You have declined to admit to a simple error you made

Not me, must be you! 😂

that early calculators lacked a stack,

They didn't 🙄

that basic four function calculators all did and still do

Have a stack, yes. I have one and it quite happily says that 2+3x4=14, something it can't do without putting "2+" on the stack while it does the 3x4 first 🙄

There’s no point having a discussion with someone so stubborn that they can’t admit a single mistake.

says someone too stubborn to admit making a mistake 🙄

I’m not sure whether you’re trying to wind people up or just a bit dim

Neither. I'm the one doing fact-checks with actual, you know, facts, like my simple calculator having a stack and correctly evaluating 2+3x4=14. It's the one I had in Primary school. The one in the first manual works the exact same way

this conversation is like trying to explain something to a particularly stuck-up dog

So maybe start listening to what I've been trying to tell you then. 🙄 It's all there in textbooks, if you just decide to read more than 2 sentences out of them.

The real tragedy is that you claim to be out there teaching kids this overcomplicated and false drivel.

Facts, as per the syllabus and Maths textbooks. Again, you need to read more than 2 sentences to discover that 🙄

only if you show that you’re not just a troll.

says person who has thus far refused to read more than 2 sentences out of the textbook 🙄

You can do that by admitting that you were wrong to say that all calculators have stacks

I wasn't wrong 🙄 The first manual that was linked to proved it. If you don't press the +/= button before the multiply then it will put the first part on the stack and evaluate the multiplication first, something it doesn't do if you press the +/= first to make it evaluate what you have typed in so far. 🙄 Every calculator will evaluate what you have typed in so far if you press the equals button, as pointed out in the first manual

because I showed you two examples

The first of which had a stack 🙄 the second of which was a chain calculator, designed to work that way. You're the one being dishonest

you were wrong

No I wasn't

that this screenshot

Which is a 1912 textbook. It also calls Factorising "Collections", and The Distributive Law "The Law of Distribution", and Products "Multiplication". Guess what? The language has changed a little in the last 110 years 🙄

it’s from Advanced Algebra by J.V. Collins, pg 6

Yep, published in 1912

On page 3, the concept of juxtaposition is introduced

And we now call them Products. 🙄 You can see them being called that in Modern Algebra, which was published in 1965. In fact, in Lennes' infamous 1917 letter, he used the word Product (but didn't understand, as shown by his letter), so the language had already changed then

admitting to an error on your part

There was no error. The language has changed since 1912 🙄

you actually are capable of admitting error

Of course I am. Doesn't mean I'm going to "admit" to an error when there is none 🙄

Fuck where this started

I'll take that as an admission that you're wrong. Thanks for playing

P.S. show me where the squared is in...

you know, the actual topic, which you're trying to avoid because you know you are wrong

So when you sneer that rules and notation are different, you don’t know what those words mean

says the actual person who doesn't know what they mean 😂

when someone says ‘imagine a different notation,’ you literally can’t

Yes, you literally can't go rewriting all the rules of Maths that we've had for centuries just because you randomly want to do something different now that we've decided to add Brackets to it 😂 Your whole argument is based on pretending that all the rules of Maths were all written at the same time 🤣🤣🤣

Show me any textbook that gets the answers you insist on

Pick any of them which show a(b+c)=(ab+ac) 🙄

Yes we could

No you can't! 😂

it’s a theoretical different notation

In other words against the rules of Maths that we have, got it

does not break down, if you have to put add explicit brackets to 1/(ab)

But it does breakdown if you treat ab as axb 🙄

if you have to put add explicit brackets to 1/(ab)

We explicitly don't have to, because brackets not being needed around a single Term is another explicit rule of Maths, 🙄 being the way everything was written before we started using Brackets in Maths. We wrote things like aa/bb without brackets for many centuries. i.e. they were added on after we had already defined all these other rules centuries before

Mathematics does break down when you insist a(b)2 gets an a2 term

No it doesn't. If you meant ab², then you would just write ab². If you've written a(b)², then you mean (axb)²

for certain values of b

Got nothing to do with the values of b

It’s why you’ve had to invent exceptions to your made-up bullshit

says person still ignoring all these textbooks

pretend 2(8)2

There's no pretending, It's there in the textbooks

when simplified from 2(5+3)2 versus 2(8*1)2

You know it's called The Distributive Property of Multiplication over additon, right? And that there's no such thing as The Distributive Property of Multiplication over Multiplication, right? You're just rehashing your old rubbish now

‘If a+b equals b+a, why is 1/a+b different from 1/b+a?’

Because they're not identically equal 🙄 Welcome to you almost getting the point

ab means a*b

means, isn't equal

That’s why 1/ab=1/(a*b)

Nope, it's because ab==(axb) <== note the brackets duuuhhh!!! 😂

But we could just as easily say 1/ab = (1/a)*b

No you can't! 😂

because that distinction is only convention

Nope! An actual rule, as found not only in Maths textbooks (see above), but in all textbooks - Physics, Engineering, Chemistry, etc. - they all obey ab==(axb)

None of which excuses your horseshit belief that a(b)2

says person still ignoring all these textbooks

You sneered about 1/ab five minutes ago

Yet again, I have no idea what you're talking about

Troll

says person who can't back up anything they say about Terms with textbook references 🙄

That’s convention for notation

Nope, still rules

not a distinction between a*b and ab

says person who only read 2 sentences out of the book, the book which proves the statement wrong 😂

a*b and ab both being the product of a and b

Nope, only ab is the product, and you would already know that if you had read more than 2 sentences 😂

You have to slap 1/ in front of things and pretend that’s the subject

"identically equal", which you claimed it means, means it will give the same answer regardless of what's put in front of it. You claimed it was identical, I proved it wasn't.

avoid these textbooks telling you

It kills you actually, but you didn't read any of the parts which prove you are wrong 🙄just cherry pick a couple of sentences out of a whole chapter about order of operations 🙄

They are the same thing. They are one term

Nope! If they were both 1 term then they would give the same answer 🙄

1/ab=1/(axb)=1/(2x3)=1/6

1/axb=1/2x3=3/2=1.5

Welcome to why axb is not listed as a Term on Page 37, which if you had read all the pages up until that point, you would understand why it's not 1 Term 🙄

You poor thing…

You don't know what Maths textbooks say because you were too poor to go to school? I'm sorry to hear that

You can’t keep your own horseshit straight

No idea what you're talking about, again, I've been saying the same thing the whole time

You insist they’re not the same. How?

Not difficult, I already did in another post. If a=2 and b=3...

1/ab=1/(axb)=1/(2x3)=1/6

1/axb=1/2x3=3/2=1.5

Convention saying 1/a(b+c)2 is 1/(a(b+c)2)

There's no such convention, given it would violate The Distributive Law 🙄