# Sets with negative number of elements?

1. Jan 18, 2007

### Boris Leykin

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.

Last edited by a moderator: May 2, 2017
2. Jan 18, 2007

### Hurkyl

Staff Emeritus
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.

3. Jan 21, 2007

### Boris Leykin

http://www.math.ucr.edu/home/baez/cardinality/" [Broken] :yuck:

Thank you.
All my excitement vanished.

Last edited by a moderator: May 2, 2017
4. Jul 9, 2008

### karrerkarrer

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.

best
karrerkarrer

5. Jul 24, 2008

### dark3lf

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?

6. Jul 25, 2008

### gel

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.

7. Aug 26, 2008