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What I assert and believe to have demonstrated in this and earlier works is that following the finite there is a transfinite (which one could also call the supra-finite), that is an unbounded ascending ladder of definite modes, which by their nature are not finite but infinite, but which just like the finite can be determined by well-defined and distinguishable numbers.

— Georg Cantor Understanding the Infinite (1994)

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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)

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

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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.