“ But where the primes are numbers that are the product of just one factor, 1 is the product of zero factors, a very different status.”
What do you mean?
The factors of 3 are 3 and 1. The factors of 1 are 1?
What do you mean?
The factors of 3 are 3 and 1. The factors of 1 are 1?
3 is the product of the members of {3}.
1 is the product of the members of the empty set.
We’re excluding the unit when defining these factor sets (ie, multiplicative identity) because it removes unique factorization.
That 1 is the unit is also why it’s the value for the product of the empty set because we want the product of a union of sets to match the product of a product of sets. But we don’t exclude it from the primes for that reason.
Oh! So it’s like Python’s `reduce(multiply,s,initial=1)`, such that s={} still gets you 1. Alright, that makes sense.