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Can you guys help me prove: Given a continuous and differentiable function (or surface) f: R^2 -> R, such that f(x,y) = z ... contour lines can always be drawn... the function is NOT bijective.

I've been thinking of choosing any arbitrary point and showing that the curves that intersect to form that point (over y-axis and x-axis) always manage to have certain z-values that are equal.

How do I point this is in mathematical terms?

I've been thinking of choosing any arbitrary point and showing that the curves that intersect to form that point (over y-axis and x-axis) always manage to have certain z-values that are equal.

How do I point this is in mathematical terms?

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