Great innovation only happens when people aren’t afraid to do things differently.
GEORG CANTORA set is a Many that allows itself to be thought of as a One.
More Georg Cantor Quotes
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Had Mittag-Leffler had his way, I should have to wait until the year 1984, which to me seemed too great a demand!
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A false conclusion once arrived at and widely accepted is not easily dislodged and the less it is understood the more tenaciously it is held.
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Mathematics, in the development of its ideas, has only to take account of the immanent reality of its concepts and has absolutely no obligation to examine their transient reality.
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The 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.
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The transfinite numbers are in a sense the new irrationalities they stand or fall with the finite irrational numbers.
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I entertain no doubts as to the truths of the tranfinites, 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.
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Every transfinite consistent multiplicity, that is, every transfinite set, must have a definite aleph as its cardinal number.
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Don’t always blindly follow guidance and step-by-step instructions; you might run into something interesting.
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A set is a Many that allows itself to be thought of as a One.
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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.
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In mathematics, the art of asking questions is more valuable than solving problems.
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In mathematics the art of proposing a question must be held of higher value than solving it.
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There 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.
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The 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 CANTOR