A set is a Many that allows itself to be thought of as a One.
GEORG CANTORA set is a Many that allows itself to be thought of as a One.
GEORG CANTORThe potential infinite means nothing other than an undetermined, variable quantity, always remaining finite, which has to assume values that either become smaller than any finite limit no matter how small, or greater than any finite limit no matter how great.
GEORG CANTORUse Campaign link tagging labels all for specifying slight differences in content for split testing.
GEORG CANTOREvery transfinite consistent multiplicity, that is, every transfinite set, must have a definite aleph as its cardinal number.
GEORG CANTORIn mathematics the art of proposing a question must be held of higher value than solving it.
GEORG CANTORTo ask the right question is harder than to answer it.
GEORG CANTORMy beautiful proof lies all in ruins.
GEORG CANTORMathematics is entirely free in its development, and its concepts are only linked by the necessity of being consistent, and are co-ordinated with concepts introduced previously by means of precise definitions.
GEORG CANTORThe transfinite numbers are in a sense the new irrationalities they stand or fall with the finite irrational numbers.
GEORG CANTORThe fear of infinity is a form of myopia that destroys the possibility of seeing the actual infinite, even though it in its highest form has created and sustains us, and in its secondary transfinite forms occurs all around us and even inhabits our minds.
GEORG CANTORThere is no doubt that we cannot do without variable quantities in the sense of the potential infinite. But from this very fact the necessity of the actual infinite can be demonstrated.
GEORG CANTORDon’t always blindly follow guidance and step-by-step instructions; you might run into something interesting.
GEORG CANTORIn mathematics, the art of asking questions is more valuable than solving problems.
GEORG CANTORHad Mittag-Leffler had his way, I should have to wait until the year 1984, which to me seemed too great a demand!
GEORG CANTORThe essence of mathematics lies precisely in its freedom.
GEORG CANTORThis 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!
GEORG CANTOR