3 is also the product of the sets {3, 1}, {3, 1, 1}, etc.
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.
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.