And you were proven wrong elsewhere (since you ran your rubbish to the maximum comment depth), but admitted to not reading it, speaking of proving you were the bad faith one all along 🙄
So, now that I’ve found a place I can reply to your other non-repliable posts…
Even if you corner them on something
Which no-one ever has 🙄
they absolutely will not budge
See how many Mathematicians and Maths teachers you can gaslight into believing that they and Maths textbooks are all wrong, I’ll wait.
I like many others brought up calculators and how common basic calculators only evaluate from left to right
And you hilariously provided a manual that proved you were wrong about that! 😂
He asserted (without evidence) that the first does not operate in this way
It’s right there in the manual, as I pointed out 😂
even though the manual says that you must re-order some expressions so that bracketed sub-expressions come first
That’s right, because it doesn’t have brackets keys 🙄 So you have to enter that first, then press the equals key to make it evaluate that first, because it doesn’t evaluate from left to right otherwise, it will do the multiplication first 🙄
still will not admit that he was wrong about his claim
says person who still will not admit he was wrong about his claim that all basic calculators working that way, even though the manual proves there are some that don’t 😂
you will not convince him of anything no matter what the evidence is
Says person refusing to believe all evidence, including the calculator manual 😂
he fundamentally cannot separate mathematics from the notation
Nope liar. I’m the one who keeps pointing out they are different 🙄 Go ahead and find a screenshot of me saying they’re the same, I’ll wait
He calls a×b multiplication and ab a product.
As per Maths textbooks, which you keep ignoring 🙄
These are, of course, the exact same thing
says person who not only can’t give a single textbook which says that, but refused to answer my question about
For a=2, b=3
1/ab=1/(2x3)=1/6
1/axb=1/2x3=3/2
which of those, according to you, is the correct answer, given you insist they are “the same thing” 🙄
implicit multiplication
There’s no such thing. Go ahead and find a Maths textbook that says so, I’ll wait
ab can, by some conventions, have a higher precedence than does the explicit multiplication in a×b
Literally always does, as per the rules of Maths, as found in Maths textbooks 🙄
he has taken that to mean that they are fundamentally different
So go ahead and explain how “the same thing”, according to you, can give different answers in all textbooks. I’ll wait
He thinks that a(b+c)=ab+bc is something to do with notation
The Distributive Law actually, another rule of Maths 🙄
not a fundamental relationship between multiplication and addition
There’s no multiplication in The Distributive Law, only in The Distributive Property 🙄
I will say that no author would distinguish those two terms
Except, of course, for all the ones who do 😂
because they’re just too easily confused
says person confused about the difference between a Law and a Property 😂
And many authors explicitly say that one is also known as the other
says person who can’t even cite a single example of such
He says that a×(b+c) = ab + bc is an instance of the “distributive property”
ax(b+c)=axb+axc actually.
You seem to think notation is only correct at exactly the level you claim to teach
Nope, every level after Primary school
Elementary school children get taught parentheses means you do stuff inside parentheses first
Because they haven’t been taught The Distributive Law yet, and there is no outside brackets for them - they don’t learn that until Year 7
college calculus students get taught parentheses mean you do stuff inside parenthesis first
No they don’t.
despite two centuries of textbooks showing that is in fact how parentheses work
You’re the one ignoring the 2 centuries of textbooks dude 😂
All published textbooks and all pragmatic mathematics operate as though your pet peeve does not exist
says person who can’t cite a single such example, again 🙄
It’s almost like the shit you insist upon is completely made-up, and does not matter to anyone besides you
says person who actually made up that Multiplication and Products are the same thing 🙄
I thought they were called “products” not “multiplications”
That’s right. You know you’re referring to a 1912 textbook, right? Terminology has moved on since then, as demonstrated by the 1965 textbook 😂
I’m just trying to give you more opportunities to prove that you’re not just a troll
says person who ignored all the textbooks I posted, whilst not citing any themselves 🙄
You insist you’re talking about mathematical rules that cannot be violated, so it should be no problem to find an explicit mention of them
I provided many, which you ignored 🙄
you are saying that the practice of calculators, mathematical tools, programming languages and mathematical software are all wrong
Nope, liar. All my calculators give correct answers (Sharp, Casio, Omron - only Texas Instruments breaks the mold these days), and programmers disobeying the rules of Maths doesn’t prove they not rules of Maths. 🙄 You are the one claiming that Sharp and Casio calculators are giving wrong answers. 🙄 I’m guessing that your calculator, if you even have one (which seems doubtful from what I’ve seen) is a Texas Instruments one.
that you are right
My caclulators and textbooks are correct, yes. 🙄
that my interpretation of your own textbooks is wrong
says person who read one sentence and stopped there and did some mental gymnastics with it, ignoring that the whole rest of the book contradicts that interpretation 🙄
if you show no ability to admit error
says the person who actually made errors.
admit that disagreement from competing authorities
There isn’t any “disagreement from competing authorities”. 😂 Every single textbook, not just Maths, but Physics, Chemistry, Engineering, etc., obeys the exact same rules 😂
As my own show of good faith, I
didn’t look at any of the examples about Distribution and Terms, speaking of proving you are the bad faith person 🙄
I’ll explain why I think this is a bad convention
and you would be wrong, just like you are about everything else
why the formal first-order language of arithmetic doesn’t have this convention
No-one cares why a niche topic, only taught at University, is different to the general rules taught to everyone at high school 🙄
the distributive law is something you must do instead of a property of multiplication that you can use to aid in the manipulation of algebraic expressions but don’t have to
That’s right, as per Maths textbooks
Folded into their inability to understand that some aspects of maths are custom and convention
Says person who has an inability to tell the difference between a convention and the rules 🙄
Somewhere along the way he seems to think that distributivity is something to do with brackets instead of something to do with addition and multiplication
Law Vs. Property, not complicated!
if I can get him to actually cop to any of his verifiable mistakes
Of which there are none as opposed to you who has several verifiable mistakes 🙄
back up any of his whackadoodle claims with direct references
You’ve been given them, and you ignored them
Tomorrow I’m expecting another wall of text responding to every single word except the ones where I ask for such an admission
says person who has still failed to show anywhere that I was mistaken 🙄 On the other hand you have refused to admit to your mistakes
I’ll have satisfied myself he’s a lost cause
Actually, you admitted to not even reading it - that’s something which people who know they are wrong do 🙄
been pushing his wrong ideas of what the distributive law are, since 2023
says person again ignoring the Maths textbooks 🙄
Notice how the text never says “you MUST use the distributive law”?
I notice how you have comprehension and/or honesty issues
It always says some variation of “in order to simplify, you must…”?
Which part of the word “must” don’t you understand? 😂 Also, which part of simplifying Brackets is part of the order of operations don’t you understand? 😂
No, you don’t notice, because you’re blind
cough cough 😂 Here’s another one, in case you’re still in any doubt…
don’t understand what distributivity actually is.
says the person who actually doesn’t understand what The Distributive Law is
You also got me confused with someone else trying to explain in short words how you’re wrong
Nope. Tweedle Dum and Tweedle Dee say very similar things, but one can still tell them apart.
I don’t know which comment you’re replying to but I’m pretty sure you already replied to it, because in every comment chain I remember I had written it up with a very simple explanation of what you needed to do if you wanted to continue the discussion.
I’ve read plenty of your nonsense by now and told you explicitly why I’m not reading more; don’t get all weepy when I follow through.
You’re still not doing any of the very simple things to demonstrate that it’s worth having a discussion with you. Feel free to start, then I can get back to reading fully. Yes, you need to do them in a short comment. That won’t be a problem if you actually wanted to do it. Bye!
You’re still not doing any of the very simple things to demonstrate that it’s worth having a discussion with you
says person still not reading the posts where I did 🙄
Feel free to start
Been doing it the whole time dude. You’re the one ignoring the textbooks that prove you are wrong 🙄
then I can get back to reading fully
There’s nothing stopping you doing that now
Yes, you need to do them in a short comment.
So don’t post so much BS in the first place and it won’t turn into a long reply 🙄
Ok, here’s something short for you, you said…
Where in your textbook does it say explicitly that ab is not a multiplication, or that a multiplication is different from a product in any substantive sense, eh?
Ok, so yet again you have ignored my repeated please to you to read more, but you have again refused, so this emabrassment is of your own making…
Page 23, a÷bxc=axc÷b…
Page 282, answers on Page 577, a÷b(c+d) is a over b(c+d), and not ax(c+d) over b 🙄
You going to reply now? Or just gonna ignore it as usual?
provide an actual textbook example where any of the disputed claims you make are explicitly made
It’s in the actual textbook I already gave you, and you refused to read more than 2 sentences out of it 🙄
Where’s your textbook which says “ab is a product, not multiplication”?
Same textbook. See previous point.
there is a textbook reference saying “ab means the same as a × b
Yep, and does not say that they are equal, for reasons they are not equal,see above, from the very same textbook you kept lying about what it said 🙄
so your mental contortions are not more authoritative
I’ve just proven it was you who was making the mental contortions, as I have been telling you all along
your ability to interpret maths textbooks is poor
says person who claimed that “means” means “equals”, in contradiction of the whole rest of the textbook 🙄
My prediction: you’ll present some implicit references
And just like everything else, you were wrong about that too, 🙄 but “oh no! too long! I’m not going to read that”
And here you are admitting to someone else what I have been telling you the whole time 🙄
While reading some of his linked textbooks I found examples which define the solidus as operating on everything in the next term, which would have 1/ab = 1/(ab) = 1/(ab) = 1/ab
This is also how we were taught though as I recall it was not taught systematically
Yes it is, literally every textbook, not just Maths, but Physics, Engineering, etc. and it’s referenced in Cajori in 1928, they all use ab=(axb).
remember one teacher when I was about 17 complaining that people in her class were writing 1/a·b but should have been writing (1/a)·b
because (1/a) is 1 Term, a fraction, but 1/a is 2 Terms, 1 divided by a.
if you have a correct understanding of what the order of operations really are
rules
you can understand that these conventions all become a bit unwieldy when you have a very complex formula
not to anyone who knows all the rules 🙄
(ab)/(bc) not ((ab)/b)c (which is what the strict interpretation of PEMDAS
No it isn’t. ab=(axb), so ab/cd=(axb)/(cxd), (axb) done in the P step, (cxd) done in the P step, then you do the division - it’s not complicated! 😂 Literally every textbook in all subjects does it that way. That is the strict interpretation of PEMDAS 🙄
because “bc” just visually creates a single thing
a TERM. Come on, you can say it. 😂
even though bc(x-1)(y-1)·sin(b) is a single term
Nope! It’s 2 Terms 🙄
Because DumbMan doesn’t understand mathematical convention
So, I just call you DumbMan from now on? Got it! 😂
looks like he’s gone to sleep again now
It’s called having a life. So sorry to hear you don’t have one
That won’t be a problem if you actually wanted to do it
I actually did it and you confessed to not reading it
Bye!
I’ll take that as an admission of being wrong then., Don’t let the door hit you on the way out.
Where in your textbook does it say explicitly that ab is not a multiplication, or that a multiplication is different from a product in any substantive sense, eh?
You going to reply now? Or just gonna ignore it as usual?
None of the screenshots you put in that reply even use the word “multiplication”, so they are certainly not saying explicitly that ab is not a multiplication or that a multiplication is different from a product, are they. This level of reading comprehension is what got you here.
I’ve not read the rest; I’m sure you were wise enough to put your best attempt first.
None of the screenshots you put in that reply even use the word “multiplication”
So what do you call 10x3, exactly? I’ll wait 😂
so they are certainly not saying explicitly that ab is not a multiplication
They are saying explicitly that bc is a Term, and goes entirely into the denominator, not c into the numerator like in a/bxc does.
that a multiplication is different from a product
So, according to you, c going into the denominator, and c going into the numerator, are somehow not different 🤣🤣🤣 a/bxc, where c goes in the numerator, and a/bc, where c goes in the denominator, go ahead, explain it to me like I’m 5, how are they the same thing according to you 🤣🤣🤣
This level of reading comprehension is what got you here
says person who can’t tell the difference between a/bxc=axc/b, and a/bc=a/(bxc) 🤣🤣🤣
I’m sure you were wise enough to put your best attempt first
Hey, I was restricting it to the same textbook like you said. If you wanna go ahead and open it up to other textbooks , then explain how a/bxc=16 and a/bc=1 are the same thing , I’ll wait. 🤣🤣🤣 I’ve never encountered anyone who has claimed 1 and 16 are the same thing, so go ahead and explain it to me 🤣🤣🤣
Not important. It’s an example, not explicit. If I asked for an explicit reference for the meaning of the word “table”, a source that discusses carpentry but never uses the word itself is not explicit. Do you need me to explain in more detail what “explicit” means? Do you need me to explain why I’m demanding you find an explicit reference?
I, for one, am content that there is no such explicit reference for your interpretation of the meaning of the word multiplication. If you are finding it difficult to find one but are still convinced, that’s fine - just fulfill one of the other options you have to demonstrate it’s worth holding a discussion about mathematics.
Your second reference says “when multiplications are denoted by juxtaposition, as in 4c ÷ 3ab”. Very interesting. Maybe we can discuss that after you demonstrate it’s worth it.
Further down you have again quoted (but not highlighted) the section which says “other rules than those just described might have been adopted” which, again, is interesting.
None of the screenshots you put in that reply even use the word “multiplication”,
So let me help you out…
It’s an example, not explicit.
It explicitly says “Multiplication” at the bottom of the page! 😂
If I asked for an explicit reference for the meaning of the word “table”, a source that discusses carpentry but never uses the word itself is not explicit
And this page does use the word “Multiplication”. Are you seeing yet why I kept telling you to read more than 2 sentences? 😂
Do you need me to explain in more detail what “explicit” means?
Do you need me to explain in more detail what “read more than 2 sentences” means?
I, for one, am content that there is no such explicit reference for your interpretation of the meaning of the word multiplication
And yet there it is, right there on page 23. Who would thought? Oh yeah, people who have read more than 2 sentences out of the whole book 😂
Your second reference says “when multiplications are denoted by juxtaposition, as in 4c ÷ 3ab”. Very interesting.
Yeah, 1912 textbooks are “very interesting”, much more so than modern textbooks which never call it such 😂
Maybe we can discuss that after you demonstrate it’s worth it
I already pointed out the problem with your not reading more than 2 sentences out of a textbook again there
“other rules than those just described might have been adopted” which, again, is interesting
It’s not actually, if you know the history behind that comment, which I have no doubt that you don’t
And you were proven wrong elsewhere (since you ran your rubbish to the maximum comment depth), but admitted to not reading it, speaking of proving you were the bad faith one all along 🙄
So, now that I’ve found a place I can reply to your other non-repliable posts…
Which no-one ever has 🙄
See how many Mathematicians and Maths teachers you can gaslight into believing that they and Maths textbooks are all wrong, I’ll wait.
And you hilariously provided a manual that proved you were wrong about that! 😂
It’s right there in the manual, as I pointed out 😂
That’s right, because it doesn’t have brackets keys 🙄 So you have to enter that first, then press the equals key to make it evaluate that first, because it doesn’t evaluate from left to right otherwise, it will do the multiplication first 🙄
says person who still will not admit he was wrong about his claim that all basic calculators working that way, even though the manual proves there are some that don’t 😂
Says person refusing to believe all evidence, including the calculator manual 😂
Nope liar. I’m the one who keeps pointing out they are different 🙄 Go ahead and find a screenshot of me saying they’re the same, I’ll wait
As per Maths textbooks, which you keep ignoring 🙄
says person who not only can’t give a single textbook which says that, but refused to answer my question about
For a=2, b=3
1/ab=1/(2x3)=1/6
1/axb=1/2x3=3/2
which of those, according to you, is the correct answer, given you insist they are “the same thing” 🙄
There’s no such thing. Go ahead and find a Maths textbook that says so, I’ll wait
Literally always does, as per the rules of Maths, as found in Maths textbooks 🙄
So go ahead and explain how “the same thing”, according to you, can give different answers in all textbooks. I’ll wait
The Distributive Law actually, another rule of Maths 🙄
There’s no multiplication in The Distributive Law, only in The Distributive Property 🙄
Except, of course, for all the ones who do 😂
says person confused about the difference between a Law and a Property 😂
says person who can’t even cite a single example of such
ax(b+c)=axb+axc actually.
Nope, every level after Primary school
Because they haven’t been taught The Distributive Law yet, and there is no outside brackets for them - they don’t learn that until Year 7
No they don’t.
You’re the one ignoring the 2 centuries of textbooks dude 😂
says person who can’t cite a single such example, again 🙄
says person who actually made up that Multiplication and Products are the same thing 🙄
That’s right. You know you’re referring to a 1912 textbook, right? Terminology has moved on since then, as demonstrated by the 1965 textbook 😂
says person who ignored all the textbooks I posted, whilst not citing any themselves 🙄
I provided many, which you ignored 🙄
Nope, liar. All my calculators give correct answers (Sharp, Casio, Omron - only Texas Instruments breaks the mold these days), and programmers disobeying the rules of Maths doesn’t prove they not rules of Maths. 🙄 You are the one claiming that Sharp and Casio calculators are giving wrong answers. 🙄 I’m guessing that your calculator, if you even have one (which seems doubtful from what I’ve seen) is a Texas Instruments one.
My caclulators and textbooks are correct, yes. 🙄
says person who read one sentence and stopped there and did some mental gymnastics with it, ignoring that the whole rest of the book contradicts that interpretation 🙄
says the person who actually made errors.
There isn’t any “disagreement from competing authorities”. 😂 Every single textbook, not just Maths, but Physics, Chemistry, Engineering, etc., obeys the exact same rules 😂
didn’t look at any of the examples about Distribution and Terms, speaking of proving you are the bad faith person 🙄
and you would be wrong, just like you are about everything else
No-one cares why a niche topic, only taught at University, is different to the general rules taught to everyone at high school 🙄
That’s right, as per Maths textbooks
Says person who has an inability to tell the difference between a convention and the rules 🙄
Law Vs. Property, not complicated!
Of which there are none as opposed to you who has several verifiable mistakes 🙄
You’ve been given them, and you ignored them
says person who has still failed to show anywhere that I was mistaken 🙄 On the other hand you have refused to admit to your mistakes
Actually, you admitted to not even reading it - that’s something which people who know they are wrong do 🙄
says person again ignoring the Maths textbooks 🙄
I notice how you have comprehension and/or honesty issues
Which part of the word “must” don’t you understand? 😂 Also, which part of simplifying Brackets is part of the order of operations don’t you understand? 😂
cough cough 😂 Here’s another one, in case you’re still in any doubt…
says the person who actually doesn’t understand what The Distributive Law is
Nope. Tweedle Dum and Tweedle Dee say very similar things, but one can still tell them apart.
Don’t let the door hit you on the way out! 😂
I don’t know which comment you’re replying to but I’m pretty sure you already replied to it, because in every comment chain I remember I had written it up with a very simple explanation of what you needed to do if you wanted to continue the discussion.
I’ve read plenty of your nonsense by now and told you explicitly why I’m not reading more; don’t get all weepy when I follow through.
Yep, and you admitted to not reading it 🙄
And when I had, in your next comment you posted, you admitted you didn’t read it 🙄 I even posted the screenshot of you saying that
but admitted to not reading the proof that you were wrong 🙄
What you said: too long
What you meant: not reading anything which proves I’m wrong
says person who admitted to not following through 🤣🤣🤣
You’re still not doing any of the very simple things to demonstrate that it’s worth having a discussion with you. Feel free to start, then I can get back to reading fully. Yes, you need to do them in a short comment. That won’t be a problem if you actually wanted to do it. Bye!
says person still not reading the posts where I did 🙄
Been doing it the whole time dude. You’re the one ignoring the textbooks that prove you are wrong 🙄
There’s nothing stopping you doing that now
So don’t post so much BS in the first place and it won’t turn into a long reply 🙄
Ok, here’s something short for you, you said…
Ok, so yet again you have ignored my repeated please to you to read more, but you have again refused, so this emabrassment is of your own making…
Page 23, a÷bxc=axc÷b…
Page 282, answers on Page 577, a÷b(c+d) is a over b(c+d), and not ax(c+d) over b 🙄
You going to reply now? Or just gonna ignore it as usual?
It’s in the actual textbook I already gave you, and you refused to read more than 2 sentences out of it 🙄
Same textbook. See previous point.
Yep, and does not say that they are equal, for reasons they are not equal,see above, from the very same textbook you kept lying about what it said 🙄
I’ve just proven it was you who was making the mental contortions, as I have been telling you all along
says person who claimed that “means” means “equals”, in contradiction of the whole rest of the textbook 🙄
And just like everything else, you were wrong about that too, 🙄 but “oh no! too long! I’m not going to read that”
And here you are admitting to someone else what I have been telling you the whole time 🙄
Yes it is, literally every textbook, not just Maths, but Physics, Engineering, etc. and it’s referenced in Cajori in 1928, they all use ab=(axb).
because (1/a) is 1 Term, a fraction, but 1/a is 2 Terms, 1 divided by a.
rules
not to anyone who knows all the rules 🙄
No it isn’t. ab=(axb), so ab/cd=(axb)/(cxd), (axb) done in the P step, (cxd) done in the P step, then you do the division - it’s not complicated! 😂 Literally every textbook in all subjects does it that way. That is the strict interpretation of PEMDAS 🙄
a TERM. Come on, you can say it. 😂
Nope! It’s 2 Terms 🙄
So, I just call you DumbMan from now on? Got it! 😂
It’s called having a life. So sorry to hear you don’t have one
I actually did it and you confessed to not reading it
I’ll take that as an admission of being wrong then., Don’t let the door hit you on the way out.
None of the screenshots you put in that reply even use the word “multiplication”, so they are certainly not saying explicitly that ab is not a multiplication or that a multiplication is different from a product, are they. This level of reading comprehension is what got you here.
I’ve not read the rest; I’m sure you were wise enough to put your best attempt first.
So what do you call 10x3, exactly? I’ll wait 😂
They are saying explicitly that bc is a Term, and goes entirely into the denominator, not c into the numerator like in a/bxc does.
So, according to you, c going into the denominator, and c going into the numerator, are somehow not different 🤣🤣🤣 a/bxc, where c goes in the numerator, and a/bc, where c goes in the denominator, go ahead, explain it to me like I’m 5, how are they the same thing according to you 🤣🤣🤣
says person who can’t tell the difference between a/bxc=axc/b, and a/bc=a/(bxc) 🤣🤣🤣
Hey, I was restricting it to the same textbook like you said. If you wanna go ahead and open it up to other textbooks , then explain how a/bxc=16 and a/bc=1 are the same thing , I’ll wait. 🤣🤣🤣 I’ve never encountered anyone who has claimed 1 and 16 are the same thing, so go ahead and explain it to me 🤣🤣🤣
Not important. It’s an example, not explicit. If I asked for an explicit reference for the meaning of the word “table”, a source that discusses carpentry but never uses the word itself is not explicit. Do you need me to explain in more detail what “explicit” means? Do you need me to explain why I’m demanding you find an explicit reference?
I, for one, am content that there is no such explicit reference for your interpretation of the meaning of the word multiplication. If you are finding it difficult to find one but are still convinced, that’s fine - just fulfill one of the other options you have to demonstrate it’s worth holding a discussion about mathematics.
Your second reference says “when multiplications are denoted by juxtaposition, as in 4c ÷ 3ab”. Very interesting. Maybe we can discuss that after you demonstrate it’s worth it.
Further down you have again quoted (but not highlighted) the section which says “other rules than those just described might have been adopted” which, again, is interesting.
Says person who said…
So let me help you out…
It explicitly says “Multiplication” at the bottom of the page! 😂
And this page does use the word “Multiplication”. Are you seeing yet why I kept telling you to read more than 2 sentences? 😂
Do you need me to explain in more detail what “read more than 2 sentences” means?
And yet there it is, right there on page 23. Who would thought? Oh yeah, people who have read more than 2 sentences out of the whole book 😂
Yeah, 1912 textbooks are “very interesting”, much more so than modern textbooks which never call it such 😂
I already pointed out the problem with your not reading more than 2 sentences out of a textbook again there
It’s not actually, if you know the history behind that comment, which I have no doubt that you don’t