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 🙄
You failed to demonstrate any good faith so this is the end of this conversation. Your reply reveals that you even understand that you were wrong (“it’s designed that way”; “the language changed”) but are so prideful, so averse to ceding ground, that you just… can’t… say it!
I’m not sure you have enough theory of mind to understand what that’s like for a normal interlocutor, unfortunately.
The children you really ought to stop teaching are more mature than this. You’re an embarrassment to the profession.
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 🙄
Since your reply is too long for me to see easily if you’ve taken any of the steps to demonstrate good faith, I’m not reading it. If you want to do that, you can make a short reply, then we can continue, but so far it looks like trying to convince you of anything is a waste of time so those are your options…
I have one and it quite happily says that 2+3x4=14
Then that’s the wrong kind of calculator, genius. The kind that gets 20 does not have a stack. Which isn’t wrong, just different, because it’s not doing 2+3x4, it’s doing 2 += 3, x= 4.
Would you understand it if someone said its notation has “implicit brackets” that work out to be left-to-right?
A calculator which gives the correct answer is the wrong kind of calculator, genius? BWAHAHAHAHAHAHAHAHAHAAH 🤣🤣🤣🤣🤣 Now I’ve heard everything
The kind that gets 20 does not have a stack
And they are chain calculators, as it said in the manual, 🙄 not the “simple calculators” (of which mine is one) which was your original argument, but now you’re moving the goal-posts again because it’s been proven wrong, again 😂
Which isn’t wrong, just different,
Nope, it’s wrong
it’s not doing 2+3x4, it’s doing 2 += 3, x=
It was neither, liar. It was doing (a+b)xc, which, since it doesn’t have brackets, it tells you to do a+b=xc=, so as to evaluate the a+b first, because if you don’t press the equals at that point, and just enter a+bxc=, it will put the a+ on the the stack, and do the multiplication first, just like my calculator does 🙄
Would you understand it if someone said its notation has “implicit brackets” that work out to be left-to-right?
No, RPN has “implicit brackets” as you put it, and it most definitely does not go “left to right”, only chain calculators do 🙄
Yes, an infix calculator is the wrong kind of calculator, when talking about four-function calculators that do not have a stack… because it has a stack. Insisting ‘but mine does have a stack!’ is the problem. And read usernames, you illiterate dingus.
The Sinclair Executive in that manual does not have an equals key. What the fuck are you talking about?
If you know what a chain calculator is, and you know how they work, why are you playing stupid?
when talking about four-function calculators that do not have a stack
Chain calculators, as the second one said in the manual
Insisting ‘but it does have a stack!’ is the problem
The first one does have a stack. 🙄 You refusing to see it is the problem
And read usernames
Your mind’s been bleached - explains a lot 😂
The Sinclair Executive in that manual does not have an equals key
It has a += key. If the next keypress is a number it’s interpreted as +, if the next key pressed isn’t a number, like the x button, it’s interpeted as equals Duuuuhhh It even explicitly points out to you that the result of that keypress is (a+b) 🙄
What the fuck are you talking about?
The example in the manual. What are you talking about? 😂
It was neither, liar. It was doing (a+b)xc, which, since it doesn’t have brackets, it tells you to do a+b=xc=, so as to evaluate the a+b first, because if you don’t press the equals at that point, and just enter a+bxc=, it will put the a+ on the the stack, and do the multiplication first, just like my calculator does
Yeah hey which of us said += and which of us said “press the equals” afterward?
Yeah hey which of us said += and which of us said “press the equals” afterward?
I said both. you said “does not have an equals key” - even though it quite clearly does, but you wanted to gaslight us into believing it doesn’t have one because it proved you were wrong 🤣🤣🤣
That just displays the accumulator. It’s why the very next page of this very short manual says (a+b)c+(d+e)f “cannot be done as a simple calculation, it must be split into two parts.” Because there’s no stack.
Which is a single value stack, 🙄 but this calculator does indeed have a multivalue stack, so as to be able to do a+bxc, where it will put a+ on the stack (that’s two values, a and +), calculate bxc, then pop the stack and do the addition. If you instead want to do (a+b)xc, you have to press equals after a+b so that it will get evaluated before the Multiplication, because it doesn’t have Brackets keys 🙄
(a+b)c+(d+e)f “cannot be done as a simple calculation, it must be split into two parts.” Because there’s no stack
No, that’s because it doesn’t have any brackets keys 🙄 You can get away with one set of brackets as per the method shown, but you can’t do that with multiple brackets. You really have no idea how Maths or calculators work! 🤣🤣🤣
Here’s an online emulator for the Sinclair Cambridge, the upgraded scientific model
We’ve already established that’s a chain calculator Mr. needs remedial reading classes 🙄
Not me, must be you! 😂
They didn’t 🙄
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 🙄
says someone too stubborn to admit making a mistake 🙄
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
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.
Facts, as per the syllabus and Maths textbooks. Again, you need to read more than 2 sentences to discover that 🙄
says person who has thus far refused to read more than 2 sentences out of the textbook 🙄
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
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
No I wasn’t
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 🙄
Yep, published in 1912
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
There was no error. The language has changed since 1912 🙄
Of course I am. Doesn’t mean I’m going to “admit” to an error when there is none 🙄
You failed to demonstrate any good faith so this is the end of this conversation. Your reply reveals that you even understand that you were wrong (“it’s designed that way”; “the language changed”) but are so prideful, so averse to ceding ground, that you just… can’t… say it!
I’m not sure you have enough theory of mind to understand what that’s like for a normal interlocutor, unfortunately.
The children you really ought to stop teaching are more mature than this. You’re an embarrassment to the profession.
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 🙄
Since your reply is too long for me to see easily if you’ve taken any of the steps to demonstrate good faith, I’m not reading it. If you want to do that, you can make a short reply, then we can continue, but so far it looks like trying to convince you of anything is a waste of time so those are your options…
Keys To Algebra 1-4’s answer booklet, page 19, upper right: “book 2, page 9” expands 6(ab)3 to 6(ab)(ab)(ab), and immediately after that, expands (6ab)3 to (6ab)(6ab)(6ab).
Rub rub rub.
Yes, that’s right. a(bc)²=ab²c². That’s got nothing to do with a(b+c)=(ab+ac) 🙄
Stop rubbing yourself off - it’s clearly making you blind 🤣🤣🤣
You weren’t talking about a(b+c), you were talking about a(b)2. Which doesn’t work the way you said… according to this maths textbook.
Dude, I’ve always been talking about a(b+c) Mr. abysmal reading comprehension 🙄
Nope! Textbooks write ab² if they mean (axb²). They never write a(b)²
It works exactly the way I said 🙄
This Maths textbook is about a(bc)², not a(b+c) 🙄 You need remedial reading classes
Yes, this textbook says a(bc)2 works differently from how you say it works.
You don’t have an answer for that because you’re a fraud.
If you want textbooks that also disprove how you pretend a(b+c)n works, here’s four in a row.
No it doesn’t 🤣🤣🤣 I have said the whole time that a(bc)²=ab²c², which is exactly what this textbook does 🙄 a(b+c) is different to a(bc)², duuuhhh 🙄
says person who can’t quote any part saying it works differently to how I said, and in fact quoted a part showing it works exactly how I said 🤣🤣🤣
been telling you the whole time it’s irrelevent to a(b+c) which has no exponent Mr. False Equivalence 🙄
Then that’s the wrong kind of calculator, genius. The kind that gets 20 does not have a stack. Which isn’t wrong, just different, because it’s not doing 2+3x4, it’s doing 2 += 3, x= 4.
Would you understand it if someone said its notation has “implicit brackets” that work out to be left-to-right?
A calculator which gives the correct answer is the wrong kind of calculator, genius? BWAHAHAHAHAHAHAHAHAHAAH 🤣🤣🤣🤣🤣 Now I’ve heard everything
And they are chain calculators, as it said in the manual, 🙄 not the “simple calculators” (of which mine is one) which was your original argument, but now you’re moving the goal-posts again because it’s been proven wrong, again 😂
Nope, it’s wrong
It was neither, liar. It was doing (a+b)xc, which, since it doesn’t have brackets, it tells you to do a+b=xc=, so as to evaluate the a+b first, because if you don’t press the equals at that point, and just enter a+bxc=, it will put the a+ on the the stack, and do the multiplication first, just like my calculator does 🙄
No, RPN has “implicit brackets” as you put it, and it most definitely does not go “left to right”, only chain calculators do 🙄
Yes, an infix calculator is the wrong kind of calculator, when talking about four-function calculators that do not have a stack… because it has a stack. Insisting ‘but mine does have a stack!’ is the problem. And read usernames, you illiterate dingus.
The Sinclair Executive in that manual does not have an equals key. What the fuck are you talking about?
If you know what a chain calculator is, and you know how they work, why are you playing stupid?
Chain calculators, as the second one said in the manual
The first one does have a stack. 🙄 You refusing to see it is the problem
Your mind’s been bleached - explains a lot 😂
It has a += key. If the next keypress is a number it’s interpreted as +, if the next key pressed isn’t a number, like the x button, it’s interpeted as equals Duuuuhhh It even explicitly points out to you that the result of that keypress is (a+b) 🙄
The example in the manual. What are you talking about? 😂
Yeah hey which of us said += and which of us said “press the equals” afterward?
I said both. you said “does not have an equals key” - even though it quite clearly does, but you wanted to gaslight us into believing it doesn’t have one because it proved you were wrong 🤣🤣🤣
That just displays the accumulator. It’s why the very next page of this very short manual says (a+b)c+(d+e)f “cannot be done as a simple calculation, it must be split into two parts.” Because there’s no stack.
Here’s an online emulator for the Sinclair Cambridge, the upgraded scientific model. Enter 2 + 3 x 4 =. Tell me what it says.
Which is a single value stack, 🙄 but this calculator does indeed have a multivalue stack, so as to be able to do a+bxc, where it will put a+ on the stack (that’s two values, a and +), calculate bxc, then pop the stack and do the addition. If you instead want to do (a+b)xc, you have to press equals after a+b so that it will get evaluated before the Multiplication, because it doesn’t have Brackets keys 🙄
No, that’s because it doesn’t have any brackets keys 🙄 You can get away with one set of brackets as per the method shown, but you can’t do that with multiple brackets. You really have no idea how Maths or calculators work! 🤣🤣🤣
We’ve already established that’s a chain calculator Mr. needs remedial reading classes 🙄