Aha, modulus x is continuous because its graph is an unbroken 'V' shape—no lifting your pen. But at that sharp vertex at zero, which side is the tangent? Left slope is -1, right is +1, so it has no single derivative there. This always felt like dry theory until I saw my father's ration shop accounts: the graph of our savings was a sharp 'V' after my sister's fees, continuous in struggle but not differentiable at that decision point. Chhaan, the maths of real life is clearer than any textbook.
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