Full Idea
It is a mistake to think of an infinite number as a very large number. Infinite numbers differ qualitatively from finite numbers.
Gist of Idea
Infinite numbers are qualitatively different - they are not just very large numbers
Source
John Heil (The Universe as We Find It [2012], 03.5)
Book Reference
Heil,John: 'The Universe as We Find It' [OUP 2012], p.43
A Reaction
He cites Dedekind's idea that a proper subset of an infinite number can match one-one with the number. Respectable numbers don't behave in this disgraceful fashion. This should be on the wall of every seminar on philosophy of mathematics.