4 ms·
The exclusion of negative numbers is not arbitrary. Depending on your exact definition, you would be left with the current prime numbers, these plus their negat
by tgv 3y ago
The exclusion of negative numbers is not arbitrary. Depending on your exact definition, you would be left with the current prime numbers, these plus their negatives, or none at all (since 2 is divisible by -2).
- contravariant 3y agoThe notion of 'negative' doesn't transfer too well to other rings. It vaguely makes sense to only look at the natural numbers (excluding 0), primality predates negative numbers as a concept after all, but from the point of view of the more general definition it is mostly arbitrary.
- gizmo686 3y agoPrimality is defined for any ring (although some rings have no primes). If you are asking about prime integers, then negative primes are themselves prime. Most of what you know of primality still holds if you add 'up to unit multiples' to all of your theroums.