I forgot…
Explain to me how division isn’t the reciprocal of multiplication???
James already addressed that:
Oh… And before you bother me by saying that multiplication has no order of operations and division does…
How is division not reciprocal in the context of that order of operations??
Explain all this to me
Thanks phyllo…
What about reciprocal do you both not understand!?!?!
Of course the multipliers will be the inverse of the dividers!
Perhaps we would understand better if you wrote that out in math notation.
I want to comment on this more, because my sentence was a throwaway sentence.
You have to understand reciprocal more…
It’s not simply changing back and forth…
The actual structure of the rules are inverse between divisors and multipliers.
You’re applying multiplier rules to divisor rules instead of doing an actual inversion.
Yes, there is no way that 31*0 = 31
(31 zero times)
However, 31 times 0, is 31 . 31 0 times is 0. This is a very precise point about your notation.
To look closer at order of operations…
0 31 times is zero.
0 times 31 is zero.
You can’t multiply zero without it just staying zero.
But somehow… You can divide zero and develop undefined???
The order of operations for multiplication change if the 31 is first as above
I edited the above post for clarity
If you have a rectangular piece of land, the area cannot be different when multiplying length times width versus multiplying width times length.
However, you are saying the area of a strip of land which 0 feet by 31 feet has two areas depending on the how you do the multiplication … either 0 square feet or 31 square feet. 
It’s the way the language works…
31 square feet multiplied by no quantity is still 31 square feet.
No quantity multiplied by 31 square feet is still no quantity.
Multiplication also has an order of operations, a subtle point missed only when it comes to zero.
Think it through!
My mistake…
You said feet, not square feet.
So the question here is…
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
I’ll try to simplify this…
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
A line has no substance, so no.
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.
That’s exceedingly clear James.
I’m doing 31 is taken times 0
And you’re doing 31 is taken 0 times
Now we’ve clarified
The way the language is used can certainly facilitate my perspective on multiplication and division without twisting or convoluting language.
Your interpretation of the language is not the normative btw, so I think you can forgive me using normative language and arguing from there.
We don’t generally say 31 4 times, we say 31 times 4
It most certainly is, but you go do your independent thing.
But also remember as they say, “God has no respect for the individual”.
I edited my post but it didn’t get through…
We don’t say 31 4 times, we say 31 times 4
Attend more to what is meant by people than what is said by people, and you will make far more progress.
So you’re saying that there’s no value in the distinction of:
1.) 31 times 4
2.) 31 4 times
?
It’s not an issue until you hit zero…
31 0 times is zero
31 times zero implies the existent not being acted upon…
Which is the one people always use??
If everyone means what you explained, then why don’t they use language to speak to it?
Math has been here for thousands of years from logiticians!!!
That is called Reverse Polish Notation notation and it’s equivalent to the ‘usual’ way of saying it which is called infix notation.
Thanks phyllo,
Read my last post about meaning, just above yours