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Single Idea 7556

[from 'Mathematics and the Metaphysicians' by Bertrand Russell, in 6. Mathematics / A. Nature of Mathematics / 5. The Infinite / b. Mark of the infinite ]

Full Idea

A collection of terms is infinite if it contains as parts other collections which have as many terms as it has; that is, you can take away some terms of the collection without diminishing its number; there are as many even numbers as numbers all together.

Gist of Idea

A collection is infinite if you can remove some terms without diminishing its number

Source

Bertrand Russell (Mathematics and the Metaphysicians [1901], p.86)

Book Reference

Russell,Bertrand: 'Mysticism and Logic' [Unwin 1989], p.86


A Reaction

He cites Dedekind and Cantor as source for these ideas. If it won't obey the rule that subtraction makes it smaller, then it clearly isn't a number, and really it should be banned from all mathematics.