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 🤣🤣🤣

The contents of the book day nothing about the “rules” only about the symbols

says person proving they didn't read it. Who woulda thought you might refuse to read something that would prove you wrong. 🙄

In general, responding to a question with “you haven’t read enough” is, indeed, deflection

says person revealing they don't know what deflection means either 🙄

a sign you can’t answer

I can answer if you go ahead and book some online tutoring with me to cover the history behind the comment.

If you could, you would! Simple

It's not my job to educate you dude, unless you book some online tutoring with me, in which case it is my job. I gave you a book which answers it, for free, in extreme detail, and you lied about what it even contains, cos you never even looked at it, simple.

Not, according to you

Which part of "every single post" do you have trouble comprehending? Honestly dude, need to go back to school and learn to read 🙄

You underlined some crap in the manuals that doesn’t mean what you said it meant

= doesn't mean equals??? BWAHAHAHAHAHAHAHAHA! 🤣🤣🤣🤣🤣🤣

Why’d you bring up your calculator if you don’t actually want to talk about it?

Which part of you've been proven wrong so there's nothing further to discuss didn't you understand? 🙄 See above about learning to read

Are not necessary to evaluate such expressions.

says person contradicting the manual which says you cannot do it 🤣🤣🤣🤣

but sure, go ahead and tell us how you can do a simple calculation that has multiple brackets, but without brackets, and without splitting it up, I'll wait 🤣🤣🤣

You can use a calculator that uses RPN.

Yes, a calculator where the brackets are built-in, unlike this calculator 🙄

but was not available on mass market models because… it requires

Brackets

Now do you get why pocket calculators had no stack?

says person ignoring that we've already established that they did have a stack. Dude, you're just going in circles.

you have no explanation for why the calculator could not perform the expression without splitting it, since bracket keys are not necessary to do so

says person who has yet to show how it can be done without brackets, since it can't be done without brackets. 🙄 a(b+c)+d(e+f) is the example from the manual - go ahead and tell us how you can do it without brackets and without splitting it up.

exists in the use of the += button - is never discussed in the manual.

BWAHAHAHAHAHAAH! (deep breath) HAHAHAHAA! It's right there in the examples! 🤣🤣🤣🤣🤣

you just made it up

says person making up that the lack of brackets keys is somehow not the reason you can't do expressions with multiple brackets in them, even though they can't come up with a way to do so 🤣🤣🤣

you’ve been called out on

nothing. You still haven't come up with a way to do an expression with multiple brackets on a calculator that has no brackets. How can I do a(b+c)+d(e+f) on a calculator with no brackets, and GO! 🤣🤣🤣

You could get out of all this by just admitting that the Sinclair Executive had no stack and operates from left to right.

the proof is right there in the example that it doesn't 🙄 A fact which you still haven't admitted to

Sure there is.

says person unable to produce any Maths textbook that it's in, because there isn't any such thing

What you mean is, you prefer not to use the term “implicit multiplication”

No, I mean there is literally no such thing, hence why it's not in any Maths textbooks

if you google the term, you can find the definition

If you Google unicorns and fairies you can find them as well, but you won't find them in any Science textbooks either.

like a mathematician

exactly what I did, unless you think there are Mathematicians who would entertain discussion about fairies being real beyond "there's no such thing"?

In your imaginary classroom you can make your poor students use whatever terminology you like

We don't use terminology with things we don't teach them. Do you think some teachers teach their students about unicorns and fairies being real?

I, and the rest of the internet, can use the terminology we agree upon.

Yes, delusional people can agree upon their delusions, no disagreement from me there! 🤣🤣🤣

Read to the end of the comment before shooting off your comment, and you wouldn’t be such an embarrassment.

No embarrassment from me - I've proven everything in the comment wrong.

• they don't emulate scientific calculators

• they don't emulate basic four-function calculators

In both cases they just give wrong answers

I have never used Microsoft Maths Solver but it bears no resemblance to a calculator so I don’t care

I'll take that as an admission of being wrong - all software calculators (MathSolver wasn't the only one I discussed, which you would've known had you bothered reading it), somehow bear no resemblance to actual calculators, got it. Been telling you that all along BTW 🤣🤣🤣

You still haven’t come up with a good explanation

which part didn't you understand in different programmers work on different parts?

And honestly, I think it’s disgusting that you never wash yourself.

No idea what you're talking about, must be another case of Projection.

Do you not remember that there were two manuals?

Which part did you not understand in the second one was a chain calculator? You're going round in circles again

Either way, you have no explanation

I already explained dude. Saying I didn't doesn't magically make it disappear.

Try and find one that gives an example of typing in a + b x c and getting a+bc. You can’t.

Umm, the first one does, as I already pointed out 🤣🤣🤣 Guess what happens you you omit the circled keypress...

if people have been using these (“niche!!1”) calculators for decades

Go ahead and see if you can find any engineers using them. I'll wait

The only reason you must do so is to pass high school maths

and for planes to not fall out of the sky

The goal of the game is for you to put the brackets in, OK?

You know the order of operations rules predate use of Brackets in Maths by many centuries, right? How do you think they knew what to do, without brackets? I'll wait 🤣🤣🤣

You put the word “smart” in your name,

says person proving how often they make wrong assumptions. 🤣🤣🤣🤣 You could've just asked me about it, but no, you literally never check facts first, just launch into provably wrong made up statements 🤣🤣🤣

so I’m hoping you’re smart enough to work it out!

Person it refers to agrees with me - who woulda thought?? 🤣🤣🤣

answer the question, deflecter :)

I haven't deflected. I told you to go read up on the history of it and you would discover what was being talked about. Since you apparently don't know how to use Google either, here's a link for you

you said that something never happens

happens - present tense

which, in fact, has happened

happened - past tense. Even you wrote that in different tenses 🤣🤣🤣 I'll take that as another admission that you were wrong then

I assume you’d really agree that I am never wrong - right?

Every single post you make is wrong! You are continuously wrong all the time, and I'm guessing always have been wrong as well 🤣🤣🤣

it’s strange you didn’t take up my offer to show this calculator of yours

No it's not. We've already settled that you claim was wrong and moved on, and I already said so at the time Mr. abysmal reading comprehension, and we know you hate long responses, so go back and read the short replies again 🤣🤣🤣

“a problem such as (a+b)c + (d+e)f cannot be done as a simple calculation, it must be split into two parts.”

that's because it has no brackets keys dude. We've already been over it. You're so wrong you've run out of arguments to make and you're now trying to rehash other stuff

There is no reason that it would need to be split if the calculator had

brackets keys

You have no explanation for why this calculator could not perform this calculation without splitting it.

no brackets keys 🙄

Now, you’ve done a silly with the software calculators there,

says person deflecting from the fact that they've been proven wrong, again, and can't man up and admit to having been wrong, again 🙄

we’re talking about order of operations,

which you were proven wrong about.

not how calculators render implicit multiplication

there's no such thing as "implicit multiplication" is why we weren't talking about it

you really ought to keep these things straight in your mind

says person trying to pretend they didn't say "even though they (developers) can make scientific calculator modes work correctly!" - which I then proved wrong, so more deflection ensues

which they don't make them work correctly

I’ll rephrase: you have no sane explanation for why scientific mode tends to obey a different order of operations than basic mode on software calculators

I see you didn't even try any of them (nor even read my thread about them). Had you done so, you would've discovered that ones such as the Microsoft Maths Solver sometimes does, sometimes doesn't, so where in your "sane" explanation can you account for the same calculator only sometimes obeying the rules. Spoiler alert: different programmers with different ideas of what the order of operations rules are, as I have been saying all along - you're wrong again dude. 🤣🤣🤣 yet again charging into easily proven wrong statements, rather than checking facts first

I do, and it’s because they’re emulating basic, four-function calculators which had no stack

which you were proven wrong about by the manual you posted. So we're all done then. Don't let the door hit you on the way out

about a page saying “other rules may have been adopted” suggests anything others than that different rules may have been adopted?

says person revealing they haven't read about the history behind that comment 🙄

You know by know that no-one but you agrees with your interpretations.

All the textbooks agree dude, which you would know if you had read more, but you've chosen to remain an ignorant gaslighter

You can’t find a single explicit agreement with them

With what?

Reposting the same pages that you are misinterpreting is very silly, isn’t it

says person who can't post anything that agrees with their silly interpretation 🤣🤣🤣

Because every single textbook you’ve cited, I absolutely guarantee it… was written in the past!

But being used in schools right now, and you're desperately trying to twist my words around to mean something else because you can't find any textbooks which say juxtaposition, except for one from 1912 🤣🤣🤣

How shall we make sense of this conundrum?

You're the only one who has issues with understanding present and past tense dude, you're the only one trying to use a 1912 textbook in the argument.

“I never use drugs” doesn’t mean the same as “I am not using drugs at the moment”

Yes it does, because "I never use drugs" isn't the same as "I have never used drugs" 🙄

So yeah, you absolutely said the wrong thing

I absolutely didn't Mr. I can only find it in a 1912 textbook 🤣🤣🤣

your reason for using it is stupid.

says person trying to bring a 1912 textbook into the argument only to avoid admitting having been wrong 🙄

If you were any kind of reasonable person and not someone incapable of admitting the slightest mistake

So not like you, which I'm not 😂

you would have said, “oh, sorry, I meant that textbooks don’t use the word ‘juxtaposition’ any more”

It's already there in the use of the present tense

Mate, try and keep track. We’re talking about a specific calculator and its specific manual.

And it specifically says you are wrong 🙄

Your calculator is not relevant to that one.

So when you said all, you didn't really mean all, so an admission that you were wrong about "all". Got it. Thanks for playing. Glad we're done with the "basic" calculator topic then

“Says person lying” is your favourite

statement of fact

deflection

says person talking about calculators that don't have brackets because he's absolutely proven wrong about The Distributive Law, and is trying to deflect away from admitting being wrong about that 🙄

the calculators we all had in primary school, If you press the following sequence of buttons: 2 + 3 x 5 =, the answer it will give is

17

even though they can make scientific calculator modes work correctly!

Nope! They don't! With the exception of MathGPT, they all ignore The Distributive Law, you know, the actual original topic 🤣🤣🤣 The Windows calculator in Scientific mode says 8/2(1+3)=16, because, when you type it in, it changes it to 8/2x(1+3). It's hilarious how you just keep making easily proven wrong statements and bring more embarrassment upon yourself, instead of just, you know, checking facts first 🤣🤣🤣

Sharp calculator obeying The Distributive Law

Note that neither MathGPT, nor the Sharp calculator, forcibly add in a multiply sign where it doesn't belong. Welcome to dumb programmer who has forgotten how The Distributive Law works and didn't bother checking in a Maths textbook first.

yet there’s such a simple explanation! They’re emulating basic four-function calculators that have existed for decades

No they're not! Just like they're also not emulating Scientific calculators that have existed for decades! 🤣🤣🤣