[gowld]

The abstraction can clarify the boundaries and scope.

For example:

  I'm thinking of a *number* between 1 and 10, for example, 3 or 7.

Is 1 allowed? Is 10 allowed? non-integers? Irrationals?

A definition and theorems can seem trivial, if you latch onto the first trivial example and treat it as the canonical situation. This is very common difficulty when learning intro abstract math.