Georg Cantor
Created set theory and theory of transfinite numbers
Quotes by Georg Cantor
I place myself in a certain opposition to widespread views on the mathematical infinite and to oft-defended opinions on the essence of number.
The finite has been the sole object of mathematics up to now; I have been the first to investigate the infinite.
The transfinite numbers are not less real than the finite numbers, but they have a different mode of existence.
The Absolute can only be acknowledged and admitted, never known, not even approximately.
The distinction between the finite and the infinite is the most fundamental and far-reaching of all mathematical distinctions.
The totality of all that is thinkable constitutes an inconsistent multiplicity, a multiplicity such that the assumption that all its elements 'exist together' leads to a contradiction.
The concept of the continuum is the true stumbling block in the theory of manifolds.
The transfinite numbers are in a sense the new irrationalities... they are the 'atoms' of the new arithmetic.
The highest perfection of a being lies in its ability to create.
The foundation of my theory of transfinite numbers is the definition of the 'power' or 'cardinal number' of a set.
The fear of the actual infinite is a prejudice that has its origin in a misunderstanding of the nature of the human mind.
Every well-defined set has a cardinal number.
The transfinite sequence of numbers is just as necessary and just as definite as the finite number sequence.
The infinite is nowhere to be found in reality, no matter what experiences, observations, and knowledge are appealed to.
My theory is as necessary for mathematics as, say, the theory of the irrational numbers.
The power of the continuum is the same as that of the set of all functions of a real variable.
The concept of 'well-ordered set' is fundamental to the entire theory of transfinite numbers.
The transfinite numbers are not mere symbols; they express a definite reality.
The creation of the transfinite numbers is the act of pure thought.
The history of mathematics shows that every great step forward has been met with opposition and misunderstanding.