kebetulan english awak pas2an pula. tadi aku coba meraba2 artikel tsbt, n aku dapetkan main idea-nya,katanya: "0/0 is a number". benarkah? gue jadi ingat mainan2 zaman doeloe waktu gue es em u, dari persaman berikut ini:
a^2-a^2 = a^2-a^2 (a+a)(a-a)=a(a-a) a+a = a 2a=a 2=1 nah, loh... gimana? zaman doeloe "theorema" tersebut GAGAL because ala ni sebab "0/0" entu ndak tentu ! lah, sekarang? pie, toh? catetan: a^2 adalah " a pangkat 2" bobby formula --- In [email protected], Ronsen™ <[EMAIL PROTECTED]> wrote: > > http://www.bbc.co.uk/berkshire/content/articles/2006/12/12/nullity_061212_feature.shtml > > 'Nullity is a number, and that makes a difference' By Ollie Williams > > University of Reading academic Dr James Anderson insists his theory of > nullity is 'revolutionary', despite criticism from all quarters > following a video report in which he suggested a new means of dividing > by zero. > > Here, Dr Anderson answers some of the comments we received following > last week's video report. > > "Nullity is a fixed number with value 0/0," Dr Anderson tells us. "It is > not undefined, it is not indeterminate. > > "That changes the way you do mathematics - that statement is > revolutionary. It remains to be seen whether it is correct or not, > whether people accept it or not, but that's my position." > > We invited Dr Anderson to the BBC in order to follow up the 1,000-plus > comments and criticisms we received in the wake of an article published > on 6 December 2006, entitled: '1200-year-old problem "easy"'. > > What is nullity? > > "To be quite precise: I am saying that the number 0/0 is a number. It is > a fixed number, not an undefined number or anything like that. That is > different to what goes on currently in computing, and in mathematics." > Has your theory been peer-reviewed? > > "The work was developed over ten years, it's been peer reviewed and > reported in seminars in mathematics and computing departments in the UK, > and it's been reported at a learned society. > > "The work has been proved consistent twice, by hand, by me, and has been > checked at another university by computer. > > "The work arises from computing. There were problems that couldn't be > solved using the existing floating point numbers. It's been a long > process of solving a practical problem. > > "It's now in the form where it can be submitted to mathematics journals > - it has been a long journey from computer science to mathematics and > that's entirely normal." > > Have any of the comments received caused you to rethink your theory? > > "I have examined all of the comments and over a hundred counter-proofs > to my work. > > "Each was incorrect except one, which challenged a clause in equation 10 > of the analysis paper. That challenge is entirely correct but it does > not change the substance of what I said in public, and I had a second > published theorem which establishes the result as well. > > "As far as I can see the work is sound, it is computing work, and now it > can be developed as mathematical work. It is entirely normal for the > work to be controversial when it is developed in other subjects before > it is accepted by mathematicians." > Isn't this just NaN ('not a number'), a device in use for decades, under > a different name? > > "NaN is, as it says, not a number. Nullity is a number - that makes a > difference. It is a paradigm shift in the way you think. If you think of > 0/0 as a fixed number it changes the way that you do calculus. > > "It is true that the IEEE float standard defines NaN, which deals with > exceptional cases on the basis that 0/0 and various other things are > undefined or indeterminate. > > "That's difficult, the IEEE standard defines some unusual behaviour. For > example NaN is not equal to NaN - that makes sense if you think NaN is > an indeterminate value, but not if NaN is a fixed number. > > "It's much more natural for programmers to think of variables as being > equal if they're identical. > > "With IEEE float it is not entirely clear what you're supposed to do > with NaN as an argument to a function. Are you required to return NaN as > a result or may you return something else? > > "That is perfectly clear with my arithmetic - nullity is just a number, > you can use it in arguments, you can return any value you like. The > semantics is simpler, it's clearer and easier for programmers to handle." > > What can you achieve with nullity that you can't with an error message > on a calculator? > > "Nullity has a precise arithmetical value. The trans-real arithmetic is > total, and complete, and contains real arithmetic as a sub-set. > > "You can calculate values with nullity and those are meaningful. The > arithmetic is simpler than IEEE-float. > > "Trans-real numbers I have defined to be the real numbers augmented with > plus infinity, minus infinity, and nullity. > > "What I have done is to take algorithms from arithmetic that happen to > work for division by zero, collected them together, developed them as > algorithms, proved that they're consistent, then axiomatising it and > proving it by computer." > Can you express nullity in binary? > > "There are many, many ways of coding these numbers in binary, and I've > done it. If anyone doubts me I can hit them over the head with a > computer that does it." > Why do you think so many mathematicians have so much trouble accepting > your theory? > > "I say that 0/0 is a fixed number and mathematicians are entirely used > to thinking of it as undefined. I take a different stance and I believe > I can maintain that stance. I'm prepared to step into the mathematical > arena and argue my case there. > > "If you are used to thinking of programming in terms of the real numbers > then you will only be able to think of nullity as an exceptional state. > That's undeniably true and is the way most programmers and > mathematicians think. > > "If, however, you make the paradigm shift and accept that 0/0 is a fixed > number, then new equations become possible." > > -- > Ronsen >
