If there is some determinate succession of defined whole real numbers, among which there exists no greatest, on the basis of this second principle of… - Georg Cantor

I realize that in this undertaking I place myself in a certain opposition to views widely held concerning the mathematical infinite and to opinions frequently defended on the nature of numbers.

I entertain no doubts as to the truths of the transfinites, which I 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.

This view [of the infinite], which I consider to be the sole correct one, is held by only a few. While possibly I am the very first in history to take this position so explicitly, with all of its logical consequences, I know for sure that I shall not be the last!