I love how confident you are about something you clearly have no knowledge of.
says person confidently proving they have no knowledge of it to a Maths teacher 🤣
At least if we’re judging by word count
from Maths textbooks, which for you still stands at 0
My dude sit in a university lecture for math majors
You know I have a Masters in Maths, right? 🤣
Your school books arent gospel
Proofs are, and these things are very easy to prove 🙄
My dude sit in a university lecture for math majors
You know I have a Masters in Maths, right? 🤣
Your school books arent gospel
Proofs are, and these things are very easy to prove 🙄
Wikipedia
isn't a Maths textbook 🙄 far out, did you learn English from Wikipedia too? You sure seem to have trouble understanding the words Maths textbook
You don’t trust Wikipedia?
The site that you just quoted which is proven wrong by Maths textbooks, THAT Wikipedia?? 🤣🤣🤣
you’ve yet to explain why notations like prefix and postfix dont need these “rules”.
Umm, they do need the rules! 😂
how could they only apply to certain notations?
They don't, they apply to all notations 🙄
Do you teach classes like this? “That’s not a product, it’s a multiplication”
Yep! And if you read more than 2 sentences out of the textbook you would know why 🙄
those are the same thing.
Says person who only read 2 sentences out of a whole chapter 🙄
Shouldn’t you, as a teacher, be explaining the difference, if you say there is one?
Yep, and it's right there in the textbook! 🙄
I’m starting to believe you don’t think they’re is one
So you think if a=2 and b=3, then...
1/ab=1/(2x3)=1/6
1/axb=1/2x3=3/2
Are somehow the same answer?? 😂 Which one is it then? 1/6 or 3/2?? 😂
You could argue that “product” refers to the result of the multiplication rather than the operation
Yep by definition!
there’s no sense in which the formula “a × b” does not refer to the result of multiplying a and b
There's no sense in which it does refer to the result you mean. The result of axb is ab. If a=2, b=3, axb=ab. 2x3=6, axb=2x3, ab=6
you don’t bother to even make such an argument
Says someone revealing that they haven't read a word I've said 🙄
you’re not actuality smart enough to understand the words you’re using
says someone who has just proven they haven't been reading them 🙄
It’s interesting, isn’t it, that you never provide any reference to your textbooks to back up these strange interpretations
Yes I did, and you only read 2 sentences out of it 😂
Where in your textbook does it say explicitly that ab is not a multiplication
Read on dude, read on, like I have been telling you the whole time. Oh wait, that would prove you were wrong. Oh, I wonder why you haven't read it... 🙄
It doesn’t, does it?
The page that you only read one sentence from 🙄
You’re keen to cite textbooks any time you can, but here you can’t
I already did and you only read 2 sentences out of it 🙄
You complain that people don’t read enough of the textbook, yet they read more than you ever refer to
says person who has repeatedly proven they've only read 2 sentences 🙄
In the other thread I said I wouldn’t continue unless you demonstrated your good faith by admitting to a simple verifiable fact that you got wrong
And I pointed out that in fact you got it wrong, and Mr. Hypocrite has failed to admit it 🙄
provide an actual textbook example where any of the disputed claims you make are explicitly made
Same one I already told you and you only read 2 sentences out of a whole chapter
there should be some textbook somewhere which says that mathematics would not work with different orders of operations
It's easy enough to prove yourself, like I did. Go ahead and try it out and let me know how you go.
you’ve never found a textbook which says anything like this
No, I was able to prove it myself 🙄
only things like “mathematicians have agreed”
Because it was proven 🙄
where’s your textbook which says that “a × b is not a term”?
Same textbook that you only read 2 sentences from
Where is the textbook that says 5(17) requires distribution?
It tells you tight there on the same page that you must remove all brackets, 🙄 which you also haven't admitted to being wrong about yet, surprise, surprise, surprise
Where’s your textbook which says “ab is a product, not multiplication”?
Same one you only read 2 sentences from
there is a textbook reference saying “ab means the same as a × b”,
And you stopped reading at that point didn't even finish the page, never mind the chapter 🙄 Just started making false claims (contradicted by same textbook) that "means" means "equals", instead of realising they have explicitly not said equals 🙄
so your mental contortions are not more authoritative
Says person who made the mental contortion that "means" means "equals" instead of reading the rest of the page
your ability to interpret maths textbooks is poor
says person who only read 2 sentences out of a whole chapter 🙄
we can have a productive discussion
when you decide to read more than 2 sentences 🙄
My prediction: you’ll present some implicit references
Wrong, as usual
try to argue they mean what you want
says person trying to argue that "means" means "equals" 🙄
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
As opposed to a Maths teacher who knows there are no corrections made at a higher level. Go ahead and look for a Maths textbook which includes one of these mysterious "corrections" that you refer to - I'll wait 😂
A high school Maths textbook most certainly is an infallible source of "college level" information, given it contains the exact same rules 😂
Well, that's you! 😂 The one who quoted Wikipedia and not a Maths textbook 😂
You again 😂 Wikipedia isn't a Maths textbook