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and infinite. Each of these was further subdivided into three orders:

* Enumerable: lowest, intermediate and highest
* Innumerable: nearly innumerable, truly innumerable and innumerably innumerable
* Infinite: nearly infinite, truly infinite, infinitely infinite

They also distinguished five types of infinity: infinity in one direction, infinity in two directions, infinity in area, infinity in all directions (that is, in volume), and perpetual infinity.

Views from the Renaissance to modern times

Galileo

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