Georg Cantor

The power of the set of all real numbers is greater than the power of the set of all natural numbers.

Every well-defined set has a power.

The arithmetic of the transfinite numbers is a natural generalization of the finite arithmetic.

The creation of the transfinite numbers is, in a certain sense, the opposite of the creation of the finite irrational numbers.

I entertain no doubts as to the truth of the transfinites, which I have recognized with God's help and which, in their diversity, I have studied for more than twenty years; every year, and almost every day brings me further in this science.

The Absolute is incomprehensible for the human understanding.

The transfinite numbers are not mere symbols; they denote well-defined realities.

The history of mathematics shows that the introduction of new concepts, however bold they may seem, has always been fruitful.

My theory is as clear as day. I have not hidden any difficulties.

The heart of my theory is the concept of well-ordering and the ordinal numbers.

The totality of all alephs is not a set.

The difficulties and paradoxes of set theory arise only when one considers 'inconsistent multiplicities', i.e., multiplicities that cannot be conceived as a unified whole.

I have never let the criticism of others deter me from following the path that I recognized as correct.

The beauty of mathematics lies in its internal harmony and the clarity of its concepts.

God created the integers, all else is the work of man.

The value of a theory is measured by its fruitfulness.

I thank God, the all-wise, that He has granted me the joy of seeing the harmony and beauty in this part of His creation.

The opposition I have encountered has only strengthened my conviction in the truth of my discoveries.

A false conclusion once drawn is, in science, not only useless but positively harmful.

The transfinite numbers are like a bridge leading from the finite to the Absolute.