The context is that f is a real-valued function on a plane such that for every non-degenerate square ABCD in the plane, f(A)+f(B)+f(C)+f(D)=0....

What does this word mean here? I've found that "in mathematics, a degenerate case is a limiting case in which an element of a class of objects is qualitatively different from the rest of the class and hence belongs to another, usually simpler, class" (Wikipedia), but it's still a little unclear to me. Can someone help explain this more simply?

Thanks! Much appreciated.

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    $\begingroup$ A point is a square with side length 0; I'd guess the author intends to exclude that case. $\endgroup$ – Mose Wintner Mar 1 '16 at 20:23
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    $\begingroup$ Or if A = B and C = D, we'd have a line segment. $\endgroup$ – DylanSp Mar 1 '16 at 20:26
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    $\begingroup$ A line is also considered a degenerate rectangle (or square). I guess any rectangle with a zero side. $\endgroup$ – Luis Vera Mar 1 '16 at 20:26
  • $\begingroup$ Ohh, gotcha, thank you so much. Seemed pretty insignificant, but definitely important. Thanks again. $\endgroup$ – Grant Stenger Mar 1 '16 at 20:26
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    $\begingroup$ So in this context it means specifically that $A, B, C$ and $D$ are four distinct points. $\endgroup$ – Arthur Mar 1 '16 at 20:53

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