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serb language : pojam tacke u geometriji se odredjuje tako da je tacka beskonacno mala , identicna, i nedeljiva sto je u sustini tacno, ali to je je jedna logicka konstrukcija koja je imaginarna. U stvarnosti tacka je beskonacno mala , deljiva i moze biti razlicite velicine, navescu neke primere sve su ovo tacke u geometriskom smislu npr. 0,000...1 ili 0,000...7 ili 0,000...0005 ili 0.000...000003 da li je ova moja tvrdnja tacna ?

Added: Translation to English. (Copy-pasted from Google Translate. @experienced speakers, help improve the wording.)

The term "point" in the geometry is defined to be infinitely small, identical, and indivisible. That is basically true, but it is a logical structure that is imaginary. In reality the point is infinitely small, divisible and can be of different sizes. Let me give examples of all these points in geometrical terms, eg. 0.000 ... 0.000 ... 1 or 7, or 0.000 ... ... 0005 or 0000 000 003 if this my statements are true?

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This could be improved. Oops- I accidentally starred this question! Stupid smartphone ... –  The Chaz 2.0 Jul 30 '11 at 17:18
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I added the translation to English given by Google Translate. It seems that Google Translate does not speak fluent Serbian. Please consider improving the wording. Thanks! –  Srivatsan Jul 30 '11 at 17:33
    
I upvoted the question from -1 to 0 since I think it's interesting to ponder the logical ramifications. –  Shaun Ault Jul 31 '11 at 4:25
    
I don't see any logic to downvote a question. Even if it was irrelevant. I made it 0 from -1 proudly. Think positive and do more positive. From any post there are something to learn. –  Developer Oct 31 '11 at 11:39

1 Answer 1

Mathematics deals with abstractions, not with physical points. Whether it makes physical sense to subdivide space to arbitrary precision and to treat elementary particles such as the electron as point-like is an open question, but mathematically speaking, it makes no sense to ask for the size of a point; a point is simply an element in the sets that allow us to mathematically define notions of size, such as length, area and volume, in the first place. If you then use those notions to measure the size of a one-point set, it is exactly zero.

P.S.: There are serious attempts, relevant to quantum gravity, to mathematically model physical space other than as a set of individual points; the work of Andrei Rodin and of Jeff Russell might be of interest to you.

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I like joriki's answer, but I hope an example can be of some use... If points on the real line could have nontrivial "sizes", then for example the point at coordinate 0 may be 0.000002 in length. For the sake of argument, suppose this point at 0 extends a bit to the right, so that it "covers" the coordinate 0.000001. Now we have a dilemma. Is the point at 0.000001 supposed to be the same point at the point at 0? Or are we to have a distinct point at 0.000001 that just happens to overlap with the point at 0? Following the logic we'd have a terrible time getting Calculus to work! –  Shaun Ault Jul 31 '11 at 4:24

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