Cantorian set theory demonstrates that infinite sets can be placed in bijection with proper subsets, undermining the Aristotelian assumption that infinite extension entails unmeasurable magnitude.

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Aristotelian assumption(the traditional view being challenged): A belief from the ancient philosopher Aristotle that infinity must mean something immeasurably large and cannot be precisely compared or counted.
Bijection(in set theory and mathematics): A perfect one-to-one matching between two sets, where every element in one set pairs with exactly one element in the other, and nothing is left unpaired.
Cantorian set theory(the main subject being discussed): A mathematical system developed by Georg Cantor that studies collections of objects (called sets) and how to compare the sizes of infinite collections in precise ways.
Infinite extension(in mathematics): The complete, never-ending list of all things that fit a rule or definition. If a recursive rule generates numbers, its infinite extension would be every single number it generates, going on forever.

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