mm-1799 === Subject: Re: Definition? Yes, definitions are handy things. On my bi-conics basis, all conic sections are a type of ellipse - and I'm sticking to that. > I'd define the parabola and hyperbola, in biconic terms, as geometrics > which are outside (at least partly) the monocone. It depends somewhat, even then, if their directional arms are envisaged as going off at a tangent, or recombining to meet elliptically. Which is where definition is important. > Well, you can choose to call Spain Holland, and a > mouse elephant, but you're going to run into > certain difficulties conversing with people who > already have working definitions of those terms. === Subject: Re: Definition? > Yes, definitions are handy things. > On my bi-conics basis, all conic sections are a type of ellipse - and I'm > sticking to that. Thus instantly (and very efficiently) relegating yourself and your ideas to the realm of the ignored. Also, your top-posting isn't helping, either. === Subject: Re: Definition? That's alright. All new ideas take a while to percolate. I'll investigate biconics in any case. As to top-posting, I go along with OE which puts cursor at top LH side of a blank line at top of any Reply Group; in which case previous commentaries are footnotes; there for reference. > Yes, definitions are handy things. > On my bi-conics basis, all conic sections are a type of ellipse - and I'm > sticking to that. > Thus instantly (and very efficiently) relegating yourself > and your ideas to the realm of the ignored. > Also, your top-posting isn't helping, either. === Subject: Re: proof by induction Does maths take values into account, or is it confined to enumeration? Arithmetic, for example, is adding and subtracting (multiplication and division are special cases). Algebra brings in general numbers, denoted by letters (a,b,c for constants; x,y,z for variables). Set theory is where apples & pears *should* appear, but do they? Or, are we still dealing with abstract enumeration? Proof by induction is an enumeration, yet again, and values haven't really been considered. This is where mathematical induction has the same flaw as logical induction - extension from the known to the unknown can be dangerous, as it involves an assumption of uniformity which may not be warranted. Hence, +1, while numerically alright, may not be so in an actual value example. All cats have tails - until we come to the Manx cat. > Not quite sure if this should be the way. I was taught usually after we > proved a base case (n=1), we assume the n case is true, and construct a say > it's true for all n. > Thuan Seah >> > >> how the hell do you do it? >> >> >> bill >> > > You show its true for 1. > > Then you show that if it is true for n, it is true for n+1. > > Therefore it is true for all numbers. > > Proof: > > You have shown it is true for 1. > You have shown that if it is true for n, then it is true for n+1. > So if its true for 1 (which it is), it must be true for 2. > If its true for 2, it must be true for 3. > If its true for 3, it must be true for 4. > And so on ... >> >> how do you show it's true for n? > You dont. You show that IF it works for n, it ALSO works for n+1. > In other words you end up with two axioms: > True_for(1). > True_for(n) True_for(n+1). > See http://mathworld.wolfram.com/PrincipleofMathematicalInduction.html > gtoomey === Subject: Logarithms...character and mantissa help To those with knowledge: Napier is credited for inventing logarithms. Immediately after, he and Biggs began working on the development of log tables. At the same time, Galileo was battling the Catholics on his/their theory of planet motion. He won and the planets changed their course and began orbiting the Sun...coincidence of course(s)...pun. Back to Logs... The of Log10 = 1, Log100 = 2, Log1000 = 3, etc... These we term as characters of the exponent, but there are those numbers in-between these integer values of base 10. For these numbers the result is an exponent of two segments: the character value plus the mantissa (decimal segment). An example...the Log25.119 = 1.400, the character is 1 and the mantissa is 0.400. That part is easy...and my calculator tells me it's true. Question... What formula did Biggs and Napier use to determine/calculate the actual value of the mantissa? Clive Life is not short...it is eternal. It is we who have the short pleasure passing through it ! http://amitron2001.tripod.com/cgi-bin/all_topics.htm === Subject: Re: Logarithms...character and mantissa help > To those with knowledge: > Napier is credited for inventing logarithms. Immediately after, he and Biggs > began working on the development of log tables. At the same time, Galileo > was battling the Catholics on his/their theory of planet motion. He won and > the planets changed their course and began orbiting the Sun...coincidence of > course(s)...pun. > Back to Logs... > The of Log10 = 1, Log100 = 2, Log1000 = 3, etc... These we term as > characters of the exponent, but there are those numbers in-between these > integer values of base 10. > For these numbers the result is an exponent of two segments: the > character value plus the mantissa (decimal segment). > An example...the Log25.119 = 1.400, the character is 1 and the mantissa is > 0.400. > That part is easy...and my calculator tells me it's true. > Question... > What formula did Biggs and Napier use to determine/calculate the actual > value of the mantissa? > Clive > Life is not short...it is eternal. > It is we who have the short pleasure passing through it ! > http://amitron2001.tripod.com/cgi-bin/all_topics.htm They worked the other way: starting with 1.0001 = invlog(0.0001) they multiplied 1.0001 with 1.0001 (rounding the result to 4 decimal places) and added 0.0001 to 0.0001 over and over again. This gives log(1.0001^10000) = 1 (natural logarithm basis e !) They did not use the decimal logarithm. Ciao, Norbert === Subject: Re: Logarithms...character and mantissa help Norbert: Found the answer to the Log question. Best. Clive Life is not short...it is eternal. It is we who have the short pleasure passing through it ! http://amitron2001.tripod.com/cgi-bin/all_topics.htm > To those with knowledge: > Napier is credited for inventing logarithms. Immediately after, he and > Biggs > began working on the development of log tables. At the same time, Galileo > was battling the Catholics on his/their theory of planet motion. He won > and > the planets changed their course and began orbiting the Sun...coincidence > of > course(s)...pun. > Back to Logs... > The of Log10 = 1, Log100 = 2, Log1000 = 3, etc... These we term as > characters of the exponent, but there are those numbers in-between these > integer values of base 10. > For these numbers the result is an exponent of two segments: the > character value plus the mantissa (decimal segment). > An example...the Log25.119 = 1.400, the character is 1 and the mantissa is > 0.400. > That part is easy...and my calculator tells me it's true. > Question... > What formula did Biggs and Napier use to determine/calculate the actual > value of the mantissa? > Clive > Life is not short...it is eternal. > It is we who have the short pleasure passing through it ! > http://amitron2001.tripod.com/cgi-bin/all_topics.htm > They worked the other way: starting with 1.0001 = invlog(0.0001) > they multiplied 1.0001 with 1.0001 (rounding the result to 4 decimal places) > and added 0.0001 to 0.0001 over and over again. > This gives log(1.0001^10000) = 1 (natural logarithm basis e !) > They did not use the decimal logarithm. > Ciao, > Norbert === Subject: Re: Logarithms...character and mantissa help Ciao: I think I have a handle on your explanation. Your last statement ...This gives log(1.0001^10000) = 1 (natural logarithm basis e !)... took a little time to work out. But drifting away from Ln...how was the Log (base 10) system calculated? Best. Clive Life is not short...it is eternal. It is we who have the short pleasure passing through it ! http://amitron2001.tripod.com/cgi-bin/all_topics.htm === Subject: AUSTRALIA LED BY MURDERERS, HENCE 9.2 QUAKE ! I could have been back in Sydney this Saturday 15th, and planned the route with only ONE fuel stop only, so as to be on time to sway the mighty hand of fate. I had arranged indeed for a Bombardier charter plane to pick me up at La Rochelle relief airport this very evening at 18:00. The cost ? A waddle of 320 000 Euros thrown out, BUT to save 2 millions Australians from certain death, and therefore quite justified expenses, in my view anyway ! . Of course full public apologies from the Political Convict-Strain Federal & WA Members, Supporters of the Mining Criminals of Newmont / Newcrest / BHP / WMC / BORAL over 35 years, and the needed paper work fulfilled, returning my stolen Great Sandy Desert Mining Properties to rightful owner, were just a Australian cadavers rotting all over NSW and QLD on the scorched ground, and blowing up under the searing heat of the Summer Sun. BEHOLD ! Howard, Gallop & sundries have thought otherwise, and in their view apparently it is of foremost importance to retain their prebends from the Mining Criminals, than to save the lives of their OWN Australian citizens ! I know there is a precedent to that with the Port Arthur Holocaust, a mass murder psy-ops orchestrated indeed from start to finish by that very same Howard Government in power now ! Well, if those Political Bastards of the Howard Government are able to conduct in cold blood the murder of 3 dozens good Australians so as to twist the opinion ... it make sense that they will not lift their fingers concerning steps to be taken in protecting the lives of Sydney & vicinity 5 millions good people and will pull the Natural Phenomena excuse to save their deviant unhuman ' hides. I anticipate indeed quite a big chunk of NSW & Qld going to be involved in the coming 9.2 Quake Upheaval and consecutive 100 m Tsunami visiting Eastern border shores up to 40 km inland... at mere 200mph too ! IT FOLLOWS THAT IN MY BOOK AUSTRALIA IS LEAD BY MURDERERS OR IN CLEAR THOSE HOWARD & CREW BASTARDS PRESENTLY AT THE HELM OF DOOMED AUSTRALIA ! 1) With on their en dirty hands the blood of those 3 dozens good Australians they framed in the infamous Port Arthur Holocaust psy-ops, all busted right on the head by the top shot of the 100 strong military foreign commando ! 2) The poor mentally retarded they framed and made scapegoat of the whole massacre, while in fact that poor chap had no military training at all, and was demonstrated further as unable to kill a fly ! 3) That Australian Mining Pioneer, Sir Turcaud, whom the Mining Criminals of Newmont, Newcrest, BHP, WMC and Boral tried to murder, while only successful in murdering Corporate prospector Berth Rutherford, the one who denounced the whole 100 Billions USD Telfer Mine fraud, and whom they pushed quickly to the grave. Honour to you brave Berth Rutherford, I will always honour your memory in my heart, and all the time I will live ! Those Mining Criminals whom the Howard's ( & Gallop 's ) Criminal Crew protects and still covers up ! 4) That whole population of NSW & Qld waiting like sitting duck, and in total ignorance of the terrible fate going to befall it! ... and that Howard Crew being warned of impeding disaster and NOT lifting his little finger to save millions of his own people ! A typical irresponsible, careless and in the circumstances Quite Criminal Attitude indeed ! Quite in line with the Port Arthur Holocaust Howard Government 's geared up & further cover up following orchestrated by same ! 5) The keeping at bay from Australia and this since decades of Australia Mining Pioneer, Sir Turcaud, who is in the circumstances the only one who has remedy to that desperate situation. Situation which has only two remedies : Volcanic blasting or electrostatic field build-up neutralisation by the immediate return of steady & sustained rain over the whole country ! I can only do the second thing ! A thing Sir Turcaud to do and very well at that ! CONSIDERING THAT ACCORDING TO HER ROYAL MAJESTY'S LAW NO MURDERING CREW CAN BE LEADING AUSTRALIA, AND NO MURDERER PREMIER, AS HOWARD IS PROVEN TO BE, IS ALLOWED TO LEAD THE COUNTRY ! REQUEST TO GOVERNOR GENERAL TO INVALIDATE LAST ELECTION ON THAT GROUND ! AND FURTHER HAVE THEN CRIMINALS HOWARD, ANDERSON & COSTELLO DIRECTLY SENT TO THE GALLOWS ON HER MAJESTY 'S FULL AUTHORITY ! IT FOLLOWS THAT FROM THAT POINT IN TIME, AS AN AUSTRALIA MINING PIONEER, THE ONLY TRUE PRIME MINISTER OF AUSTRALIA TO WHOM I WILL RECOGNISE A LEGAL AND TO WHOM I WILL REPORT IS GOVERNOR GENERAL TO IMMEDIATELY TAKE OVER CONTROL OF AUSTRALIA AFFAIRS AND NOT LOSE ANYTIME INDEED TO HAVE THE HOWARD MURDERING CREW CLAPPED IN IRONS !!! QUOTE TODAY FROM CHARTER OPERATOR WITH BOMBARDIER GLOBAL EXPRESS TO TAKE ME THERE ASAP ! ONLY IF I RETURN WILL I BE ABLE TO OFFSET THE WHEEL OF FATE, AND THIS SIMPLY AS SAID BY BRINGING THE RAIN BACK ALL OVER THE COUNTRY, AS I KNOW TO DO THAT AND HAVE DONE IT ALL THE TIME ! A GOD GIVEN TALENT HANDED TO ME AT BIRTH ! 2 Millions Australian lives are in the balance now, poor Bastards, and grabbing that balance are the horny, long dirty claws of those Mining Criminals & Political Gallows Birds ! ... en Federal Government & WA Government Drivels indeed , preventing it to lean on the right side ! Will an Australian Mining Pioneer desperate attempt to save 2 millions Australian lives fail, ... because of that Criminals Scum presently risen at the top ? Has Opposition Leader Right Hon Latham the guts to take the necessary steps to save Sydney & the Millions of people living there ? Future will tell us very soon ! WILL THE FORCES OF EVIL MUST NOT PREVAIL !!!! HONOUR TO OUR CELTIC GOD ! ! JE COMMANDE ET LA NATURE OBEIT A MA VOIX * PS In any case, if I am not there in time, I will issue my last recommendation on Sunday so as to save a maximum of Australian lives. Sir Jean-Paul Turcaud Australia Mining Pioneer Discoverer & Legal Owner of Telfer, Kintyre & Nifty Mines The Great Sandy Desert.of Australia Discoverer of the South Atlantic Submarine Gold Placers ( 40 Millions Tons estimate ) FOUNDER OF THE TRUE GEOLOGY THE GOLDEN RULE Gold and Intrigue in the Desert The true story of the discovery of the Telfer gold mine Author : Bob Sheppard, President of the Australian Prospectors' Union Author's contact & web page : www.tnet.com.au/~warrigal/ Order from : Hesperian Press, PO Box 317 Victoria Park, 6979 W.Australia. AUS 40.00 + post Published in Perth 15th December 2002 to Australia Greatest & True Geologist 's Site http://users.indigo.net.au/don/index.html ~~Ignorance Is The Cosmic Sin, The One Never Forgiven ! ~~ === Subject: instructions how to authorise, register, including the authorization, registration, and installation serial numbers for 20,000 plus programs instructions how to authorise, register, including the authorization, registration, and installation serial numbers for 20,000 plus programs please send e-mail tel@mail.gr, tel@mailbox.gr, http://homepages.pathfinder.gr/code_fu/CDROMS_430_up_to_10000.zip http://homepages.pathfinder.gr/code_fu/CDROMS_10001_up.zip http://homepages.pathfinder.gr/code_fu/CDROMS_BY_CATEGORY.zip === Subject: Any familiarity with this mathematical oddity? Wow. What charm. Given any four consecutive whole numbers, the difference between the cube and the square of the highest number, minus 3 times the difference between the cube and the square of the next lower number, plus 3 times the difference between the cube and the square of the 2nd lowest number, minus the difference between the cube and the square of the lowest number; always equals six. Know any of those famed Indian math enthusiasts, there downunder? Heard of this one before? It's a gem, to be sure! -Ben Bean === Subject: Truth tables? Does a truth table really tell us anything new? If, for example, a bivalent conjunctive truth table has one statement which is true, and another false, is the result false - or partly true and partly false? But it all works! you may say. Yes, and very handy when dealing with the 0/1 of a computer. Yet, a computer will follow any rules you devise, whether true or false, provided you are consistent. === Subject: Re: Truth tables? > Does a truth table really tell us anything new? > If, for example, a bivalent conjunctive truth table has one statement > which is true, and another false, is the result false - or partly true > and partly false? > But it all works! you may say. Yes, and very handy when dealing with > the > 0/1 of a computer. Yet, a computer will follow any rules you devise, > whether true or false, provided you are consistent. If standarn Booloean logic, you get 16 truth tables for a binary relation eg and, or, nor, nand, xor, material implication (=>),equivalence, etc. And you have the equivalent set-theoretoc equivalents eg union, intersection, etc See http://en.wikipedia.org/wiki/Truth_table http://en.wikipedia.org/wiki/Boolean_logic All this has been known from the 1800s. gtoomey