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Sets with negative number of elements?

  1. Jan 18, 2007 #1
    Hi. :)
    Look what I've found here http://math.ucr.edu/home/baez/nth_quantization.html" [Broken]
    Can anyone say is this nonsense or what, negative cardinality?
    I am very curious. :eek:
    Last edited by a moderator: May 2, 2017
  2. jcsd
  3. Jan 18, 2007 #2


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    Such generalizations are easy enough to construct. I imagine you have no trouble with the notion of a multiset: a set that's allowed to contain multiple copies of something. e.g. <1, 1, 2> would be different from <1, 2>.

    It's easy to see that a multiset can be described as a function that tells you how many copies of an object there are. e.g. if S = <1, 1, 2>, then S(1) = 2, S(2) = 1, and S(x) = 0 for anything else.

    From there, it's a small step to allow functions to have negative values. Then *voila*, you have a generalization of the notion of a set that permits a set to have a negative number of elements.

    I don't know exactly what sort of generalization that article is planning on discussing, though. It might be this one, or it might be something entirely different.
  4. Jan 21, 2007 #3
    http://www.math.ucr.edu/home/baez/cardinality/" [Broken] :yuck:

    Thank you. :smile:
    All my excitement vanished.
    Last edited by a moderator: May 2, 2017
  5. Jul 9, 2008 #4
    isn't that a good methodological abbreviation for anything that is "hyper-nonexistent"?

    of similar interest would be considering circles with a negative radius (my favourite object) etc.
    any ideas about this??

  6. Jul 24, 2008 #5
    This would imply that the circle's negative radius causes the circle to "fold in on itself" so-to-speak into a negative dimension below the circle's two. This raises the question of negative dimensions... Theories?
  7. Jul 25, 2008 #6


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    Quite simple. A circle of radius r is the solutions to x2+y2=r2. So negative radius circle is the same as positive radius.

    imaginary radius is probably more interesting. You'd get the hyperbolic plane, depending on how you define it.
  8. Aug 26, 2008 #7


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