michael_nielsen

(as opposed to requiring the *, or defining the implicit operator as addition for something wacky; this is a possibility, but get ready for equations like "y = (1/2) * x + 9" and shit, and actually does that need to be (1 / 2) maybe?) but it's even more than that

Let's say we disallow the implicit operator bc fuck readability and common sense. You still wind up with the same "problem" the wikipedia page says is created by implicit multiplication. This author literally is wrong about OoO I think?

Like, if you've got 3*x in there somewhere, amidst "mixed multiplication and division", and you decide to declare that 3*x = Z and do everything and then expand the Z back out last, if you get different results, your OoO is fucking broken

So it isn't that M takes precedence over D and it has nothing to do with implicit operators I. *IF* variables are a valid thing, and I can declare 3*x = Z and that changes nothing, and I can make 3 = Q or something, and now 9 = 3*Q, and Z = Q*x and

II. *IF* division is defined such that when, say, 3*x = Z that x = Z/3 AND

III. *IF* the commutative property of multiplication is a thing THEN division isn't really a thing; it's the inverse operation of multiplication and the two can be interchanged arbitrarily THUS M takes precedence over D because D is not real; indeed, D is M^E, and E>M

Like it's not an option, it absolutely has to work that way. If you insist on keeping D and S in your PEMDAS, you're going to have a bad time. D is M^E and S is M*A Understanding how there is no D and there is no S is the only way to never ever fuck up OoO

You may be entertained to hear that I mentally formalized all of this in 8th grade during class just dicking around with excessive parenths on my TI-83 when I became bothered with all the contradictions I could immediately generate with PEMDAS and the teacher got lost for a week