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

— Georg Cantor

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Source, in full

in "Über die verschiedenen Ansichten in Bezug auf die actualunendlichen Zahlen" ["Over the different views with regard to the actual infinite numbers"] - Bihand Till Koniglen Svenska Vetenskaps Akademiens Handigar (1886).

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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.

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.

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)

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

Infinity and the Mind (1995)

All Georg Cantor quotes →

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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.

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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.