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Every transfinite consistent multiplicity, that is, every transfinite set, must have a definite aleph as its cardinal number.

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
Must
Every
Cardinal
Cardinals
Multiplicity
Definite
Consistent
Number
Numbers

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