *any* integral base ... unless it might be one > that was (some how) specifically "constructed" to do that, > with no other use for it. > I didn't say that, and its not true. > if you can't take the heat, get out of the frying-pan, or > reduce the size of teh bed of coals to traverse. > Or actually quote me properly. > the problem of "0.999.... not equal to one" is, > almost always, stated by the math-newbie in those terms; > whereas, what is really meant, is if there is a non-infinitessimal > difference > between the two real numbers, cf. 1.000.... (and, > this was all covered in Simon Stevin's booklet, > _The Decimals_, way back in when ever .-) > I didn't even discuss whether 0.999... = 1, or anything to do with it. That has been done to death in this newsgroup, the FAQ, and elsewhere.
From: Aatu Koskensilta on 25 May 2010 13:03
Transfer Principle <lwalke3(a)lausd.net> writes: > So Aatu and spudnik do point out that the poster who asks about > 0.999... and 1 is asking whether the two numbers, considered as > _reals_, are equal to each other. I was only pointing out that by a > _loophole_ in the definition, one could argue that 0.999... and 1 > really are different. Yes, yes, very clever of you. But also totally uninteresting and pointless. -- Aatu Koskensilta (aatu.koskensilta(a)uta.fi) "Wovon man nicht sprechan kann, dar�ber muss man schweigen" - Ludwig Wittgenstein, Tractatus Logico-Philosophicus |