Ideas of Carl Friedrich Gauss, by Theme

[German, 1777 - 1855, Professor of Astronomy at Göttingen. One of the greatest mathematicians.]

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6. Mathematics / A. Nature of Mathematics / 5. The Infinite / d. Actual infinite
Actual infinities are not allowed in mathematics - only limits which may increase without bound
     Full Idea: I protest against the use of an infinite quantity as an actual entity; this is never allowed in mathematics. The infinite is only a manner of speaking, in which one properly speaks of limits ...which are permitted to increase without bound.
     From: Carl Friedrich Gauss (Letter to Shumacher [1831]), quoted by Brian Clegg - Infinity: Quest to Think the Unthinkable Ch.7