https://groups.google.com/d/forum/sci.mathsci.mathMathematical discussions and pursuits.Google GroupsJustin Thyme2015-11-26T22:52:35Zhttps://groups.google.com/d/topic/sci.math/URtFahR_aGoRe: So many zeros, also infinity defined.. Theory of a method roughed in.>> On the other hand, I find your statement >> "if (1-1) is defined as +/-y" >> to be worrisome. > > In a way I do to. For two reasons: It is widely believed that 1 - 1 = 0. Do you have an alternative theory of subtraction (or perhaps subtraction and unity) in which that is not so?Simon Roberts2015-11-26T22:05:21Zhttps://groups.google.com/d/topic/sci.math/URtFahR_aGoRe: So many zeros, also infinity defined.. Theory of a method roughed in.of a > > method related to "transfinite numbers". These numbers are not transfinite. > > Also found, was a reference to division by zero: > > https://en.wikipedia.org/wiki/Division_by_zero. > > It the consensus is that division by zero is undefined. I contend that it > > does not haveJulio Di Egidio2015-11-26T21:50:32Zhttps://groups.google.com/d/topic/sci.math/-EMwTyl260ERe: Properties of numbers with a twistNope: a number is "what we can do with it"... JulioArchimedes Plutonium2015-11-26T21:35:27Zhttps://groups.google.com/d/topic/sci.math/nIBGPP9y4zMCalculus made supereasy by polynomials defining all functionsAlright, I need to rewrite the High School text on Calculus of its 10 pages, because of the importance of the well defined function is a polynomial. Now I first thought we can throw out the Chain Rule and Arclength and so many other contraptions of Old Math, but as it comes to pass, whatArchimedes Plutonium2015-11-26T21:19:57Zhttps://groups.google.com/d/topic/sci.math/bVU08qmggBURe: high theory question of why the Maxwell Equations are pre-structuredOn Wednesday, November 25, 2015 at 2:43:02 PM UTC-6, Archimedes Plutonium wrote: > Now it is going to take me some time to get the experiment set up to report data, and in the meantime I have unanswered questions of high theory value. > > The highest theory value question is why and whetherJustin Thyme2015-11-26T19:35:27Zhttps://groups.google.com/d/topic/sci.math/-EMwTyl260ERe: Properties of numbers with a twistJust to get it clear in my own mind, and considering the natural numbers 0,1,2,... . We might defined "x < y" to mean "there is a z such that 1 + z + x = y". So we have defined the property "being less than" in terms of the operation of addition. And are you interested in properties eitherRoss A. Finlayson2015-11-26T19:10:19Zhttps://groups.google.com/d/topic/sci.math/57ulAJDeXKMRe: What is "applied" mathOn Thursday, November 26, 2015 at 11:07:46 AM UTC-8, Ross A. Finlayson wrote: > On Thursday, November 26, 2015 at 10:50:54 AM UTC-8, Arturo Magidin wrote: > > On Thursday, November 26, 2015 at 12:37:49 PM UTC-6, Ross A. Finlayson wrote: > > > On Thursday, November 26, 2015 at 6:57:29 AM UTC-8,Ross A. Finlayson2015-11-26T19:07:46Zhttps://groups.google.com/d/topic/sci.math/57ulAJDeXKMRe: What is "applied" mathwrote: > > On Thursday, November 26, 2015 at 6:57:29 AM UTC-8, FredJeffries wrote: > > > <quote> > > > C*-algebras are an esoteric subject - "the most abstract nonsense that exists in mathematics" > > > </quote> > > > > > > https://www.quantamagazine.org/20151124-kadison-singer-math-problem/Dan Christensen2015-11-26T19:05:05Zhttps://groups.google.com/d/topic/sci.math/-EMwTyl260ERe: Properties of numbers with a twistOn Thursday, November 26, 2015 at 11:55:10 AM UTC-5, seim...@gmail.com wrote: > Hi, > > When we google "properties of numbers" we see > associativity, commutavity, distributivity, etc. > > This instantly draws one's attention to properties > as in operations applied toArturo Magidin2015-11-26T18:57:00Zhttps://groups.google.com/d/topic/sci.math/-EMwTyl260ERe: Properties of numbers with a twistOn Thursday, November 26, 2015 at 10:55:10 AM UTC-6, seim...@gmail.com wrote: > Hi, > > When we google "properties of numbers" we see > associativity, commutavity, distributivity, etc. > > This instantly draws one's attention to properties > as in operations applied toArturo Magidin2015-11-26T18:55:04Zhttps://groups.google.com/d/topic/sci.math/8ZOqsN6JMSgRe: Error in Edgar, Number TheoryOn Thursday, November 26, 2015 at 6:12:07 AM UTC-6, quasi wrote: > While my current preference is to allow 0|0 (since 0 = 0*0), > I just wanted to point out that a significant proportion of > well regarded texts explicitly disallow it. I think it used to be disallowed because of the idea thatArturo Magidin2015-11-26T18:50:54Zhttps://groups.google.com/d/topic/sci.math/57ulAJDeXKMRe: What is "applied" mathOn Thursday, November 26, 2015 at 12:37:49 PM UTC-6, Ross A. Finlayson wrote: > On Thursday, November 26, 2015 at 6:57:29 AM UTC-8, FredJeffries wrote: > > <quote> > > C*-algebras are an esoteric subject - "the most abstract nonsense that exists in mathematics" > > </quote> > > > > https://wRoss A. Finlayson2015-11-26T18:37:49Zhttps://groups.google.com/d/topic/sci.math/57ulAJDeXKMRe: What is "applied" mathexists in mathematics" > </quote> > > https://www.quantamagazine.org/20151124-kadison-singer-math-problem/ Are these C^\infty or C^{0..\infty}, these? Are C* like the Kleene star and representing any matching, through the unbounded alphabet, or, all, or even: each and every? Or, maybeRoss A. Finlayson2015-11-26T18:29:58Zhttps://groups.google.com/d/topic/sci.math/-EMwTyl260ERe: Properties of numbers with a twistNumbers are usually useful members of spaces that maintain inequalities, for example, under operations, as to establish values, for value spaces. About matrices and general matrix products and their reversibility or lack thereof, in cumulants, orthogonants, and other evolutive terms inBill2015-11-26T18:18:02Zhttps://groups.google.com/d/topic/sci.math/-EMwTyl260ERe: Properties of numbers with a twistMaybe you would be happy with a vector space over the binary field (base 2)? Look at the set of 2 by 2 matrices under multiplication, and you'll see they lack plenty of the properties you wish to avoid. > > Sincerely, > Seima Rao. > > >Bill2015-11-26T18:08:57Zhttps://groups.google.com/d/topic/sci.math/bCUbQeqy9tsRe: History: Walter Rudin, Georg CantorThank you for a very interesting post! (please excuse my top-posting). "Jürgen R." wrote: > In Rudin's autobiography there is an interesting commentary on his > dissertation. The topic is uniqueness of series of spherical harmonics. > > What Rudin proves is the analogue of Cantor's theoremsFredJeffries2015-11-26T17:32:34Zhttps://groups.google.com/d/topic/sci.math/oSonkAluUZIRe: Colouring the Binary Treesize when transferred to another location. No bijections possiblke between sets written in different places of a sheet of paper. Hey, Professor! Words DO change their meaning in differing contexts and circumstances and at different times. It is your magic spells which must always and everywhereFredJeffries2015-11-26T17:29:13Zhttps://groups.google.com/d/topic/sci.math/bCUbQeqy9tsRe: History: Walter Rudin, Georg CantorIn fact, the Professor, being unwilling or unable to master the techniques of abstraction and metaphor, was outstripped 20,000 years ago: http://www.realclearscience.com/blog/2015/11/the_earliest_evidence_of_logical_reasoning.htmlAlan Smaill2015-11-26T17:10:13Zhttps://groups.google.com/d/topic/sci.math/x9QQJm_Zv-URe: The trap of uncountabilityWM <wolfgang.m...@hs-augsburg.de> writes: > Am Donnerstag, 26. November 2015 13:15:07 UTC+1 schrieb Alan Smaill: > >> > There is no algorithm that outputs each natural number because at >> > every step most of them are missing. >> >> I did not say otherwise; >> I referred to properties ofBast...@aol.com2015-11-26T16:55:51Zhttps://groups.google.com/d/topic/sci.math/GFxKQRD9qDgRe: Note about my booksHello: I have to clarify that we have got a lot of solving on my PDF files of CDs. Computations are very heavy and lengthy. You need to have at least 4 GB memory on computer. Some PDF files contain over 400 pages of computations. Volume 1 is fully instructional. It will teach you step byseim...@gmail.com2015-11-26T16:55:10Zhttps://groups.google.com/d/topic/sci.math/-EMwTyl260EProperties of numbers with a twistHi, When we google "properties of numbers" we see associativity, commutavity, distributivity, etc. This instantly draws one's attention to properties as in operations applied to numbers. Is there a field of algebra or math that studies properties of numbers devoid ofWM2015-11-26T16:45:33Zhttps://groups.google.com/d/topic/sci.math/x9QQJm_Zv-URe: The truth of uncountabilityalgorithm > > > > > > is listed. > > > > > > > > > > But those very infinite regressions that WM specifically requires > > > > > are forbidden in all sane set theories. > > > > > > > > Whether or not they are forbiddeen in what you consider "sane" > > > > threories is irrelevant. It isWM2015-11-26T16:45:32Zhttps://groups.google.com/d/topic/sci.math/x9QQJm_Zv-URe: The trap of uncountabilityAm Donnerstag, 26. November 2015 13:15:07 UTC+1 schrieb Alan Smaill: > > There is no algorithm that outputs each natural number because at > > every step most of them are missing. > > I did not say otherwise; > I referred to properties of only those algorithms that *are* output. > > For theWM2015-11-26T16:39:45Zhttps://groups.google.com/d/topic/sci.math/x9QQJm_Zv-URe: The trap of uncountabilityon the contrary. There infinite may by finished. But all these details are irrelevant. There is one simple touchstone that allows to distinguish between useless matheology and useful mathematics. It is this unary representation of all natural numbers n < aleph_0: o oo ooo ... If we assumecasagi...@optonline.net2015-11-26T16:28:26Zhttps://groups.google.com/d/topic/sci.math/sUXMSkKNxSwRe: Gravity Simulation (0/1)On Wed, 25 Nov 2015 20:08:01 -0500, casagi...@optonline.net wrote: >FYI ... > >https://cdburnerxp.se/help/Data/copydata > >On Wed, 25 Nov 2015 17:33:53 +0000 (UTC), Jens Stuckelberger ><Jens_Stuc...@nowhere.net> wrote: > >>On Wed, 25 Nov 2015 08:49:09 -0500, casagiannoni wrote: >> >>> IWM2015-11-26T16:23:15Zhttps://groups.google.com/d/topic/sci.math/oSonkAluUZIRe: Colouring the Binary TreeAm Donnerstag, 26. November 2015 15:04:43 UTC+1 schrieb Martin Shobe: > > Without translation invariance every proof would fail. > > Very few proofs require translation invariance. Wrong. Every word could change its meaning, every number could change its size when transferred to anotherJens Stuckelberger2015-11-26T16:13:09Zhttps://groups.google.com/d/topic/sci.math/sUXMSkKNxSwRe: Gravity Simulation (0/1)On Wed, 25 Nov 2015 19:24:57 -0500, casagiannoni wrote: > Well, the program's attached, Where? I can't see any attachements in any of your posts.Virgil2015-11-26T15:44:46Zhttps://groups.google.com/d/topic/sci.math/bCUbQeqy9tsRe: History: Walter Rudin, Georg CantorIn article <n36pel$tqa$1...@dont-email.me>, "Jürgen R." <jur...@web.de> wrote: > In Rudin's autobiography there is an interesting commentary on his > dissertation. The topic is uniqueness of series of spherical harmonics. > > What Rudin proves is the analogue of Cantor's theorems on theFredJeffries2015-11-26T15:42:13Zhttps://groups.google.com/d/topic/sci.math/x9QQJm_Zv-URe: The truth of uncountability> > Only a highly foolish mind can think so. "Real" means real. > > Are the numbers we label as mathematically "real" numbers any more real > in any non-mathematical meaning of the word than the ones we label as > "imaginary"? But the Professor knows nothing about mathematical definitions.Virgil2015-11-26T15:39:02Zhttps://groups.google.com/d/topic/sci.math/x9QQJm_Zv-URe: The truth of uncountabilityIn article <n374b9$l07$1...@dont-email.me>, Martin Shobe <martin...@yahoo.com> wrote: > On 11/26/2015 1:30 AM, Virgil wrote: > > In article <0203bf22-be5d-4e76-87ec-60bf1879aa32@googlegroups.com>, > > WM <wolfgang.m...@hs-augsburg.de> wrote: > > > >> Am Mittwoch, 25. November 2015 22:42:44Virgil2015-11-26T15:27:48Zhttps://groups.google.com/d/topic/sci.math/x9QQJm_Zv-URe: The truth of uncountabilityIn article <9457d7d2-44ac-495a-a14c-523bdb6aaa75@googlegroups.com>, WM <wolfgang.m...@hs-augsburg.de> wrote: > Am Donnerstag, 26. November 2015 08:30:46 UTC+1 schrieb Virgil: > > In article <0203bf22-be5d-4e76-87ec-60bf1879aa32@googlegroups.com>, > > WM <wolfgang.m...@hs-augsburg.de> wrote:FredJeffries2015-11-26T15:22:50Zhttps://groups.google.com/d/topic/sci.math/x9QQJm_Zv-URe: The trap of uncountabilityThat may be the "definition" in mysticism and magic, but, fortunately, science and mathematics have more useful definitions. Hey, Professor! Clue: we already have a word meaning "incomplete". It's "incomplete".Dan Christensen2015-11-26T15:16:34Zhttps://groups.google.com/d/topic/sci.math/DAJjfGAr5aAMore goofy math spam from JGWhat you should know about the Psycho Troll John Gabriel, in his own words: JG's God Complex: "I am the Creator of this galaxy." -- March 19, 2015 "I am the last word on everything." -- May 6, 2015 "Whatever I imagine is real because whatever I imagine is well defined." -- March 26,Dan Christensen2015-11-26T15:14:42Zhttps://groups.google.com/d/topic/sci.math/k1p13gBdD_ERe: Even Newton had blond moments...What you should know about the Psycho Troll John Gabriel, in his own words: JG's God Complex: "I am the Creator of this galaxy." -- March 19, 2015 "I am the last word on everything." -- May 6, 2015 "Whatever I imagine is real because whatever I imagine is well defined." -- March 26,Virgil2015-11-26T15:13:58Zhttps://groups.google.com/d/topic/sci.math/oSonkAluUZIRe: Colouring the Binary TreeIn article <n373cq$i1a$1...@dont-email.me>, Martin Shobe <martin...@yahoo.com> wrote: > On 11/26/2015 12:56 AM, WM wrote: > > Am Donnerstag, 26. November 2015 03:36:48 UTC+1 schrieb Martin Shobe: > > > > > >>> If finally there were aleph_0 columns, then translation invariance of > >>>Virgil2015-11-26T15:08:02Zhttps://groups.google.com/d/topic/sci.math/oSonkAluUZIRe: Colouring the Binary TreeIn article <38ad9098-a81b-47ac-bea1-a2e11a5d6ebd@googlegroups.com>, WM <wolfgang.m...@hs-augsburg.de> wrote: > Am Donnerstag, 26. November 2015 08:48:08 UTC+1 schrieb Virgil: > > > > What sets does WM claim are simultaneously less-infinite than aleph_0 > > and still infinite? > > AllVirgil2015-11-26T15:03:12Zhttps://groups.google.com/d/topic/sci.math/x9QQJm_Zv-URe: The trap of uncountabilityIn article <1d1d5670-afa6-4695-adf5-53cca6f0906b@googlegroups.com>, WM <wolfgang.m...@hs-augsburg.de> wrote: > I need not ponder about that topic THose who so limit themselves are putzers\s, not ponderers! -- Virgil "Mit der Dummheit kampfen Gotter selbst vergebens." (Schiller)FredJeffries2015-11-26T14:57:29Zhttps://groups.google.com/d/topic/sci.math/57ulAJDeXKMWhat is "applied" math<quote> C*-algebras are an esoteric subject - "the most abstract nonsense that exists in mathematics" </quote> https://www.quantamagazine.org/20151124-kadison-singer-math-problem/Dave Smith2015-11-26T14:49:47Zhttps://groups.google.com/d/topic/sci.math/IE3aULG_wSgRe: Reductio Ad Absurdum.Shut up, idiot. "John Gabriel" wrote in message news:b7283e00-bc9f-4d6f-939e-34b619282199@googlegroups.com...Danny Green2015-11-26T14:45:53Zhttps://groups.google.com/d/topic/sci.math/GFxKQRD9qDgRe: Note about my books1) google-poster 2) aol.com 3) idiotMartin Shobe2015-11-26T14:20:55Zhttps://groups.google.com/d/topic/sci.math/x9QQJm_Zv-URe: The truth of uncountabilityYou need to get out more. Look into non-well-founded set theories like Quine's NF. Martin ShobeMartin Shobe2015-11-26T14:04:43Zhttps://groups.google.com/d/topic/sci.math/oSonkAluUZIRe: Colouring the Binary Treemathematical expressions would be violated. That is a contradiction. >> >> Only if you can prove that translation invariance holds. Good luck with >> that. > > No proof required. So, no contradiction. The proof is required for there to be a contradiction. > Without translation invarianceJohn Gabriel2015-11-26T12:24:15Zhttps://groups.google.com/d/topic/sci.math/bCUbQeqy9tsRe: History: Walter Rudin, Georg CantorWalter Rudin and Cantor were a couple of nobodies.Alan Smaill2015-11-26T12:15:07Zhttps://groups.google.com/d/topic/sci.math/x9QQJm_Zv-URe: The trap of uncountabilityWM <wolfgang.m...@hs-augsburg.de> writes: > Am Donnerstag, 26. November 2015 11:05:12 UTC+1 schrieb Alan Smaill: >> WM <wolfgang.m...@hs-augsburg.de> writes: >> >> > Am Mittwoch, 25. November 2015 15:30:14 UTC+1 schrieb Alan Smaill: >> >> WM <wolfgang.m...@hs-augsburg.de> writes: >> >> >> >>quasi2015-11-26T12:12:07Zhttps://groups.google.com/d/topic/sci.math/8ZOqsN6JMSgRe: Error in Edgar, Number TheoryMany respected number theory texts (but perhaps not a majority) define a|b with the restriction a != 0. Here are some examples of texts which make that restriction: Baker A Comprehensive Course in Number Theory 2012 Hardy & Wright An Introduction to the Theory of Numbers, 4th Ed 1960WM2015-11-26T11:39:08Zhttps://groups.google.com/d/topic/sci.math/x9QQJm_Zv-URe: The truth of uncountabilityOnly a highly foolish mind can think so. "Real" means real. Regards, WMWM2015-11-26T11:38:45Zhttps://groups.google.com/d/topic/sci.math/x9QQJm_Zv-URe: The trap of uncountabilitythe > >> > definition that infinite means incomplete. > >> > >> You really don't want to answer the question, do you? > >> > >> What is your personal opinion on this question: > >> > >> is there some algorithm that ouputs a potentially infinite list of > >> algorithms, such that (1) for eachWM2015-11-26T11:31:58Zhttps://groups.google.com/d/topic/sci.math/oSonkAluUZIRe: Colouring the Binary TreeAm Donnerstag, 26. November 2015 08:48:08 UTC+1 schrieb Virgil: > What sets does WM claim are simultaneously less-infinite than aleph_0 > and still infinite? All infinite sets. For instance the set of natural numbers or the set of seconds of the age of the universe. Proof: If aleph_0"Jürgen R."2015-11-26T11:14:50Zhttps://groups.google.com/d/topic/sci.math/bCUbQeqy9tsHistory: Walter Rudin, Georg CantorIn Rudin's autobiography there is an interesting commentary on his dissertation. The topic is uniqueness of series of spherical harmonics. What Rudin proves is the analogue of Cantor's theorems on the uniqueness of trigonometric series, dating from 1870 and later (in 'Gesammelte Abhandlungen,Richard Tobin2015-11-26T11:05:09Zhttps://groups.google.com/d/topic/sci.math/8ZOqsN6JMSgRe: Error in Edgar, Number TheoryIn article <n36o2s$7jj$1...@dont-email.me>, Robin Chapman <R.J.C...@ex.ac.uk> wrote: >> Edgar defines divisibility as b|c iff there is a unique integer x >> such that c = bx. The uniqueness is to prevent 0|0. >Why on earth does he want to prevent that? He doesn't explain it, but perhaps he