Hi Kim,

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On 04 Jun 2009, at 14:28, kimjo...@ozemail.com.au wrote: > OK - I find this quite mind-blowing; probably because I now > understand it for the first > time in my life. So how did it get this rather ridiculous name of > "square root"? What's it > called in French? Racine carrée. Literally "square root". It comes from the fact that in elementary geometry the surface or area of a square which sides have length x, is given by x*x, also written x^2, which is then called the "square of x". Taking the square root of a number, consists in doing the inverse of taking the square of a number. It consists in finding the length of a square knowing its area. Mathematician and especially logician *can* use arbitrary vocabulary. It is the essence of the axiomatic method in "pure mathematics" that what is conveying does not depend on the term which are used. Hilbert said once that he could have use the term "glass of bear" instead of "line" in his work in geometry. > >> A = {x such that x is even and smaller than 100} = {x ⎮ x is even >> & x > special character, abbreviating "such that", and I hope it goes > through the mail. > > > Just an upright line? It comes through as that. I can't seem to get > this symbol happening so I will > use "such that" Yes, "such that" is abbreviated by an upright line. Sometimes also by a half circle followed by a little line, but I don't find it on my palette! > > > > > > If not I will use "such that", or s.t., or things like that.The > expression {x ⎮ x is even} is > literally read as: the set of objects x, (or number x if we are in > a context where we talk > about numbers) such that x is even. > >> Exercise 1: Could you define in intension the following infinite >> set C = {101, 103, 105, > ...}C = ? > > > C = {x such that x is odd and x > 101} Correct. > > > >> Exercise 2: I will say that a natural number is a multiple of 4 if >> it can be written as 4*y, > for some y. For example 0 is a multiple of 4, (0 = 4*0), but also > 28, 400, 404, ... Could > you define in extension the following set D = {x ⎮ x < 10 and x is > a multiple of 4}? > > D = 4*x where x = 0 but also { 1, 2, 3, 4, 8 } Hmm... Marty made a similar error. D is a set. May be you wanted to say: D = {4*x where x = 0 but also { 1, 2, 3, 4, 8 }}. But this does not make much sense. Even if I try to imagine favorably some meaning, I would say that it would mean that D is the set of numbers having the shape 4*x (that is capable of being written as equal to 4*x for some x), and such that x belongs to {0, 1, 2, 3, 4, 8}. A proper way to describe that set would be D = {y such that y = 4x and x belongs-to {0, 1, 2, 3, 4, 8}}. But that would makes D = {0, 4, 8, 12, 32}. The set D = {x ⎮ x < 10 and x is a multiple of 4} is just, in english, the set of natural numbers which are little than 10 and which are a multiple of 4. The only numbers which are little than 10, and multiple of 4 are the numbers 0, 4, and 8. D = {0, 4, 8}. > > > > I now realise I am doomed for the next set of exercises because I > cannot get to the special > symbols required (yet). As I am adding Internet Phone to my system, > I am currently using an > ancient Mac without the correct symbol pallette while somebody > spends a few days to flip a single > switch...as soon as I can get back to my regular machine I will > complete the rest. Take it easy. No problem. > > > In the meantime I am enjoying the N+1 disagreement - how refreshing > it is to see that classical > mathematics remains somewhat controversial! The term is a bit too strong. It is a bit like if I told you that "I am Napoleon", and you conclude that the question of the death of Napoleon is still controversial. I exaggerate a little bit to make my point, but I know only two ultrafinitists *in math*, and I have never understood what they mean by "number", nor did I ever met someone understanding them. What makes just a little bit more sense (and I guess that's what Torgny really is) is being ultrafinitist *in physics*, and being physicalist. You postulate there is a physical universe, made of a finite number of particles, occupying a finite volume in space-time, etc. Everything is finite, including the "everything". Then by using the "unintelligible identity thesis" (and thus reintroducing the mind-body problem), you can prevent the comp white rabbits inflation. Like all form of materialism, this leads to eliminating the person soon or later (by the unsolvability of the mind- body problem by finite means). Ultrafinitist physicalism eliminates also mathematics and all immaterial notions, including all universal machines. Brrr... The real question is "do *you* think that there is a biggest natural number"? Just tell me at once, because if you really believe that there is a biggest natural number, I have no more clues at all how you could believe in any of computer science nor UDA. Remember that Thorgny pretends also to be a zombie. It has already eliminate its own consciousness. Note that after the step seven, you can still use ultrafinitist physicalism to eliminate the inflation of white rabbits *discourses*. After step 8, normally this move stop working unless you eliminate consciousness and persons. I think Thorgny is aware of that, and that is why he defends the idea that he is a zombie. From that point of view he is remarkably coherent with respect to the UD reasoning. But in front of person eliminators I can only say ... Brrr... Bruno http://iridia.ulb.ac.be/~marchal/ --~--~---------~--~----~------------~-------~--~----~ You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to everything-list@googlegroups.com To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/everything-list?hl=en -~----------~----~----~----~------~----~------~--~---