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There is no doubt that we cannot do without variable quantities in the sense of the potential infinite. But from this very fact the necessity of the actual infinite can be demonstrated.

— Georg Cantor

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Mathematics

More quotes by Georg Cantor

My theory stands as firm as a rock; every arrow directed against it will return quickly to its archer.

Journey Through Genius (1990)

In mathematics the art of asking questions is more valuable than solving problems.

Had Mittag-Leffler had his way, I should have to wait until the year 1984, which to me seemed too great a demand!

Letter (1885)

Each potential infinite, if it is rigorously applicable mathematically, presupposes an actual infinite.

A set is a Many that allows itself to be thought of as a One.

Infinity and the Mind (1995)

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Anyone who believes exponential growth can go on forever in a finite world is either a madman or an economist.

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If the doors of perception were cleansed, everything would appear to man as it is: infinite.

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Pure mathematics consists entirely of assertions to the effect that, if such and such a proposition is true of anything, then such and such another proposition is true of that thing.

Bertrand Russell

The land of easy mathematics where he who works adds up and he who retires subtracts.

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Attribution

Quote text and notes from Wikiquote: Georg Cantor (page history), available under CC BY-SA 4.0. Source quality and labels are our own summary of what Wikiquote records.