Local maxima/minima and removable discontinuities

Not by a strict definition of minimum: f has a (global) minimum at x* if f(x*) ≤ f(x) for all x (in the domain of f).

For any x* > 0, f(x*) = x*^2. But then f(x*/2) = x*^2/4 = f(x*)/4 < f(x*), so x* is not a minimum.

Ah. Never mind. I remember this now. It's the same thing as the 0.999... = 1 argument. It's always possible to find a point smaller than the point deemed to be the minimum.

0.000...1 = 1/∞ = 0, which doesn't exist on the domain.