Andrew Coppin wrote:
7 is a number. 7 is an integer, and integers are numbers.
7 is not a field. 7 is an element of [at least one] field, but 7 itself is not a field.
7 is not a group.
Why not? It might be useful to use the notation '7' for the cyclic group with 7 elements.
7 is a member of the set of integers, but the set of integers is not a group either. The set of integers form a group when taken together with the addition operator. (And, actually, forms another, different, group when taken with the multiplication operator.)
The integers endowed with the usual multiplication is not a group. (The only invertible elements of this monoid are 1 and -1.)
Now, here's the question: Is is correct to say that [3, 5, 8] is a monad?
In what sense would this be a monad? I don't quite get your question. Cheers, Jochem -- Jochem Berndsen | jochem@functor.nl