Georg Cantor

Mathematics is entirely free in its development, and its concepts are only bound by the absence of contradiction, which is the only criterion for their legitimacy and for their existence, and for their profound significance in the realm of human knowledge and scientific inquiry.

A set is a collection into a whole of definite, distinct objects of our intuition or of our thought. These objects are called the elements of the set. The set itself is a single object, which can be an element of another set, and so on.

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, which is of the greatest importance for the progress of mathematics and for the understanding of the universe and its infinite possibilities, and for the advancement of human knowledge and scientific understanding.

The actual infinite is not an absurdity, but a reality, and it is the task of mathematics to explore it and to make it accessible to human thought and understanding, and to reveal its profound implications for philosophy and theology, and for our understanding of the divine and the nature of existence.

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 by the human mind and intellect, and to reveal its profound implications for our understanding of reality and the universe and our place within it.

Mathematics is entirely free in its development, and its concepts are only bound by the absence of contradiction, which is the only criterion for their legitimacy and for their existence, and for their profound significance in the realm of human knowledge and scientific inquiry and philosophical contemplation.

My theory of transfinite numbers is so far-reaching that it will be a long time before it is fully understood and appreciated.

I entertain no doubt that the transfinite numbers are just as real as the finite ones.

I am so firmly convinced of the truth of my theory that I cannot doubt it for a moment.

The fear of infinity is a form of myopia that destroys the possibility of seeing the truly great.

I am not a prophet, but I am a mathematician, and I know that my theory is true.

My work is a struggle against the prejudices of the past.

I have been persecuted for my ideas, but I will not give up.

The transfinite numbers are not just a game; they are a reality.

I see it, but I don't believe it!

I am convinced that the infinite is not a mere potentiality, but a reality.

Every good mathematician is at least half a philosopher, and every good philosopher is at least half a mathematician.

My theory stands as a rock, and I am convinced that it will prevail.

I am a mathematician, not a theologian.

The true infinite is not to be found in the finite, but in the transfinite.