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Artwork for Reasonable Hope (Math)
Reasonable Hope (Math) · Yesterday · 4 min

Everywhere, Yet Taking Up No Space

Fractions are dense: between any two numbers, we can always find more of them. Yet the rational numbers have measure zero on the number line. This surprising result reminds us that before asking whether an infinite set is big, we must define what “big” means.

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Fractions are dense: between any two numbers, we can always find more of them. Yet the rational numbers have measure zero on the number line. This surprising result reminds us that before asking whether an infinite set is big, we must define what “big” means.

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