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The transfinite numbers are in a sense the new irrationalities [ ... they] stand or fall with the finite irrational numbers.

Georg Cantor

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Georg Cantor
Age: 72 †
Born: 1845
Born: March 3
Died: 1918
Died: January 6
Mathematician
Philosopher
University Teacher
St. Petersburg
Georg Ferdinand Ludwig Philipp Cantor
Cantor
Irrational
Mathematics
Numbers
Stand
Fall
Sense
Irrationality
Finite

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The essence of mathematics lies precisely in its freedom.
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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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To ask the right question is harder than to answer it.
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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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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 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.
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A set is a Many that allows itself to be thought of as a One.
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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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Great innovation only happens when people aren't afraid to do things differently.
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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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