Georg Cantor

I protest against the use of infinite as a finished quantity, which in mathematics is never permissible.

A set is a many that allows itself to be thought of as a one.

The transfinite numbers are in a certain sense only an extension of the finite numbers.

The actual infinite is not an absurdity, but a reality.

My theory of transfinite numbers is not a mere game of ideas, but a natural and harmonious extension of the ordinary number concept.

The fear of infinity is a form of myopia that destroys the possibility of seeing the actual infinite, even though it is there, in all its splendor, waiting to be discovered.

Mathematics is entirely free in its development and its concepts are only bound by the absence of contradiction.

The transfinite numbers are in a certain sense only an extension of the finite numbers, and their introduction into mathematics is not only justified but also necessary.

The actual infinite exists in three relations: first, as it is realized in the supreme perfection, in the absolutely infinite, wholly independent of any finite determination; second, as it occurs in the contingent, created world; third, as it is conceived in the mind, as a mathematical concept.

I am so in love with the transfinite that I have no fear of being attacked by it.

Every set has a cardinal number.

The power of a set is its cardinal number.

The continuum hypothesis is a question of such a nature that it is not possible to answer it by means of the usual methods of set theory.

The transfinite numbers are not only an extension of the finite numbers, but they also open up a new world of mathematical thought.

The actual infinite is not a contradiction, but a reality.

The essence of mathematics lies in its freedom from contradiction.

My theory of transfinite numbers is a natural and harmonious extension of the ordinary number concept.

The transfinite numbers are not only an extension of the finite numbers, but they also open up a new world of mathematical thought and discovery.

The actual infinite is not an absurdity, but a reality, and it is the task of mathematics to explore it.

The fear of infinity is a form of myopia that destroys the possibility of seeing the actual infinite, even though it is there, in all its splendor, waiting to be discovered and explored.