especially for mixed division and multiplication, have changed over time

and yet, have not changed since he died. 😂 Keep going - you're on the right track but the rabbit hole is deeper

Supporting my point that these “rules” are not in fact rules of maths

says person who doesn't know the difference between rules and conventions, and thus does not support what you are saying 😂

instead rules of mathematicians

who proved them, yes

associative relations which obey the distributive law

Property, not Law, yes

may break one set of rules of precedence

there's only one set! 😂

those are rules made by mathematicians not by the fundamental working of the universe

says person failing to give a single example of such 😂

How do I know this?

Same way you "know" everything - you just make it up as you go along, but never can produce any evidence to support you 😂

at the time he was writing, there was “no agreement” over the order in which to perform divisions and multiplications if both occur in an expression

Yep, and why was that, or have you already forgotten the assignment? 😂

So here’s a question for you: do you agree with Cajori that at one time there was no agreement over which order to perform multiplications and divisions, or not?

Of course, and I, unlike you, know exactly what he was talking about 😂

do you then agree that, for there to be agreement now

There isn't, given he was talking about conventions, and now, same as then, different people use different conventions, but all of them obey the rules 🙄

that change must be through rules created by mathematicians

from proof of same

rules given to us from the universe itself?

NOW you're getting it!

Because the universe certainly didn’t change in the meantime, did it?

Nope, and neither have the rules 😂

If you don’t agree then that would rather expose your fetishisation of textbooks as hollow trolling, of course.

And, yet I did agree, sorry to spoil your fun. 🤣🤣🤣 BTW Cajori isn't a textbook, in case you didn't notice 😂

You said every single post is wrong - present tense

Nope! I covered the past as well Mr. Abysmal Reading Comprehension

There is no “=” button on the Sinclair Executive, and you aren’t saying the +=

and what's that second symbol in +=?? 😂

you aren’t saying the += button means “equals”,

Yes I am! 😂 I told you exactly when it's interpreted as a plus, and exactly when it is interpreted as an equals 🙄

you’re saying it omits the manipulation of the (non existent) stack

No, I'm saying omitting that keypress will evaluate a+bxc, instead of (a+b)xc, because it does have a stack. It's not complicated. All my calculators work the same way, even the one I have that doesn't have brackets keys (though according to you it doesn't have a stack if it doesn't have brackets keys 😂 )

The part where you haven’t proven anything, of course

Well, that part never happened, so...😂

An example in the manual of it obeying order of operations in violation of right to left execution

says person proving they didn't read it! 😂 Go ahead and type in a+=bxc+=, I'll wait.

Also...

Oh look. it remembers the division whilst we enter other things! I wonder how it does that?? 🤣🤣🤣 And look, it remembers four numbers, not, you know limited to three numbers like you insisted was it's limit! 🤣🤣🤣

Also, (a+b)/(c+d) has three operands, and somehow it manages to remember all of them. I wonder how it does that, considering you said it could only take one operand! 🤣🤣🤣

The specifications saying how much stack memory it had

You know the stack isn't hardware, right? Go ahead and find any calculator manual which specifies how big the stack is. I'll wait 😂

A video of someone using it to show it using order of operations in violation of right to left execution

says person who hasn't provided a video of anyone entering 2+=3x4+= and it going "left to right". Also, you have failed to explain how it is possible to do a(b+c)+d(e+f) without brackets and without splitting it up

An emulator where you can see the same

You're arguing about calculators that precede the internet, and you're expecting an emulator to exist for it?! 🤣🤣🤣 But sure, go ahead and find an emulator for you calculator, type in 2+=3x4+=, and tell me what you get. I'll wait 🤣🤣🤣

You have none of that.

says person who has none of anything 🤣🤣🤣

Instead you have an example in the manual where the calculator executes strictly left to right,

No it doesn't! 🤣🤣🤣

but you have said, without evidence

says person, who said without evidence that it goes strictly left to right

that a button on the calculator is preventing us from seeing its normal behaviour

No idea what you're talking about. It explicitly shows you how it works 🙄

You can’t evaluate that expression without splitting it up? I can.

and yet, you have still failed to explain how 🙄

Just fuckin’ evaluate it normally!

Normally is a(b+c)+d(e+f)=, but sure, go ahead and explain to us how you can evaluate that "normally" without brackets and without splitting it up. I'll wait, again 🤣🤣🤣

That sentence is talking about the calculator’s capability

which is limited because no brackets keys.

my unskilled friend

says person who claims you can do a(b+c)+d(e+f)= without brackets and without splitting it up, but sure, go ahead, and tell us how we can do that oh master genius of the universe - we're all waiting for your almighty instruction! 🤣🤣🤣

Brackets are notation; RPN doesn’t use them

and so is the missing + in 2+3, and yet we know it's there, which you have acknowledged you saw in the textbook 🤣🤣🤣

What you’ve said by implication is that a calculator doesn’t need buttons for brackets in order to calculate a complex expression

Nope, I've explicitly said they are required, for complex equations, as per the manual telling you that you can't do it, unless you split it up, liar

So, we understand it’s not a lack of brackets buttons holding back the Sinclair Cambridge

says person who has still not said how to magically do it without brackets and without splitting it up. We are still awaiting your almighty instruction master genius 🤣🤣🤣

What is holding them back then, is lack of

Brackets

Bet you’ll deflect

says person still deflecting from how to magically do a(b+c)+d(e+f)= without brackets and without splitting it up

If you’ve established it, you’d have evidence in the form of one of the four bullet points above

Yep, point 1. I'll take that as an admission of being wrong, yet again 🤣🤣🤣

I’d write it out in rpn

Is it an RPN calculator? No it isn't Mr. deflection

You’re saying that example tells you what would happen when the += key was not pressed a second time?

Nope, it's right there in the manual that pressing it a second time puts it in brackets, and I've asked you, oh master genius of which we are not worthy, what answer it would give if we don't press it a second time. Not complicated, and yet you still avoid answering 🤣🤣🤣

Do explain how an example tells you what happens in a situation other than the one in the example

Yes, because I want you to explain it. I already know what answer it's going to give, and you do too, which is why you're avoiding answering 🤣🤣🤣

Nope, still not a proof of anything except that, in that example, the calculator executes from left to right.

No it doesn't! It puts (a+b) on the stack whilst we type out the rest of it, duuuhhh!! 🤣🤣🤣

You don’t teach them that ab means a×b?

NOW you're getting it! We teach them that ab=(axb), as I have been saying all along 🤣🤣🤣 You know, like in this textbook...

“That’s pro–” oh do be quiet

says person deflecting form the fact that Products and "implied multiplication" aren't the same thing, oh Mr. just Google it to see how it works 😂

I just told you I don’t care what you call it

says person who apparently doesn't care if I call a horse a unicorn, even though we know unicorns don't exist

and you told me it doesn’t exist

Yep, hence why you won't find it in any Maths textbooks 🙄

You did not say “we teach this concept, but with a different name”.

Correct. We don't teach them about the mythical "implied multiplication" that gets mentioned by people who got the wrong answer 😂

All evidence suggests you aren’t actually capable of understanding the difference between a concept and the name for that concept.

says person that evidence suggests can't tell the difference between a horse and a unicorn, nor the difference between 1 and 16 😂

find a manual with an example of it behaving differently

You already provided one! 🤣🤣🤣

if you press 2+3+×5, it behaves exactly as the example in the Sinclair Executive manual

Yep! Which is (2+3)x5, and not 2+3x5. 🙄 The manual even explicitly tells you that is how to do an expression with one set of brackets, and yet the Windows calculator returns that answer when you enter an expression without brackets. 🙄 It's hilarious that now you're even proving yourself wrong 🤣🤣🤣

So I’m pretty sure according to you that proves that it obeys the order of operations, right?

Nope! 2+3x4=14, not 20 🤣🤣🤣 (2+3)x4=20, which is the answer the Windows calculator gives when you type in 2+3x4.

I washed myself recently

says proven liar - I knew that was Projection on your part🤣🤣🤣

Well, it would be a guess

Hence proof that you don't understand Maths nor calculators 🙄

That’s all you have, a guess

Nope. I have a calculator which behaves the exact same way 🙄

So why does ms calc work in the exact same way as an immediate execution calculator?

you know they have Standard in the name, and that's definitely not Standard, right?? 😂

it’s not anywhere else in the manual

It's right there in the manual that you have to do that second press to put it in brackets 🙄

And one project manager overseeing the behaviour, yes.

and yet, all different parts behaving in different ways. Sounds like the Project Manager needs to get sacked! 😂

I know you haven’t worked out where the brackets go!

says person who hasn't read the book, and thus, apparently, doesn't know how they did it before we started using brackets 🤣🤣🤣

you can substitute anywhere

And if you are rearranging algebra you have to do the exact same thing on both sides, always

You’re just another yank

BWAHAHAHA! I see you still didn't learn to check facts first. 😂😂😂

6⁄2(1+2) ⇒ 6⁄2*3 ⇒ 6⁄6 ⇒ 1

You're more patient than me to go to that trouble! 😂 But yeah, looks good. Just one technicality (and relates to how many people arrive at the wrong answer), the 2x3 should be in brackets. Yes if you had a proper fraction bar it wouldn't matter, but that's what's missing with inline writing, and is compensated for with brackets (and brackets can't be removed unless there's only 1 term inside). In your original comment, it does indeed look like 6/(2x3), but, to illustrate the issue with what you wrote, as soon as I quoted it, it now looks like (6/2)x3 in my comment.

If it was so well defined, then how did two different sets of rules regarding juxtaposition even come to be?

They didn't - neither of them is a rule of Maths.

When the @onion said there were two different sets of rules, you know as well as I do that they meant strong vs. weak juxtaposition

Neither of which is a rule in Maths, as had already been pointed out. The 2 relevant rules, both of which never got mentioned in the whole discussion, are The Distributive Law and Terms.

You’re right that in reality nobody would write an equation like this

No, that was wrong - they really would. 2(1+2) is the standard way to write a factorised term. i.e. a(b+c).

hole that exists in the standard order of operations

There's not a hole in the order of operations - there's a hole in people's memories where The Distributive Law and Terms used to be. You'll notice no students ever get this wrong, because they remember all the rules.

given no other context to do so, you would either have to pick a side

That "side" being follow the rules of Maths - works every time. :-)

And...? Not sure what your point is, but the link is VERY badly worded...

1. The Distributive Law and The Distributive Property aren't the same thing - he's applying The Distributive Law, but mistakenly calling it The Distributive Property (a lot of people make that mistake). The latter is merely a property in Maths (like the commutative property, the associative property, etc.), the former an actual rule of Maths The Distributive Law
2. Applying the Distributive Law - i.e. expanding brackets/parentheses - is part of solving brackets. i.e. the first step in BEDMAS/PEMDAS. There's no "once you've used", you've already started!
3. As I already said, this is taught in Year 7, so I'm not sure what your point is?

Even more ambiguous math notations

Except that isn't ambiguous either. See my reply to the original comment.

Geogebra has indeed found a good solution

Geogebra has done the same thing as Desmos, which is wrong. Desmos USED TO give correct answers, but then they changed it to automatically interpret / as a fraction, which is good, except when they did that it ALSO now interprets ÷ as a fraction, which is wrong. ½ is 1 term, 1÷2 is 2 terms (but Desmos now treats it as 1 term, which goes against the definition of terms)

Here you go - I found I did save a screenshot of Cajori saying ab and (ab) are the same thing - I didn't think I had.

The original comment was

it will kill PWAs

like if Apple STOPS doing it then everyone else will stop doing it. Like when Apple stopped having 3.5mm jacks everyone else stopped having 3.5mm jacks. Oh wait...

As I said, they're big spenders, not trend-setters.