### Single Idea 10855

#### [catalogued under 6. Mathematics / A. Nature of Mathematics / 5. The Infinite / d. Actual infinite]

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.

Gist of Idea

Actual infinities are not allowed in mathematics - only limits which may increase without bound

Source

Carl Friedrich Gauss (Letter to Shumacher [1831]), quoted by Brian Clegg - Infinity: Quest to Think the Unthinkable Ch.7

Book Reference

Clegg,Brian: 'Infinity' [Robinson 2003], p.78