Re: PS that's what you been saying all along... what is wrong with you.?Please Register or Log in to view the hidden image!
From ProCop: "I think I can now identify the reason why 0 is different from the other numbers. It is in the way 0 gets its value. An example: There are 2 persons X,Y. You can identify each of them positively: eg. X is young, Z is old or negatively: X is not Z and Z is not X. All numbers (except 0) have positive identification. 1 is one (mental) object, 2 is two (mental) objects etc. 0, the absence of (mental) objects is identified nagatively. 0 gets its value only from other numbers (which get their value from the world of (mental) objects) not from the referencial world of objects. " A paraphrase of the above for those who haven't figured it out yet: "I understand nothing about mathematics but I like to hear myself talk."
RE: Unfortunately also non-mathematicians use and think about the numbers. They are not as much rule-minded as maths and tend to approach the numbers in the way they aproach other systems. Specialy language has a lot common with numbers eg. it uses the same sign (often in different form) .. In laguage there is sometimes more implied than it precisely says. I have simply tried to have a look at 0 in its precise and implied form (can maths numbers have an implied meaning?). But after this course of nul-value searching I still cannot answer with a reasonable meassure of certainty the following question: you have a square A side-size a = 4 cm you have a square B side-size b = 0 cm How many B squares can be put in square A? Answer 1 none (square B does not exist) Answer 2 infinity (there is a potential of the square in 0) Answer 3 undetermined (I don't really know..) I will probably have to live with that...
Re: RE: Answers 1 and 2 could be considered correct. Answer 1 - As you said, there is no square B, so it can't be fit into square A. Answer 2 - If square B has sides that are infitesimally(sp?) small and therefore approach zero but do not actually reach zero, then one can fit an infinite number of squares in the Square A.
Re:empennage It seems that your answers contradict the following post from James R: Naturally only if you accept that the case above (squares A and B) is a sort of "graphic translation" of the formula 4/0. Then the only possible answer (according to James) is answer 3 - undetermined (I don't really know..)
Re: Re:empennage Actually, I don't think it contradicts hims at all. If there is an area A it is possible to make up that area by taking the SUM of infintesimally small areas. It does not contradict what James R was saying because he was not dealing with addition. BTW, the concept of adding infintesimally small pieces to make up a whole "object" is basically what an integral is in Calculus.
thats not what the discussion is about. its about 0!!!!!!!! 4/(the SUM of infintesimally small areas) yes that can be done 4/0 no sorry cant be done
<i>Naturally only if you accept that the case above (squares A and B) is a sort of "graphic translation" of the formula 4/0. Then the only possible answer (according to James) is answer 3 - undetermined</i> That's the right answer to this problem.
Re:empennage/question The concept "infintesimally small area" is unknown to me. Can you arive at this concept reasoning that if you have a square B side-size b = 0 then the diagonal of the square B must be d >0 so it principally represents "infintesimally small area"?
does a Sierpinski Carpet "exist"? although it may appear to, the answer is no.Please Register or Log in to view the hidden image!
Sure Sierpinski's carpet (or whatever name you give the thing) exists. If only n my mind. But what does that have to do with the curent subject?
just a little somthing to get them thinking.....afterall, the carpet is based on an infinite number of iterations
Mathematicians often use infinitessimal quantities. In fact, the whole of calculus is based on them, via the theory of limits. Many mathematical arguments start with something like: "Let epsilon be a positive quantity infinitessimally greater than zero. Then..." Given a square of side length a, how many smaller squares of side length b will fit inside it? Answer: a<sup>2</sup>/b<sup>2</sup> What happens as b approaches zero? Answer: the number of squares approaches infinity. But if b <b>equals</b> zero, the answer is undefined, because then we'd have a<sup>2</sup>/0.
RE:James R My appology if I am going to hurt somebody's feeling, but this "infinitessimallity" seem to me to be simply a trick to replace 0 with as-close-to-nul-as-possible number. In other words you are replacing a non-countable null with a countable one...
I don't think you will hurt the feelings of any except those who care about correct spelling! "Mathematicians often use infinitessimal quantities. In fact, the whole of calculus is based on them, via the theory of limits. " is not true. Only those mathematicians (and its a minority) who regularly work with "non-standard" analysis use infinitesmals. Indeed, the "theory of limits" was developed specifically to avoid infinitesmals.
yes Procop, I remeber my calculus professor defining epsilon as "the smallest number greater than zero". But it's your job to learn about limits, not ours to teach it to you. You want to learn, then go learn it. Ask appropriate questions when you get stuck.
HallsofIvy: Please give me a definition of the first derivative of the function f(x) which does not involve infinitessimals.
