Have to reply to your other post here, because you hit the maximum comment depth with your rubbish.

I thought they were called “products” not “multiplications”

That's right, as per Page 36 of Modern Algebra, published in 1965, as opposed to Advanced Algebra, published in 1912., but if you think we still call it "Multiplication" you're more than welcome to find a modern textbook which calls it that, instead of relying on a 113 year old textbook 🙄

If you can find an explicit textbook example where writing a(b)²

What did you not understand about textbooks write ab² if they meant (axb²)?

that’s another way you can prove your good faith

I already proved it with all my other textbook references, which you keep ignoring 🙄

the exponent could be anything other than 1

In other words, you refuse to believe the rule that I have already quoted multiple times, because it proves you are wrong about this meme, and so trying to derail the argument, still, with your false equivalence argument, speaking of lacking good faith 🙄

Likewise, if you can find any explicit textbook example which specifically mentions an “exception” to the distributive law

There aren't any exceptions. I'm not sure why you're having trouble with that. You want me to find evidence of something I have said all along doesn't exist 😂

I’m not saying that such an explicit example is the only way to demonstrate your claim

says person who to date has refused to accept what any textbook has said about it 🙄

I’m just trying to give you more opportunities to prove that you’re not just a troll

Since when do trolls post Maths textbooks backing them up? 🤣🤣🤣

that it’s possible to have a productive discussion.

says person who has rejected literally every Maths textbook I've posted. 🙄

You insist you’re talking about mathematical rules that cannot be violated

as per Maths textbooks 🙄

so it should be no problem to find an explicit mention of them

...and I already posted many of them, but for some reason you find them unacceptable (that reason being that they prove you are wrong 😂 )

you should remember that you are saying that the practice of calculators, mathematical tools, programming languages and mathematical software are all wrong

Nope, liar. All calculators except for Texas Instruments and e-calcs are correct - certainly all my calculators are correct (as can be seen in the video in the thread). Same thread shows the reason that programmers are almost all wrong - they don't even all get it wrong in the same way - everyone gets it wrong in different ways, which debunks the whole idea of them following any rules 😂

that my interpretation of your own textbooks is wrong

Which you would've found out for yourself, had you read more than 2 sentences out of them. 🙄 Welcome to what happens when you only read the scaffolding part of a lesson, and not the new content part of the lesson 🙄

if you show no ability to admit error

says person who has failed to admit their error about the calculators. 🙄For me to do so would require me having made an error to begin with, which I haven't, which is why you've been unable to say where I've made an error 🙄

to admit that disagreement from competing authorities casts doubt on your claims

There isn't any disagreement from competing authorities, and yet you still refuse to admit you're wrong 🙄

to evince your controversial claims with explicit examples that are not subject to interpretational contortions,

says the only person who has made such contortions, such as "means" means "equals" 🙄

the likelihood is that you’re not willing to ever see truth

You you mean, as evidenced by the fact that you had already dismissed me as being good faith in your above post before I had even seen THIS post - something, something, judge, jury, and executioner 🙄

there’s no point arguing with such a person

I'm not arguing with you - I'm debunking your rubbish claims lest any reader fall prey to them

sorry for making multiple replies on the same point

Which at the end of it all you had still failed to make a point.

As my own show of good faith, I do see that one of your textbooks (Chrystal) has the convention that a number “carries with it” a + or -, which is suppressed in the case of a term-initial positive number

No, a show of good faith by you would be 1. accepting that axb and ab are different, as per the page you reference above, which I'll come back to in a tick, 2. accepting The Distributive Law, a(b+c)=(ab+ac), is a thing found in many Maths textbooks (all of which you ignored), otherwise all you have conceded was yet another side-quest on your part because you refuse to concede anything which is actually relevant

So, you started this post with referencing Page 6 of Advanced Algebra (as proven by you quoting the bit about "Multiplication", which explicitly shows that bxc and bc ARE NOT THE SAME THING, and yet here you are still not acknowledging this fact.

a÷bxc=12÷3x4=16, a÷bc=12÷(3x4)=1

I’ll explain why I think this is a bad convention

It's not a convention, it's a rule 🙄

why the formal first-order language of arithmetic doesn’t have this convention

No-one cares 🙄 Most people don't go to university and learn niche rules, everyone goes to high school and learns the general rules

You failed to demonstrate any good faith

says the person who actually demonstrated no good faith 🙄 and was unable to back up anything they said with a textbook

so this is the end of this conversation

Don't let the door hit you on the way out

Your reply reveals that you even understand that you were wrong

Nope!

“it’s designed that way”

Yep, that shows I was correct about "simple" calculators, whereas chain calculators were designed that way, but that was used as moving goalposts by the person claiming this applied to "simple" calculators, which was disproven by the manual showing that it did indeed have a stack and obey the order of operations rules, hence the goalposts got moved, again 🙄

the language changed

You think it doesn't change?? BWAHAHAHAHAHA 🤣🤣🤣 But sure, Mr. I'm (not) showing good faith, go ahead and show us a modern textbook which calls Products "Multiplication". I'll wait. 😂 Oh wait. you said the conversation was over. Too bad you can't prove your point then... again

but are so prideful,

Correct is the word you're looking for

so averse to ceding ground,

says person who has failed to come up with a single valid point that I could therefore cede to 🙄

that you just… can’t… say it!

says person who has failed to admit they are wrong about things they have been proven wrong about 🙄

The children you really ought to stop teaching are more mature than this.

They're more mature than you yes. They have no problem at all with The Distributive Law and why it exists, and can see their calculators know this also.

You’re an embarrassment to the profession.

says the actual embarrassment who can't back up anything they say with any Maths textbook 🙄