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I'm having an issue with finding the maximizer of a very simple piecewise function.

c = 0.125;

ArgMax[{Piecewise[{{0.5 (1 - c/(2 r) - (-2 - c + 2 r )/(
        2 (-2 + r))), r == 1}}], 0 <= r <= 1}, r]

gives the result 0.641915, which is obviously not true since at r=1 the value of the function is strictly positive. Why am I having this problem?

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