An algebraic expression written as a product or quotient of numerals or variables or both is called a term
So b * c, which is a product of the variables b and c, is a term, according to this textbook.
You seem to be getting confused because none of the examples on this particular page feature the multiplication symbol ×. But that is because on the previous page, the author writes:
When a product involves a variable it is customary to omit the symbol × of multiplication.
That means that the expression bc is just another way of writing b×c; it is treated the same other than requiring fewer strokes of the pen or presses on a keyboard, because this is just a custom. That should clear up your confusion in interpreting this textbook (though really, the language is clear: you don’t dispute that b×c - or b * c - are products, do you.)
Elsewhere in this thread you are clearly confused about what brackets mean. They are explained on page 20 of your textbook, where it says that you evaluate the expression inside the (innermost) brackets before doing anything else. Notice that, in its elucidation of several examples, involving addition and multiplication, the “distributive law” is not mentioned, because the distributive law has nothing to do with brackets and is not an operation.
Thus the expression 3 × (2 + 4) can be evaluated by first performing the summation inside the brackets to get 3 × 6 and then the product to get 18. The textbook then says that it is customary to omit the multiplication symbol and instead write 3(2+4), again indicating that these expressions are merely different ways of writing the same thing.
The exact same process of course must be followed whether numbers are represented by numerals or by letters designating a variable. You cannot do algebra if you don’t follow the same procedure in both cases. So consider the expression 2(a+b)². You have suggested that you must evaluate this as (2a+2b)² because you must “do brackets first”, but this is not what “doing brackets” means. You haven’t produced any authority to suggest that it is, and your own textbook makes it clear that “doing brackets” means do what is inside the brackets first. Not what is outside the brackets. Distributing 2 over a+b is not “doing brackets”; it is multiplication and comes afterwards.
If 2(a+b)² were equal to (2a+2b)² let us try with a=b=2. Let us first evaluate (2a+2b)²: it is equal to (2×2+2×2)² = (4+4)² = 8² = 64. Now let us evaluate 2(a+b)²: it is 2(2+2)² and now, following your textbook’s instruction to do what is inside the brackets first, this is equal to 2(4)². The next highest-priority operation is the exponent, giving us 2×16 (we now must write the × because it is an expression purely in numerals, with no brackets or variables) which is 32.
The fact that these two answers are different is because your understandings of what it means to “do brackets” and the distributive law are wrong.
Since I’m working off the textbook you gave, and I referred liberally to things in that textbook, I’m sure if you still disagree you will be able to back up your interpretations with reference to it.
By the way, I noticed this statement on page 23, regarding the order of operations:
However, mathematicians have agreed on a rule to fall back on if someone omits punctuation marks.
it does rather seem like this rule is one established not by the fundamental laws of mathematics but by agreement as they say, does it not? Care to comment?
So b * c, which is a product of the variables b and c
Nope. bc is the product of b and c. bxc is Multiplication of the 2 Terms b and c.
according to this textbook
Says person who clearly didn’t read more than 2 sentences out of it 🙄
none of the examples on this particular page feature the multiplication symbol ×
and why do you think that is? Do explain. We’re all waiting 😂 Spoiler alert: if you had read more than 2 sentences you would know why
That means that the expression bc is just another way of writing b×c;
No it doesn’t. it means bxc is Multiplication, and bc is the product 🙄 Again you would’ve already known this is you had read more than 2 sentences of the book.
it is treated the same other than requiring fewer strokes of the pen
No it isn’t, and again you would already know this if you had read more than 2 sentences. If a=2 and b=3, then…
1/ab=1/(2x3)=1/6
1/axb=1/2x3=3/2
this is just a custom
Nope, an actual rule of Maths. If you meant 1/axb, but wrote 1/ab, you’ve gonna get a different answer 🙄
That should clear up your confusion in interpreting this textbook
says person who only read 2 sentences out of it 🙄
though really, the language is clear:
It sure is when the read the rest of the page 🙄
you don’t dispute that b×c - or b * c - are products, do you
What don’t you understand about only ab is the product of a and b?
Elsewhere in this thread you are clearly confused about what brackets mean
Not me, must be you! 😂
They are explained on page 20 of your textbook, where it says that you evaluate the expression inside the (innermost) brackets before doing anything else.
Until all brackets have been removed. on the very next page. 🙄 See what happens when you read more than 2 sentences out of a textbook? Who would’ve thought you need to read more than 2 sentences! 😂
the “distributive law” is not mentioned, because the distributive law has nothing to do with brackets
And yet, right there on Page 21, they Distribute in the last step of removing Brackets, 🙄 5(17)=85, and throughout the whole rest of the book they write Products in that form, a(b) (or just ab as the case may be).
is not an operation
Brackets aren’t an operator, they are grouping symbols, and solving grouping symbols is done in the first 2 steps of order of operations, then we solve the operators.
Thus the expression 3 × (2 + 4) can be evaluated by first performing the summation inside the brackets to get 3 × 6 and then the product to get 1
3x6 isn’t a Product, it’s a Multiplication, done in the Multiplication step of order of operations.
The textbook then says that it is customary to omit the multiplication symbol and instead write 3(2+4)
It says you omit the multiplication sign if it’s a Product, and 3x6 is not a Product. I’m not sure how many times you need to be told that 🙄
again indicating that these expressions are merely different ways of writing the same thing
Nope, completely different giving different answers
1/3x(2+4)=1/3x6=6/3=2
1/3(2+4)=1/3(6)=1/18
You have suggested that you must evaluate this as (2a+2b)² because you must “do brackets first”
Yep
this is not what “doing brackets” means.
Yes it is! 😂
Not what is outside the brackets.
Yes it is! 😂 Until all Brackets have been removed, which they can’t be if you haven’t Distributed yet. Again, last step of the working out…
Distributing 2 over a+b is not “doing brackets”;
Yes it is! 😂 Until all Brackets have been removed
it is multiplication and comes afterwards
Nope, it’s Distribution, done in the Brackets step, before doing anything else, as per Page 21
following your textbook’s instruction to do what is inside the brackets first, this is equal to 2(4)²
Which, when you finish doing the brackets, is 8²
The next highest-priority operation is the exponent
After you have finished the Brackets 🙄
giving us 2×16
Nope. Giving us 8²=64
we now must write the × because it is an expression purely in numerals
Nope! If you write it at all, which you don’t actually need to (the textbook never does), then you write (2x4)², per The Distributive Law, where you cannot remove the brackets if you haven’t Distributed yet. There’s no such rule as the one you just made up
The fact that these two answers are different is because
You disobeyed The Distributive Law in the second case, and the fact that you got a different answer should’ve been a clue to you that you did it wrong 🙄
what it means to “do brackets” and the distributive law are wrong
No, that would be your understanding is wrong, the person who only read 2 sentences 🙄 I’m not sure what you think the rest of the chapter is about.
Since I’m working off the textbook you gave
Says person who only read 2 sentences out of it 🙄
I referred liberally to things in that textbook
Yep, ignoring all the parts that prove you are wrong 🙄
I’m sure if you still disagree you will be able to back up your interpretations with reference to it
Exact same reference! 😂
it does rather seem like this rule is one established not by the fundamental laws of mathematics but by agreement as they say
You know Mathematicians tend to agree when something has been proven, right? 😂
Do you teach classes like this? “That’s not a product, it’s a multiplication” – those are the same thing. Shouldn’t you, as a teacher, be explaining the difference, if you say there is one? I’m starting to believe you don’t think they’re is one, but are just using words to be annoying. Or maybe you don’t explain because you don’t know.
You could argue that “product” refers to the result of the multiplication rather than the operation, but there’s no sense in which the formula “a × b” does not refer to the result of multiplying a and b.
Of course, you don’t bother to even make such an argument because either that would make it easier to see your trolling for what it is, or you’re not actuality smart enough to understand the words you’re using.
It’s interesting, isn’t it, that you never provide any reference to your textbooks to back up these strange interpretations. 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? It doesn’t, does it? You’re keen to cite textbooks any time you can, but here you can’t. You complain that people don’t read enough of the textbook, yet they read more than you ever refer to.
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. Here’s another option: provide an actual textbook example where any of the disputed claims you make are explicitly made. For example, there should be some textbook somewhere which says that mathematics would not work with different orders of operations - you’ve never found a textbook which says anything like this, only things like “mathematicians have agreed” (and by the way, hilarious that you commit the logical fallacy of affirming the consequent on that one).
Likewise with your idea of what constitutes a term, where’s your textbook which says that “a × b is not a term”? Where is the textbook that says 5(17) requires distribution? (All references you have given are that distribution relates multiplication and addition, but there’s no addition) Where’s your textbook which says “ab is a product, not multiplication”? Where’s a citation saying “product is not the same as multiplication and here’s how”? Because there is a textbook reference saying “ab means the same as a × b”, so your mental contortions are not more authoritative.
Find any one of these - explicitly, not implicitly, (because your ability to interpret maths textbooks is poor) and we can have a productive discussion, otherwise we cannot.
My prediction: you’ll present some implicit references and try to argue they mean what you want. In that case, my reply is already prepared 😁
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” 🙄
It’s amazing that you think these are explicit references. Notice how the text never says “you MUST use the distributive law”? It always says some variation of “in order to simplify, you must…”?
No, you don’t notice, because you’re blind, and don’t understand what distributivity actually is.
You also got me confused with someone else trying to explain in short words how you’re wrong, but that won’t be a problem now you demonstrated such abject failure to hold a productive discussion - bye.
There’s no sense in which it does refer to the result you mean.
“a X b is written ab.” Modern Algebra: Structure And Method, page 36. It’s only a different way of writing the exact same thing.
Go ahead and try it out and let me know how you go.
Every textbook ever written disagrees with how you think brackets work, and mathematics has not collapsed in on itself. We’ve seen your Mastodon posts lamenting how ‘university people’ all disagree with what you lie to teenagers about. All of them! Weird, right? What a bizarre coincidence. I’m not sure what would look different if you were just plain full of shit.
none of the examples on this particular page feature the multiplication symbol ×
and why do you think that is?
“When a product involves a variable, it is customary to omit the symbol X of multiplication. Thus, 3 X n is written 3n and means three times n, and a X b is written ab and means a times b.”
By all means, humiliate yourself by splitting that hair
I’ll take that as an admission that you’re wrong then, given you can’t defend your wrong interpretation of it (which you would know is wrong if you had read more than 1 paragraph of the book!) 😂
your own textbook makes it clear that “doing brackets” means do what is inside the brackets first. Not what is outside the brackets.
Which this troll admits when sneering “They say you can [simplify first] when there is Addition or Subtraction inside the Brackets.”
Except when they sneer you must not do that, because there’s addition inside the brackets. 2(3*a+2*a)2 becomes 2(5*a)2, which gets a different answer, somehow. Or maybe it’s 2(3a+2a)2 becoming 2(5a)2 that’s different. One or the other is the SpEcIaL eXcEpTiOn to a rule they made up.
Weird how nobody else in the world has this problem. Almost like a convention that requires special cases is fucking stupid, and if people meant (2(n))2, they’d just write that.
Distributing 2 over a+b is not “doing brackets”; it is multiplication and comes afterwards.
Except when they insist distribution is totally different from multiplication… somehow. But if a product is one term and multiplying two things is a product and two things being multiplied is two terms, sure, fuck it, words don’t mean things.
I actually forgot the most obvious way in which Order of Operations is a set of conventions… Some countries say “BODMAS” (division then multiplication) whilst others say “PEMDAS” (multiplication then division)…
They’re grouped, being essentially the same operation, but inverted. Ditto for addition and subtraction. There’s not a convenient word that covers both directions, like how exponents / order are the same for positive and negative powers.
Convention is saying 1/ab is 1/(ab) instead of (1/a)b, while 1/a*b is indeed (1/a)b. The latter of which this troll would say is a syntax error, because juxtaposition after brackets is foreboden… despite modern textbook examples.
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: specifically I 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 (we generally used a dot for multiplication at this point). But at this point in our education, none of us remembered ever being taught this. I suspect what happened was that when being taught order of operations some years before, we simply never used the solidus and only used ÷ or fraction notation.
Anyway, if you have a correct understanding of what the order of operations really are (conventions) you can understand that these conventions all become a bit unwieldy when you have a very complex formula, and that it’s better to write mathematics as if there were no such convention in those cases, and provide brackets for disambiguation. Thus while you might write ab ÷ bc and reasonably expect everyone to understand you mean (ab)/(bc) not ((ab)/b)c (which is what the strict interpretation of PEMDAS would say!) because “bc” just visually creates a single thing, the same is not true of the expression ab ÷ bc(x-1)(y-1)·sin(b), even though bc(x-1)(y-1)·sin(b) is a single term, and so the latter should be written more clearly.
Because DumbMan doesn’t understand mathematical convention, he doesn’t understand that these things really depend on how they’re perceived, so is incapable of understanding such a way of working.
Anyway, looks like he’s gone to sleep again now, I wonder if he’ll pop up again in a couple of days, or if it’ll take him until someone else posts some BODMAS clickbait.
Personally I tend to bracket aggressively, because I’ve been repeatedly betrayed by compilers. One in particular applied the high priority of & (bitwise and) to the low-priority && (logical and), so if( 1 < 2 && 3 ) would always fail because 2 && 3 evaluates to 1.
That was the topic the first time I dealt with this dingus and their rules of maths!!! about a year ago. The post was several months old. They’ve never understood that some things are fundamental… and some things are made up. Some things are mutable. So even if their nonsense was widespread, we could say, that’s kinda stupid, we should do something else.
The dumbest argument I’ve ever suffered online was some dingdong convinced that “two times three” meant the quantity two, three times. Even though “two times” is right there, in the sentence. Even though “twice three” literally means “two times three.” Even though the song “Three Times A Lady” obviously does not mean the quantity three, ladyce. Not even that dipshit thought two times three-squared could be thirty-six.
The result of a multiplication operation is called a product
Now you’re getting it - axb=ab. axb is Multiplication of 2 Terms, ab is the single Product. It’s the reason that 8/2(1+3) and 8/2x(1+3) give different answers 🙄
Show me one textbook where a(b+c)2 gets an a2 term
I already gave you many that tell you a(b+c)=(ab+ac) Mr. Ostrich - which part of a(b+c)=(ab+ac) are you having trouble understanding?
“When a product involves a variable, it is customary to omit the symbol X of multiplication. Thus, 3 X n is written 3n and means three times n, and a X b is written ab and means a times b.” Modern Algebra: Structure And Method, page 36. Immediately before the definition you’re now lying about.
Fuck your non-sequitur. a(b+c)2 is a*(b+c)2, as backed up by - for example - these four math textbooks. No textbook will ever say it produces an a2 term. You made it up. You’re just full of shit.
You so nearly had it, look “two things”! Yes axb is 2 Terms being Multiplied to make them one 😂
Immediately before the definition you’re now lying about
Nope! Says exactly what I already said, and I have no idea why you think it says otherwise. Now read the next page, which tells you ab is one Term and doesn’t say that axb is 1 Term. 🙄 You’re proven wrong by the very textbook you’re quoting from! 😂
Fuck your non-sequitur
Says person trying to disprove a(b+c)=(ab+ac) by dragging a(bc)²=ab²c² to try and make a false equivalence argument 😂
a(b+c)2 is a*(b+c)2
No it isn’t! 😂 The first is one term, the second is two terms
for example - these four math textbooks.
Says Mr. Ostrich, still ignoring the dozens of textbooks I posted saying a(b+c)=(ab+ac)
No textbook will ever say it produces an a2 term
No, it produces an ab term and an ac term, a(b+c)=(ab+ac) 🙄
You made it up. You’re just full of shit
Says Mr. Ostrich, now completely full of shit, still ignoring the dozens of textbooks I posted, including ones written before I was even born
Says person who can’t find a Maths textbook that says a(bxc)=(abxac) 🙄
I’m gonna presume that’s why you keep claiming a(bxc)=(abxac) 🙄
says person still not doing that 😂
No it isn’t! 😂 2xn² is
Except for authors of Maths textbooks 😂
So no answer for centuries of textbooks saying you’re full of shit.
b*c is one term.
Show me one textbook where a(b+c)2 gets an a2 term. Here’s four in a row that say you’re full of shit.
No it isn’t! 😂
says person who just proved they’re full of shit about what constitutes a Term 😂
So b * c, which is a product of the variables b and c, is a term, according to this textbook.
You seem to be getting confused because none of the examples on this particular page feature the multiplication symbol ×. But that is because on the previous page, the author writes:
That means that the expression bc is just another way of writing b×c; it is treated the same other than requiring fewer strokes of the pen or presses on a keyboard, because this is just a custom. That should clear up your confusion in interpreting this textbook (though really, the language is clear: you don’t dispute that b×c - or b * c - are products, do you.)
Elsewhere in this thread you are clearly confused about what brackets mean. They are explained on page 20 of your textbook, where it says that you evaluate the expression inside the (innermost) brackets before doing anything else. Notice that, in its elucidation of several examples, involving addition and multiplication, the “distributive law” is not mentioned, because the distributive law has nothing to do with brackets and is not an operation.
Thus the expression 3 × (2 + 4) can be evaluated by first performing the summation inside the brackets to get 3 × 6 and then the product to get 18. The textbook then says that it is customary to omit the multiplication symbol and instead write 3(2+4), again indicating that these expressions are merely different ways of writing the same thing.
The exact same process of course must be followed whether numbers are represented by numerals or by letters designating a variable. You cannot do algebra if you don’t follow the same procedure in both cases. So consider the expression 2(a+b)². You have suggested that you must evaluate this as (2a+2b)² because you must “do brackets first”, but this is not what “doing brackets” means. You haven’t produced any authority to suggest that it is, and your own textbook makes it clear that “doing brackets” means do what is inside the brackets first. Not what is outside the brackets. Distributing 2 over a+b is not “doing brackets”; it is multiplication and comes afterwards.
If 2(a+b)² were equal to (2a+2b)² let us try with a=b=2. Let us first evaluate (2a+2b)²: it is equal to (2×2+2×2)² = (4+4)² = 8² = 64. Now let us evaluate 2(a+b)²: it is 2(2+2)² and now, following your textbook’s instruction to do what is inside the brackets first, this is equal to 2(4)². The next highest-priority operation is the exponent, giving us 2×16 (we now must write the × because it is an expression purely in numerals, with no brackets or variables) which is 32.
The fact that these two answers are different is because your understandings of what it means to “do brackets” and the distributive law are wrong.
Since I’m working off the textbook you gave, and I referred liberally to things in that textbook, I’m sure if you still disagree you will be able to back up your interpretations with reference to it.
By the way, I noticed this statement on page 23, regarding the order of operations:
it does rather seem like this rule is one established not by the fundamental laws of mathematics but by agreement as they say, does it not? Care to comment?
Nope. bc is the product of b and c. bxc is Multiplication of the 2 Terms b and c.
Says person who clearly didn’t read more than 2 sentences out of it 🙄
and why do you think that is? Do explain. We’re all waiting 😂 Spoiler alert: if you had read more than 2 sentences you would know why
No it doesn’t. it means bxc is Multiplication, and bc is the product 🙄 Again you would’ve already known this is you had read more than 2 sentences of the book.
No it isn’t, and again you would already know this if you had read more than 2 sentences. If a=2 and b=3, then…
1/ab=1/(2x3)=1/6
1/axb=1/2x3=3/2
Nope, an actual rule of Maths. If you meant 1/axb, but wrote 1/ab, you’ve gonna get a different answer 🙄
says person who only read 2 sentences out of it 🙄
It sure is when the read the rest of the page 🙄
What don’t you understand about only ab is the product of a and b?
Not me, must be you! 😂
Until all brackets have been removed. on the very next page. 🙄 See what happens when you read more than 2 sentences out of a textbook? Who would’ve thought you need to read more than 2 sentences! 😂
And yet, right there on Page 21, they Distribute in the last step of removing Brackets, 🙄 5(17)=85, and throughout the whole rest of the book they write Products in that form, a(b) (or just ab as the case may be).
Brackets aren’t an operator, they are grouping symbols, and solving grouping symbols is done in the first 2 steps of order of operations, then we solve the operators.
3x6 isn’t a Product, it’s a Multiplication, done in the Multiplication step of order of operations.
It says you omit the multiplication sign if it’s a Product, and 3x6 is not a Product. I’m not sure how many times you need to be told that 🙄
Nope, completely different giving different answers
1/3x(2+4)=1/3x6=6/3=2
1/3(2+4)=1/3(6)=1/18
Yep
Yes it is! 😂
Yes it is! 😂 Until all Brackets have been removed, which they can’t be if you haven’t Distributed yet. Again, last step of the working out…
Yes it is! 😂 Until all Brackets have been removed
Nope, it’s Distribution, done in the Brackets step, before doing anything else, as per Page 21
Which, when you finish doing the brackets, is 8²
After you have finished the Brackets 🙄
Nope. Giving us 8²=64
Nope! If you write it at all, which you don’t actually need to (the textbook never does), then you write (2x4)², per The Distributive Law, where you cannot remove the brackets if you haven’t Distributed yet. There’s no such rule as the one you just made up
You disobeyed The Distributive Law in the second case, and the fact that you got a different answer should’ve been a clue to you that you did it wrong 🙄
No, that would be your understanding is wrong, the person who only read 2 sentences 🙄 I’m not sure what you think the rest of the chapter is about.
Says person who only read 2 sentences out of it 🙄
Yep, ignoring all the parts that prove you are wrong 🙄
Exact same reference! 😂
You know Mathematicians tend to agree when something has been proven, right? 😂
Yep, read the whole chapter 🙄
Do you teach classes like this? “That’s not a product, it’s a multiplication” – those are the same thing. Shouldn’t you, as a teacher, be explaining the difference, if you say there is one? I’m starting to believe you don’t think they’re is one, but are just using words to be annoying. Or maybe you don’t explain because you don’t know.
You could argue that “product” refers to the result of the multiplication rather than the operation, but there’s no sense in which the formula “a × b” does not refer to the result of multiplying a and b.
Of course, you don’t bother to even make such an argument because either that would make it easier to see your trolling for what it is, or you’re not actuality smart enough to understand the words you’re using.
It’s interesting, isn’t it, that you never provide any reference to your textbooks to back up these strange interpretations. 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? It doesn’t, does it? You’re keen to cite textbooks any time you can, but here you can’t. You complain that people don’t read enough of the textbook, yet they read more than you ever refer to.
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. Here’s another option: provide an actual textbook example where any of the disputed claims you make are explicitly made. For example, there should be some textbook somewhere which says that mathematics would not work with different orders of operations - you’ve never found a textbook which says anything like this, only things like “mathematicians have agreed” (and by the way, hilarious that you commit the logical fallacy of affirming the consequent on that one).
Likewise with your idea of what constitutes a term, where’s your textbook which says that “a × b is not a term”? Where is the textbook that says 5(17) requires distribution? (All references you have given are that distribution relates multiplication and addition, but there’s no addition) Where’s your textbook which says “ab is a product, not multiplication”? Where’s a citation saying “product is not the same as multiplication and here’s how”? Because there is a textbook reference saying “ab means the same as a × b”, so your mental contortions are not more authoritative.
Find any one of these - explicitly, not implicitly, (because your ability to interpret maths textbooks is poor) and we can have a productive discussion, otherwise we cannot.
My prediction: you’ll present some implicit references and try to argue they mean what you want. In that case, my reply is already prepared 😁
Yep! And if you read more than 2 sentences out of the textbook you would know why 🙄
Says person who only read 2 sentences out of a whole chapter 🙄
Yep, and it’s right there in the textbook! 🙄
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?? 😂
Yep by definition!
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
Says someone revealing that they haven’t read a word I’ve said 🙄
says someone who has just proven they haven’t been reading them 🙄
Yes I did, and you only read 2 sentences out of it 😂
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… 🙄
The page that you only read one sentence from 🙄
I already did and you only read 2 sentences out of it 🙄
says person who has repeatedly proven they’ve only read 2 sentences 🙄
And I pointed out that in fact you got it wrong, and Mr. Hypocrite has failed to admit it 🙄
Same one I already told you and you only read 2 sentences out of a whole chapter
It’s easy enough to prove yourself, like I did. Go ahead and try it out and let me know how you go.
No, I was able to prove it myself 🙄
Because it was proven 🙄
Same textbook that you only read 2 sentences from
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
Same one you only read 2 sentences from
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 🙄
Says person who made the mental contortion that “means” means “equals” instead of reading the rest of the page
says person who only read 2 sentences out of a whole chapter 🙄
when you decide to read more than 2 sentences 🙄
Wrong, as usual
says person trying to argue that “means” means “equals” 🙄
It’s amazing that you think these are explicit references. Notice how the text never says “you MUST use the distributive law”? It always says some variation of “in order to simplify, you must…”?
No, you don’t notice, because you’re blind, and don’t understand what distributivity actually is.
You also got me confused with someone else trying to explain in short words how you’re wrong, but that won’t be a problem now you demonstrated such abject failure to hold a productive discussion - bye.
“a X b is written ab.” Modern Algebra: Structure And Method, page 36. It’s only a different way of writing the exact same thing.
Every textbook ever written disagrees with how you think brackets work, and mathematics has not collapsed in on itself. We’ve seen your Mastodon posts lamenting how ‘university people’ all disagree with what you lie to teenagers about. All of them! Weird, right? What a bizarre coincidence. I’m not sure what would look different if you were just plain full of shit.
“When a product involves a variable, it is customary to omit the symbol X of multiplication. Thus, 3 X n is written 3n and means three times n, and a X b is written ab and means a times b.”
Illiterate fraud.
says person who thinks “means” and “equals” mean the same thing 😂
By all means, humiliate yourself by splitting that hair.
I’ll take that as an admission that you’re wrong then, given you can’t defend your wrong interpretation of it (which you would know is wrong if you had read more than 1 paragraph of the book!) 😂
Which this troll admits when sneering “They say you can [simplify first] when there is Addition or Subtraction inside the Brackets.”
Except when they sneer you must not do that, because there’s addition inside the brackets. 2(3*a+2*a)2 becomes 2(5*a)2, which gets a different answer, somehow. Or maybe it’s 2(3a+2a)2 becoming 2(5a)2 that’s different. One or the other is the SpEcIaL eXcEpTiOn to a rule they made up.
Weird how nobody else in the world has this problem. Almost like a convention that requires special cases is fucking stupid, and if people meant (2(n))2, they’d just write that.
Which this troll literally underlines when sneering about textbooks they don’t read: “A number next to anything in brackets means the contents of the brackets should be multiplied.”
Except when they insist distribution is totally different from multiplication… somehow. But if a product is one term and multiplying two things is a product and two things being multiplied is two terms, sure, fuck it, words don’t mean things.
I actually forgot the most obvious way in which Order of Operations is a set of conventions… Some countries say “BODMAS” (division then multiplication) whilst others say “PEMDAS” (multiplication then division)…
They’re grouped, being essentially the same operation, but inverted. Ditto for addition and subtraction. There’s not a convenient word that covers both directions, like how exponents / order are the same for positive and negative powers.
Convention is saying 1/ab is 1/(ab) instead of (1/a)b, while 1/a*b is indeed (1/a)b. The latter of which this troll would say is a syntax error, because juxtaposition after brackets is foreboden… despite modern textbook examples.
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: specifically I 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 (we generally used a dot for multiplication at this point). But at this point in our education, none of us remembered ever being taught this. I suspect what happened was that when being taught order of operations some years before, we simply never used the solidus and only used ÷ or fraction notation.
Anyway, if you have a correct understanding of what the order of operations really are (conventions) you can understand that these conventions all become a bit unwieldy when you have a very complex formula, and that it’s better to write mathematics as if there were no such convention in those cases, and provide brackets for disambiguation. Thus while you might write ab ÷ bc and reasonably expect everyone to understand you mean (ab)/(bc) not ((ab)/b)c (which is what the strict interpretation of PEMDAS would say!) because “bc” just visually creates a single thing, the same is not true of the expression ab ÷ bc(x-1)(y-1)·sin(b), even though bc(x-1)(y-1)·sin(b) is a single term, and so the latter should be written more clearly.
Because DumbMan doesn’t understand mathematical convention, he doesn’t understand that these things really depend on how they’re perceived, so is incapable of understanding such a way of working.
Anyway, looks like he’s gone to sleep again now, I wonder if he’ll pop up again in a couple of days, or if it’ll take him until someone else posts some BODMAS clickbait.
Personally I tend to bracket aggressively, because I’ve been repeatedly betrayed by compilers. One in particular applied the high priority of & (bitwise and) to the low-priority && (logical and), so if( 1 < 2 && 3 ) would always fail because 2 && 3 evaluates to 1.
That was the topic the first time I dealt with this dingus and their rules of maths!!! about a year ago. The post was several months old. They’ve never understood that some things are fundamental… and some things are made up. Some things are mutable. So even if their nonsense was widespread, we could say, that’s kinda stupid, we should do something else.
The dumbest argument I’ve ever suffered online was some dingdong convinced that “two times three” meant the quantity two, three times. Even though “two times” is right there, in the sentence. Even though “twice three” literally means “two times three.” Even though the song “Three Times A Lady” obviously does not mean the quantity three, ladyce. Not even that dipshit thought two times three-squared could be thirty-six.
b*c is the product of b and c.
Show me one textbook where a(b+c)2 gets an a2 term. Here’s four in a row that say you’re full of shit.
Nope! bc is the product of b and c - it’s right there in the textbook! 😂
Says person yet again who has proven they are full of shit about the definition of Terms 😂
The result of a multiplication operation is called a product.
Show me one textbook where a(b+c)2 gets an a2 term. Here’s four in a row that say you’re full of shit.
Now you’re getting it - axb=ab. axb is Multiplication of 2 Terms, ab is the single Product. It’s the reason that 8/2(1+3) and 8/2x(1+3) give different answers 🙄
I already gave you many that tell you a(b+c)=(ab+ac) Mr. Ostrich - which part of a(b+c)=(ab+ac) are you having trouble understanding?
Multiplying two things makes them one term.
“When a product involves a variable, it is customary to omit the symbol X of multiplication. Thus, 3 X n is written 3n and means three times n, and a X b is written ab and means a times b.” Modern Algebra: Structure And Method, page 36. Immediately before the definition you’re now lying about.
Fuck your non-sequitur. a(b+c)2 is a*(b+c)2, as backed up by - for example - these four math textbooks. No textbook will ever say it produces an a2 term. You made it up. You’re just full of shit.
You so nearly had it, look “two things”! Yes axb is 2 Terms being Multiplied to make them one 😂
Nope! Says exactly what I already said, and I have no idea why you think it says otherwise. Now read the next page, which tells you ab is one Term and doesn’t say that axb is 1 Term. 🙄 You’re proven wrong by the very textbook you’re quoting from! 😂
Says person trying to disprove a(b+c)=(ab+ac) by dragging a(bc)²=ab²c² to try and make a false equivalence argument 😂
No it isn’t! 😂 The first is one term, the second is two terms
Says Mr. Ostrich, still ignoring the dozens of textbooks I posted saying a(b+c)=(ab+ac)
No, it produces an ab term and an ac term, a(b+c)=(ab+ac) 🙄
Says Mr. Ostrich, now completely full of shit, still ignoring the dozens of textbooks I posted, including ones written before I was even born