4 ms·
> that AND and OR are sums and products Perhaps you meant to say that AND and XOR are products and sums.
by js8 2y ago
> that AND and OR are sums and products
Perhaps you meant to say that AND and XOR are products and sums.
- klysm 2y agoIt seems fair to think of OR as a 'saturating' sum
- js8 2y agoThe issue is then boolean functions do not form a polynomial ring with this "sum", because unlike XOR, OR is not a group operation - it doesn't have a well defined inverse.
- selecsosi 2y agoThis is an important distinction between whether we are preserving structures on rings or on a group. An example would be mapping positive to negative numbers which is a group level transformation but not structure preserving for order while still being invertible