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LESSON 5 · Calculus Without Tears

Infinity in Modern Physics

Zeno's paradox found a clean answer in calculus, but infinity still causes trouble at the frontier of physics. Black hole equations predict a point of infinite density that nobody believes is literal — a sign the theory has hit its limits. Einstein's relativity and quantum mechanics each predict infinities the other must correct.

Computer science meets the same wall. Summing the infinite series for pi can never finish in finite time, so engineers truncate: they stop once extra terms are too small to matter. GPS positioning and audio streaming both run on these deliberately interrupted sums.