Infinities as numbers: purging the epsilons and deltas from proofs

Part 6 of a six-part series of adaptations from Terence Tao’s book “Structure and Randomness".

[1.5] Ultrafilters, non-standard analysis, and epsilon management

In the previous article we saw that fruitful analogies between finitary and infinitary mathematics can allow the techniques of one to shed light on the other. Here we borrow the power of infinitary math—in particular, ultrafilters and non-standard analysis—to simplify proofs of finitary statements.

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