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I don't understand why mathematicians would need to define the mathematical concepts of diffferentiabilty and conitnuity. To be honest, I don't even understand why "f(x) tends to f(a) as x tends to a" describes continuity.

Also, I am wondering why f(x) = mod x is not differentiable at the origin. Surely, f(x) can have two tangents with opposite orientations at the origin, can't it??

Please help!!

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# Differentiability and Continuity

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