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Flo Bacus's avatar

In case any of you want to check your work:

Let x be arbitrary, and let ε > 0. Then we pick δ = ε/2. If |y-x| < δ, then |f(y)-f(x)| = |2y-2x| = 2|y-x| < 2δ = ε. Therefore f is continuous at x, and consequently at every point since x was arbitrary.

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Avi's avatar

It seems to me that a disanalogy between the mathematical analysis of continuity and this philosophical analysis of agency is that now mathematicians no longer care about common usage of the word “continuous”. The epsilon-delta definition *is* continuity now. Is this also the case for philosophical analyses? If they were shown to have clear divergences from common usage of the concepts being analyzed, would the analyses be discarded?

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