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Re: I beg you, PLEASE prove that 0.123456789101112131415 is IRRATIONAL
by Sir Robin of Locksley 17 Dec '03

17 Dec '03

-----BEGIN PGP SIGNED MESSAGE----- >Dear Cypher Punks, > >I BEG YOU TO HELP ME!!! > >Is it possible to prove that number 0.1234567891011121314151617181920... >iz irrational? Most definately. All you need to do is prove that the set of this number is uncountable, ergo is irrational. If you have friend who have done math in real analysis they can explain more. > >Or may be it is rational? > >Also, another question for math geniuses here: > >Is it REALLY true that there are real numbers that cannot be generated >by any algorithm? Some guy said that since the set of algorithms is >countable, but the set of real numbers is more than countable, there >must be some numbers for which there is no algorithms that generate them. If you show me an algorythm that calculates the real number TT (=3.14.....) I'll give you a Nobel Prize personally! > >But I still do not believe him. > >Also, is it true that the sequence of digits in e is random because the ONLY way to get to the >p'th digit is to calculate the p-1'st digits? > Exactly! This is called recursive definition. To get the p-th set in the sequence you need to find p-1 first... >Also, is it the correct definition of a real number: > >``A real number is the class of numbers which can represent the length of >an arbitrary line.'' Well, that is not entirely true... The length of any arbitrary line can be any number, rational, natural, etc. Real numbers are the numbers that defy all other categorization (they are not rational, irrational, natural, etc.) They are complex and despite any instinctual perception, there are a lot of them! I don't know if these maed a lot of sense but all of these questions are answered in a good Elementary Real Analysis book. > > >I AM REAL DESPERATE FOR YOUR ASS ISTANCE. Sincerely, Gabe -----BEGIN PGP SIGNATURE----- Version: 4.5 iQEVAgUBMuJmYqr5aWnB1HshAQH2bwf+O/C0vRosJAclWr9OhYufFtSYnGohHjnA hwbcb6wftvrRES4HyMu9GfCYZanZ37TI4erblofctiJh7RVgFmvJxK0VDbaSth8J Ns0u/c86dw6qSeE8XG+1LBQ9hH8eXJ4Mojnohea4L9IesjfqugZwh6+g/1BXngco wpOnhixj9Xxoh8Bu/N01rNtaCOcDQPziCYWg3iKTIJ0ySP0zZBPoamVq7OYAhXzY +sn5lABFZ81/VQf0Y/7drWnZhBDpJXq7xtbo4NZGkDbQ6ifNaH9AlF9+9vLJn6AS osG5SsS2TmeJLmpi3BxC0k1cNHGHI7+DGazRVMrtCZFFMeeh5RtRgQ== =ZAZJ -----END PGP SIGNATURE----- --------------------------------------------------- | Gabor K. Tozser | 1500 St. Olaf Ave. | | St. Olaf College | Northfield, MN 55057 | ---------------------------------------------------

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Wow.
by amanda＠intercon.com 17 Dec '03

17 Dec '03

Well, in the week or two since resubscribing to Cypherpunks, I've seen a trickle of postings about cryptography, security, and privacy, and a flood of insults, harangues, fighting words, and so on. Some of this reads more like a script from a Jerry Falwell TV spot than anything I recognize as "Cypherpunk" traffic. I don't care who's offended whom. I'm not interested in participating in a forum where the supposed topic is submerged underneath a lot of adolescent alpha primate chest-beating. I'm off to look for a mailing list where people are ACTUALLY DISCUSSING CRYPTOGRAPHY AND IMPLEMENTING CRYPTOSYSTEMS. This list may still be called "cypherpunks", but it doesn't have much cypherpunk left in it, as far as I can tell. Disgusted, Amanda Walker Senior Software Engineer InterCon Systems Corporation

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Re: I beg you, PLEASE prove that 0.123456789101112131415 is IRRATIONAL (fwd)
by Jim Choate 17 Dec '03

17 Dec '03

Hi, Forwarded message: > Date: Sun, 19 Jan 1997 12:20:45 -0600 > From: Sir Robin of Locksley <tozser(a)stolaf.edu> > >Is it possible to prove that number 0.1234567891011121314151617181920... > >iz irrational? > > Most definately. All you need to do is prove that the set of this number is > uncountable, ergo is irrational. If you have friend who have done math in real > analysis they can explain more. irrational means 'not expressible as the ratio of two integers', this does not imply uncountable. Whether 0.12345678910111213... is irrational or not depends on how we choose to define a rational number where the denominator and numerator are both approaching infinity and how quickly those approaches occur. [ What is your definition of infinity/infinity ?] As alluded to before, 0.12345678910111213 = 12345678910111213.... / n (where n = infinity) 0.123456789101112... is certainly countable because by the definition of countable it must be 1-to-1 with the counting numbers (ie non-negative integers), which this one clearly is since it contains each positive non-zero integer (ie the set of numbers required to produce the number are clearly less, 1 less to be exact, than the counting numbers). > If you show me an algorythm that calculates the real number TT (=3.14.....) > I'll give you a Nobel Prize personally! c=2pi*r so, pi = c/2r You have a algorithm (ie recipe) for determining pi to whatever degree of precision you are willing to go to. If you insist on using a digital computer (whose domain of operation is limited to rationals by defintion) then you are doomed to fail. However, move to analog computers (eg a compass) and it can be quite easy to calculate, though not easy to plug into an equation. > Well, that is not entirely true... The length of any arbitrary line can be any > number, rational, natural, etc. Real numbers are the numbers that defy all > other categorization (they are not rational, irrational, natural, etc.) They > are complex and despite any instinctual perception, there are a lot of them! Complex numbers are not a member of the Reals, rather the Reals are a sub-set of the Complex. [ I recognize this is not what you meant but, "The slovenliness of our language makes it easier to have foolish thoughts." George Orwell ] VNR Concise Encyclopedia of Mathematics, 15th ed. ISBN 0-442-22646-2 pp. 74 "If every segment is to have a numerical measure as its length, then a new domain of numbers is needed, an extension to the domain of rational numbers. This new domain can no longer be constructed, as in the previous case, by number pairs. But hints for its construction are provided by a theoretical analysis of the measuring process for segments." A mathematicaly rigorous defintion of the class of numbers called 'Real' is that which equates the members of that set to the possible lengths of an arbitrary line segment. Jim Choate CyberTects ravage(a)ssz.com

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Re: Enough is Never Enough -- pro-CDA alliances, from TNNN
by Dale Thorn 17 Dec '03

17 Dec '03

Dale wrote: > > This Donna Rice-Hughes couldn't possibly be the Donna Rice who sat on > > Gary Hart's lap for the famous picture, could she? > But of course... she was emotionally traumatized by the who experience > (or some such line) and is now 'reformed'. The mind boggles. I've gotten several confirmations on this, and no negatives, so.... What I remember is that Hart and Schweiker were on one of the intel committees in the early 1970's, working more-or-less side by side with Frank Church et al, uncovering the real dirty laundry of the CIA and its infiltration of nearly every college and important business and media in the USA. Hart's minor spillage to the press must have pissed someone off, so they got the famous picture with Rice in all the papers, and Hart's presidential bid went right down the toilet. Now this same girl is on the righteous team, like Chuckie Colson? Yeah, I believe it. My you-know-what is starting to pucker up.

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INV_ade
by John Young 17 Dec '03

17 Dec '03

1-19-97. NYP: "At the New Frontier of Eavesdropping." Markoff. Many phone companies are now rushing to introduce new digital services that provide better sound quality. But when security standards were set for the new systems five years ago, technical experts from the Government discouraged the phone companies from building in coding systems that would be difficult to break. Moreover, the phone companies themselves decided that real privacy was not a major issue. "Time to market turned out to be more important than real security," said John Gilmore. Indeed, in recent weeks the supposedly secret formula for scrambling digital wireless phone calls was posted to an Internet mailing list. That virtually insures that hackers will soon create a way to modify scanners like the one the Martins used, making digital calls just as vulnerable as analog calls are today. "There's a period in which privacy prevails over surveillance, but it's never for very long." ----- INV_ade

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.1234567891011... is irrational?
by Jim Choate 17 Dec '03

17 Dec '03

Hmmm, irrational means "not expressible as the ratio of two integers" and since the class of integers (I) includes the concept of infinity, .123456789101112131415 = 1234567891011121314... ------------------------ n where n -> infinity Jim Choate CyberTects ravage(a)ssz.com

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Tomorrow
by jkurfis＠interserv.com 17 Dec '03

17 Dec '03

I_Love_SPAM, Hello, If you spend time on any of the online services or the internet then I have some exciting news. The Middle Income Financial Independence Club is now excepting new members. We are an online club of Middle Income people who have joined together to pursue our financial future from the information superhighway. If you would like membership information then please email me at jkurfis(a)interserv.com Start your online future today!

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And who will "moderate" the windbag Sandfort?
by nobody＠replay.com 17 Dec '03

17 Dec '03

One of the biggest offendors in getting into long flamewars has always been Sandfort himself. Why am I not surprised that most of his recent posts have had nothing to do with crypto but a lot to do with his own flames about others? And at such length, oh vey! He said: "First, I did not use it as a legal term of art, so a legal dictionary is not appropriate. Second, I see no sustantive difference between "forejudgment" and my shorthand version (pre-judge). Third, I wrote "literal." Examine the etimology of the word for it's literal meaning. It's pretty obvious AND specific [ME.; OFr, /prejudice/ (Fr. /prejudice/); L praejudicium/, from /prae/, before, and /judicium/, a judgment, from /judex/, /judicgis/, a judge.] In other words, to pre-judge. Get it?" Blah blah blah yadda yadda yadda yadda yo momma wears army boots yadda yadda blah blah This longwinded flame is from a longwinded windbag. He proposes to screen the posts of others for "suitability" but flames others ("dont be such an ass" in another of this afternoon's posts from him) and resorts to long and boring dissections like this one. "I have no intention nor duty to satisfy everyone. That is not possible. I will use a "reasonable person" test. (I am, by the way, using this in the legal term of art sense.)" Who will moderate this "windbag"? He thinks the list is his. It may run on Gilmour's machine, but the "Cypherpunks" are not owned by Gilmour and Sandfort. "P.S. I talked to Gilmore about the holdup in getting started. He has been too busy to get the tech side going, but when he does, (a) everyone will be notifed as to the start date, and the test will still run for an entire month. Until then, it is (sadly) business as usual." Why was this new dictatoriul policy (especially making the moderated list the default, instead of offering the moderated list as a new option) announced to begin on January 11th, then? Gilmour is probly having second thoughts (a good thing) and is just dragging his feet. Disgusted.

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Igor@home = Secret Squirrel
by Jim Choate 17 Dec '03

17 Dec '03

Hi all, I am motivated to post this, something I would normaly not do, because of the issue of trust of moderators that has arisen lately. Igor and myself were in a discussion about number theory last nite. We reached a point of impass. Igor made the suggestion that we bring the discussion to cpunks. I requested that we drop the issue and specificaly not bring it to cpunks. My reasoning had several facets. First, the position that I was in is probably wrong. My motivation was to examine the methodology of dis-proof (which I was disappointed with). Also, it is not a serious issue with me and whether my particular view is right or wrong is irrelevant. Cypherpunks is not the place for truly technical discussions (as is apparent with even a cursory glance). Traffic on this list practicaly drowns my ability to filter it and more drivel I (and probably you) don't need. And finaly, the discussion was fine for a Saturday afternoon discussion, I don't have the interest or time to carry it out over days or weeks, I have to work for a living. Igor agreed to drop the issue and not to bring it to the list. However, this morning I find Secret Squirrel posting some questions which are taken practicaly verbatin from my exchange w/ Igor. Seemed like a truly improbable event. Take it for what it's worth. "An appeal to authority is an appeal to a human being just like yourself who does not have your best interests at heart. What makes you believe they are able to resolve your problems better than yourself?" Jim Choate CyberTects ravage(a)ssz.com

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Re: [STEGO] Sphere packings
by nobody＠huge.cajones.com 17 Dec '03

17 Dec '03

Tim C. May will fuck anything that moves, but he'd rather be fucking his own mother's dead body. \|/ (*,*) Tim C. May _m_-_m_

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