3 ms·
This can be explained clearly in two sentences: Division is the inverse of multiplication (a * b / b = a / b * b = a). However, multiplication by 0 is not inje
by meuk 7y ago
This can be explained clearly in two sentences:
Division is the inverse of multiplication (a * b / b = a / b * b = a). However, multiplication by 0 is not injective (we have x * 0 = 0 for every x), so multiplication by zero can't have an inverse operation, and both 0/0 and 1/0 are undefined.
- EForEndeavour 7y agoThis explanation correctly explains why 1/0 and 0/0 are not numbers, but doesn't answer the question of what makes 1/0 and 0/0 different. And they aren't both undefined. 1/0 is undefined because no value of x satisfies 1/0 = x. 0/0 is indeterminate because any value of x satisfies 0/0 = x.
- throwawaymath 7y ago0/0 is only indeterminate if your axioms allow or require it to be. Strictly speaking you can define 0/0 to mean something, but you will lose a lot of useful properties along the way. The only time 0/0 is not indeterminate is when you're dealing with something exotic and obscure like an algebraic wheel. It's correct to say 0/0 is undefined because in the vast majority of cases where someone doesn't explicitly call out the algebraic setting, they're working with a field.