Intuition depends on what you're used to. The ancient Greeks didn't think 1 was a number; as late as ~1500CE Isidore of Seville was saying "one is the seed of

Intuition depends on what you're used to. The ancient Greeks didn't think 1 was a number; as late as ~1500CE Isidore of Seville was saying "one is the seed of number but not number". After all, if there's only one thing you don't need to think of it as a set of things, so there's no counting to do. (I think in some quarters it was even argued that two isn't a number, but I forget the details. Compare the fact that some languages treat pairs of things differently in their syntax from larger groups.) But it turns out that mathematically it's a really good idea to count 1 as a number and allow sets of size 1, and these days everyone does it and no one is very confused by it. (Well, maybe by the "sets of size 1" thing. Exhibit A: Perl. Exhibit B: Matlab.) And because we're now all used to thinking of 1 as a number, it's hard even to understand how anyone might have found it unintuitive. If we all started counting from zero and taught our children to do likewise, intuitions 50 years from now might be somewhat different from what they are now.