- cypherpunks-legacy - lists.cpunks.org

Re: infinity & set membership
by nobody＠huge.cajones.com 17 Dec '03

17 Dec '03

At 4:36 PM 1/19/1997, Jim Choate wrote: >"The least upper bound of a set of real numbers is often called the >supremum, the greatest lower bound its infimum. In general the supremum and >infimum of a set ARE MEMBERS OF THE SET or at least LIMITS OF SEQUENCES OF >MEMBERS OF THE SET." > >[capitalization is mine] > >In this case the suprenum is infinity. > >Introduction to Calculus and Analysis >Courant and John >Vol. 1, pp. 97, Section e. >1965 Edition >Library of Congress: 65-16403 I presume this is a reference to Jim's earlier post: At 1:19 PM 1/19/1997, Jim Choate wrote: >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). Of course this same argument could be used to claim that pi is also rational. pi = 314159.... / n (where n=infinity). What could be the problem here? One problem might be that an integer (not including infinity) divided by "infinity" should be 0. The p/q definition of rational numbers does not rely on "infinity" being a member of the set of integers. Also, we rarely hear this dialogue: "Give me an integer." "Okay - infinity!" Still, let's define a set which contains the integers as well as positive and negative "infinity". I will call this set the "Choate-integers." Let's add some reasonable rules for working with +inf and -inf. n is a non-zero positive traditional integer. a. -inf = +inf * -1 b. +inf * n = +inf c. +inf + n = +inf d. +inf / +inf = 1 Operations involving multiplication or division of +inf and zero are undefined. Using these definitions, you will find that the p/q definition of rational numbers operates as expected on the set of Choate-integers. The argument I supplied earlier for the rational nature of 0.1234... still holds. Math Man

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Take it to sci.math
by winsock＠rigel.cyberpass.net 17 Dec '03

17 Dec '03

Will all those people who are talking about set theory and the countability of various number systems take their discussion to sci.math, please? 'Cuz 1) All that stuff is irrelevant to crypto, its science or politics. 2) Not a single math comment made by anybody on any of those threads is even remotely correct. 3) You will recieve your proper chewing out on sci.math and 4) This bullshit is extremely annoying to those of us who has some real training in math, even more so than the regular bullshit on this list. Hey Sandy, you gonna censor these creeps once you start censoring?

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Re: Dedikend Cut's and such
by Kent Crispin 17 Dec '03

17 Dec '03

Jim Choate allegedly said: > > > Hi, > > Did a little research, Dedekind Cut's and such use Integers to define a > SPECIFIC Real to a arbitrary BUT FIXED resolution. They do not define the > set of Reals. They do. The set of all numbers representable by a DC is precisely the set of reals. -- Kent Crispin "No reason to get excited", kent@songbird.com,kc@llnl.gov the thief he kindly spoke... PGP fingerprint: 5A 16 DA 04 31 33 40 1E 87 DA 29 02 97 A3 46 2F

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Re: Newt's phone calls
by Sean Roach 17 Dec '03

17 Dec '03

At 03:44 PM 1/17/97 -0600, Igor Chudov wrote: >It is my understanding that an ordinary banking consumer that >uses "pay bills by phone" service cannot transfer $$ to any arbitrary >account. There is a limited list of permitted accounts, such as utility >companies. Therefore, the risk of unauthorized transfer is very >limited. It is limited, both accounts have to have the same password, (four character, numeric.) If I want to transfer funds from another persons account to one that I control, all I have to do is change the password on one of them to that of the other, transfer funds, and change the password back. By the time that my victim found out, (via the little letter "per your request, $xxx was transferred to accnt#123456 from accnt#7890"), I would be long gone.

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Re: 'Monster' numbers
by WinSock Remailer 17 Dec '03

17 Dec '03

At 5:08 PM 1/19/1997, Jim Choate wrote: >In reference to numbers which you can't describe, if you examine the work >they are ALL in the Complex domain, none of them are Real's. This is incorrect. The argument outlined applied to real numbers only. If you wish to refute the argument please do so. You might find it helpful to review the reference in Smullyan's book. >If there existed a Real for which we could not describe this would imply >that we could not draw a line of that length. The subtlety of the idea lies in the fact that you can't make a statement like "$foo is not describable" where $foo means anything. Any number for which you can say, "I can draw a line which is $bar units long" is describable. Math Man

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Re: IMDMP: SOURCE CODE RELEASE ANNOUNCEMENT
by ichudov＠algebra.com 17 Dec '03

17 Dec '03

Dale Thorn wrote: > > AIDAS wrote: > > On Sat, 18 Jan 1997, Dr.Dimitri Vulis KOTM wrote: > > > > > > Personally, I wish they'd hurry up. I'm getting rather annoyed with the > > > > > > spam, the "you're all homosexuals" postings, the posts by morons that > > > > > > can't figure out Majordomo or their mailers, and so on and so forth. > > > > > > Not sure about "all", but someone whose name sounds like AIDS, and who > > > > > advocates censorship, most likely is one.[snip] > > Ah, very strong response indeed. I feel as if shot down in flames, > > and my mind aches from the slice of your wit. Deliver us, oh Vulis, > > for we are in need! > > It still looks like Sandy to me. Writing style for one, unwillingness > to drop an argument for two, and the use of the name AIDAS is *very* > suspicious. But Sandy gave his word publicly that he was not AIDAS! - Igor.

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Re: infinity & set membership
by Huge Cajones Remailer 17 Dec '03

17 Dec '03

At 4:36 PM 1/19/1997, Jim Choate wrote: >"The least upper bound of a set of real numbers is often called the >supremum, the greatest lower bound its infimum. In general the supremum and >infimum of a set ARE MEMBERS OF THE SET or at least LIMITS OF SEQUENCES OF >MEMBERS OF THE SET." > >[capitalization is mine] > >In this case the suprenum is infinity. > >Introduction to Calculus and Analysis >Courant and John >Vol. 1, pp. 97, Section e. >1965 Edition >Library of Congress: 65-16403 I presume this is a reference to Jim's earlier post: At 1:19 PM 1/19/1997, Jim Choate wrote: >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). Of course this same argument could be used to claim that pi is also rational. pi = 314159.... / n (where n=infinity). What could be the problem here? One problem might be that an integer (not including infinity) divided by "infinity" should be 0. The p/q definition of rational numbers does not rely on "infinity" being a member of the set of integers. Also, we rarely hear this dialogue: "Give me an integer." "Okay - infinity!" Still, let's define a set which contains the integers as well as positive and negative "infinity". I will call this set the "Choate-integers." Let's add some reasonable rules for working with +inf and -inf. n is a non-zero positive traditional integer. a. -inf = +inf * -1 b. +inf * n = +inf c. +inf + n = +inf d. +inf / +inf = 1 Operations involving multiplication or division of +inf and zero are undefined. Using these definitions, you will find that the p/q definition of rational numbers operates as expected on the set of Choate-integers. The argument I supplied earlier for the rational nature of 0.1234... still holds. Math Man

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Debt (calling) Cards Re: Newt's phone calls
by Sean Roach 17 Dec '03

17 Dec '03

At 04:58 PM 1/17/97 -0800, Rich Graves wrote: >What does concern me is personal privacy. I don't want people tracking >my movements or purchasing patterns, so I prefer to use cash or >pseudonymous debit cards. This reminds me, I got a sprint 5 minute sample calling card when I got my college texts. I suspect that other people on this list got one as well. Mine is completely unused and although transferring the actual cards would cost, (the stamp and envelope), would anyone be interested in trading the numbers? This one is registered as being handed out in Weatherford Okla. Five minutes of long distance is trivial, so I would be willing to trade in regular e-mail, as opposed to through a middleman.

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Take it to sci.math
by WinSock Remailer 17 Dec '03

17 Dec '03

Will all those people who are talking about set theory and the countability of various number systems take their discussion to sci.math, please? 'Cuz 1) All that stuff is irrelevant to crypto, its science or politics. 2) Not a single math comment made by anybody on any of those threads is even remotely correct. 3) You will recieve your proper chewing out on sci.math and 4) This bullshit is extremely annoying to those of us who has some real training in math, even more so than the regular bullshit on this list. Hey Sandy, you gonna censor these creeps once you start censoring?

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Re: Sandy and the Doc
by WinSock Remailer 17 Dec '03

17 Dec '03

Bill Frantz <frantz(a)netcom.com> writes: > I hope if such a system is set up, people who use it will realize that > email is not 100% reliable. Just because algebra.com sent mail to > toad.com, doesn't mean that toad.com actually received it. A small > fraction of a percent of these messages will be lost. Failing something catastrophic like a disk failure or a host down for more than a week, this should not be the case. Almost every site running sendmail has the Os ("SuperSafe") option set. That means sendmail will not respond to a "." at the end of a DATA command with SMTP code 250 until it has written the incoming message (and queue info) to disk and called fsync. Thus, you may get 2 copies of a message, but mail messages should not just disappear regularly at all, even if the network goes down or a machine crashes. Non-sendmail MTA's tend to be even more strict about this, not even allowing this behavior to be disabled.

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