Again, still, you are merely reading it in a convoluted way.
It is how many TIMES the 31 is taken. The 31 is taken 0 times, and thus 31 * 0 = 0, because no 31 is taken into the final sum.
By the associative property, also 0 * 31 = 0, but because 0 taken 31 times still sums to zero.
In one case, you have NO 31’s. And in the other case, you have 31 zeros.
It is THEIR language. Learn to read what THEY mean by THEIR notation. The fact that you can distort it to read something different is irrelevant. You can do the same with any language.
X divided by Y means X number of elements equally distributed across Y number of groups. The result of division is not the number of elements that remain in the original, undivided, pool of elements but the number of elements in each one of the divisions.
31 divided by 0 means 31 elements equally distributed across 0 number of groups. How many elements do we get in every group after such an operation? But there are no groups – there are 0 groups – so we can’t really answer. Therefore, the result is undefined.
Ecmandu is speaking of a different operation – not division – and he does so because he thinks that words precede concepts rather than the other way around.
Division is not a subtractive operation. You do not remove elements from the starting pool of elements using certain method then count how many elements remain. That’s not division.
Similarly, multiplication is not an additive operation.
If our language implies it, then that’s the problem of language, and you shouldn’t confuse it for a mathematical problem.
There are no existents, no states, in multiplication and division. You are speaking of different operations – ones you made up, invented, imagined, created in your head.
Because the result of division is the number of elements within each one of the groups. We are counting the number of elements within groups, not the number of elements outside of these groups. When there are no groups, there is nothing to count, therefore, the result is undefined.