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Wellsprings
mathematics

Magnitude vs. Number (Continuous and Discrete Quantity)

μέγεθος καὶ ἀριθμός

The Greeks split quantity at its root: the unbroken line you measure, the countable heap you tally—two kinds of "how much," forever kept apart.

The Greeks drew a sharp line between two kinds of quantity. A magnitude (megethos)—a length, area, or volume—is continuous: you can always divide it again, with no smallest piece, and it belongs to geometry. A number (arithmos)—a collection of units—is discrete: it is built from indivisible ones and belongs to arithmetic. Because they refused to treat a smooth line as merely a pile of points, Greek mathematicians built two separate theories of ratio and proportion, one for magnitudes and one for numbers, a divide that shaped Western mathematics for two thousand years.

Where this idea shows up

5 Greek sources·2 Jewish-canon citations

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