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.