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There are things like $x^2$ which mirror an area, which is something that exist in the real world. The same applies to $\pi$, to integers, and many other things.

Are there, on the other hand, things in math that do not represent anything in the real world?

PS: I am not saying numbers exist (or trying to enter into the discussion at all). I was saying mirror, represent a real thing.

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closed as not constructive by Javier Álvarez, Davide Giraudo, Seirios, Micah, Did Jan 31 '13 at 15:26

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How about Aronszajn trees? –  L. F. Jan 31 '13 at 14:17
Or about Klein Bottles? Also, complex numbers certainly aren't real. (bad pun.) –  anorton Jan 31 '13 at 14:19
The real line ? –  Learner Jan 31 '13 at 14:20
Complex numbers are no more non-existent than real numbers or even natural numbers. :p –  Hurkyl Jan 31 '13 at 14:25
Actually, there is nothing in mathematics that truly exists in the "real world". The connection is entirely in our minds and its interpretation of the physical universe. Numbers, for instance, do not have any true existence in the material, just in how we interpret it. –  RBarryYoung Jan 31 '13 at 14:25