💡𝚂𝗆𝖺𝗋𝗍𝗆𝖺𝗇 𝙰𝗉𝗉𝗌📱
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Man, this whole post has been embarrassing for you
Nope. I’m the only one who has backed up what they’ve said with Maths textbooks 🙄
I can’t help but notice youve once again failed to address prefix and postfix notations.
What is it that you want addressed?
And that you’ve not actually made any argument other than “nuh uh”
Backed up by Maths textbooks 🙄
We can all tell you’re not a maths teacher
Says person who actually isn’t a Maths teacher, hence no textbooks 😂
You have a masters but you can’t differentiate between notation and the concept it is trying to convey
By which you mean you mean you don’t have a Masters and can’t differentiate between notation and rules 🙄
A “teacher” who doesn’t know that all lessons are simplifications that get corrected at a higher level,
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 😂
refers to children’s textbook as an infallible source of college level information
A high school Maths textbook most certainly is an infallible source of “college level” information, given it contains the exact same rules 😂
A “teacher” incapable of differentiating between rules of a convention and the laws of mathematics
Well, that’s you! 😂 The one who quoted Wikipedia and not a Maths textbook 😂
A “teacher” incapable of looking up information on notations of their own specialization
You again 😂 Wikipedia isn’t a Maths textbook
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
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
Have to reply to your other post here, because you hit the maximum comment depth with your rubbish.
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 🙄
What did you not understand about textbooks write ab² if they meant (axb²)?
I already proved it with all my other textbook references, which you keep ignoring 🙄
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 🙄
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 😂
says person who to date has refused to accept what any textbook has said about it 🙄
Since when do trolls post Maths textbooks backing them up? 🤣🤣🤣
says person who has rejected literally every Maths textbook I’ve posted. 🙄
as per Maths textbooks 🙄
…and I already posted many of them, but for some reason you find them unacceptable (that reason being that they prove you are 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 😂
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 🙄
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 🙄
There isn’t any disagreement from competing authorities, and yet you still refuse to admit you’re wrong 🙄
says the only person who has made such contortions, such as “means” means “equals” 🙄
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 🙄
I’m not arguing with you - I’m debunking your rubbish claims lest any reader fall prey to them
Which at the end of it all you had still failed to make a point.
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
It’s not a convention, it’s a rule 🙄
No-one cares 🙄 Most people don’t go to university and learn niche rules, everyone goes to high school and learns the general rules
says the person who actually demonstrated no good faith 🙄 and was unable to back up anything they said with a textbook
Don’t let the door hit you on the way out
Nope!
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 🙄
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
Correct is the word you’re looking for
says person who has failed to come up with a single valid point that I could therefore cede to 🙄
says person who has failed to admit they are wrong about things they have been proven wrong about 🙄
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.
says the actual embarrassment who can’t back up anything they say with any Maths textbook 🙄