34 Quotes by Georg Cantor
- Author Georg Cantor
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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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- Author Georg Cantor
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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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- Author Georg Cantor
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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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- Author Georg Cantor
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The essence of mathematics lies precisely in its freedom.
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- Author Georg Cantor
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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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- Author Georg Cantor
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Mathematics 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.
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- Author Georg Cantor
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My theory stands as firm as a rock; every arrow directed against it will return quickly to its archer. How do I know this? Because I have studied it from all sides for many years; because I have examined all objections which have ever been made against the infinite numbers; and above all because I have followed its roots, so to speak, to the first infallible cause of all created things.
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- Author Georg Cantor
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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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- Author Georg Cantor
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In mathematics, the art of asking questions is more valuable than solving problems.
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