If you stipulate 31 feet exist without width, can it exist?
The issue here is that in order to first establish 31 feet, it has to exist in some way, so width is implied in the initial formulation, not matter how minuscule …
What happens with order of operations…
If you start with multiplying nothing, it stays nothing.
If you multiply a length first, even by nothing, it squares at it’s own length … The zero flips to the only other variable. It can’t be zero, because it’s an existent.
This is declared immediately when you start off “31 feet times x”
The 31 feet already exist in order of operations, the logical multiplier is 31 feet
Order of operations is that of you initially establish a quantity, it has to remain quantified for the purpose of the next operation. If the next operation is zero, the quantity remains …
When dealing with multiplication, there is a squaring of the line to keep it’s identity (only variable there is)
Divided by, leaves the initial quantity, but it must also be squared to keep it’s initial existential form.
It’s an order of operations procedure that only applies to zero
It’s implied that if 7 feet exist in one direction, that 7 feet must exist in the other direction in order for it to be quantified as an initial presentation.
If the initial presentation is zero, then zero is the multiplicative sum
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.