💡𝚂𝗆𝖺𝗋𝗍𝗆𝖺𝗇 𝙰𝗉𝗉𝗌📱, smartmanapps@programming.dev

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” 🙄

Fuck where this started

I’ll take that as an admission that you’re wrong. Thanks for playing

P.S. show me where the squared is in…

you know, the actual topic, which you’re trying to avoid because you know you are wrong

So when you sneer that rules and notation are different, you don’t know what those words mean

says the actual person who doesn’t know what they mean 😂

when someone says ‘imagine a different notation,’ you literally can’t

Yes, you literally can’t go rewriting all the rules of Maths that we’ve had for centuries just because you randomly want to do something different now that we’ve decided to add Brackets to it 😂 Your whole argument is based on pretending that all the rules of Maths were all written at the same time 🤣🤣🤣

Show me any textbook that gets the answers you insist on

Pick any of them which show a(b+c)=(ab+ac) 🙄

Yes we could

No you can’t! 😂

it’s a theoretical different notation

In other words against the rules of Maths that we have, got it

does not break down, if you have to put add explicit brackets to 1/(ab)

But it does breakdown if you treat ab as axb 🙄

if you have to put add explicit brackets to 1/(ab)

We explicitly don’t have to*, because brackets not being needed *around a single Term* is *another* explicit rule of Maths, 🙄 being the way *everything* was written *before we started using Brackets in Maths*. We wrote things like aa/bb *without brackets for many centuries. i.e. they were added on after we had already defined all these other rules centuries before

Mathematics does break down when you insist a(b)2 gets an a2 term

No it doesn’t. If you meant ab², then you would just write ab². If you’ve written a(b)², then you mean (axb)²

for certain values of b

Got nothing to do with the values of b

It’s why you’ve had to invent exceptions to your made-up bullshit

says person still ignoring all these textbooks

pretend 2(8)2

There’s no pretending, It’s there in the textbooks

when simplified from 2(5+3)2 versus 2(8*1)2

You know it’s called The Distributive Property of *Multiplication over additon*, right? And that there’s no such thing as The Distributive Property of Multiplication *over Multiplication*, right? You’re just rehashing your old rubbish now

‘If a+b equals b+a, why is 1/a+b different from 1/b+a?’

Because they’re not identically equal 🙄 Welcome to you almost getting the point

ab means a*b

*means*, isn’t equal

That’s why 1/ab=1/(a*b)

Nope, it’s because ab==(axb) <== note the brackets duuuhhh!!! 😂

> But we could just as easily say 1/ab = (1/a)*b

No you can’t! 😂

because that distinction is only convention

Nope! An actual rule, as found not only in Maths textbooks (see above), but in all textbooks - Physics, Engineering, Chemistry, etc. - they all obey ab==(axb)

None of which excuses your horseshit belief that a(b)2

says person still ignoring all these textbooks

You sneered about 1/ab five minutes ago

Yet again, I have no idea what you’re talking about

Troll

says person who can’t back up anything they say about Terms with textbook references 🙄

That’s convention for notation

Nope, still rules

not a distinction between a*b and ab

says person who only read 2 sentences out of the book, the book which proves the statement wrong 😂

a*b and ab both being the product of a and b

Nope, only ab is the product, and you would already know that if you had read more than 2 sentences 😂

You have to slap 1/ in front of things and pretend that’s the subject

*"identically equal"*, which you claimed it means, means it will give the same answer regardless of what’s put in front of it. You claimed it was identical, I proved it wasn’t.

avoid these textbooks telling you

It kills you actually, but you didn’t read any of the parts which prove you are wrong 🙄just cherry pick a couple of sentences out of a whole chapter about order of operations 🙄

They are the same thing. They are one term

Nope! If they were both 1 term then they would give the same answer 🙄

1/ab=1/(axb)=1/(2x3)=1/6

1/axb=1/2x3=3/2=1.5

Welcome to why axb is not listed as a Term on Page 37, which if you had read all the pages up until that point, you would understand why it’s not 1 Term 🙄

You poor thing…

You don’t know what Maths textbooks say because you were too poor to go to school? I’m sorry to hear that

You can’t keep your own horseshit straight

No idea what you’re talking about, again, I’ve been saying the same thing the whole time

You insist they’re not the same. How?

Not difficult, I already did in another post. If a=2 and b=3…

1/ab=1/(axb)=1/(2x3)=1/6

1/axb=1/2x3=3/2=1.5

Convention saying 1/a(b+c)2 is 1/(a(b+c)2)

There’s no such convention, given it would violate The Distributive Law 🙄

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!) 😂

They’re more than equal

They’re not equal at all 🙄

If a=2, b=3…

1/ab=1/(2x3)=1/6

1/axb=1/2x3=3/2=1.5

It’s an identity, which you’d understand

Nope! axb==ab is an identity, which is NOT how it’s written, “illiterate fraud” as per your other comment

if you weren’t lying about being a teacher

says person who is lying about what the textbook says 🙄

Illiterate fraud

says person who thinks “means” and “equals” mean the same thing 😂

“a X b is written ab and means a times b.”

Notice that it doesn’t say equals, speaking of Illiterate fraud, as per your other 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? 😂

Care to comment?

Yep, read the whole chapter 🙄

a*b and ab are both the product of a and b,

Nope. Only ab is the product of a and b. axb is Multiplication of 2 terms

As explained by the textbook you chose

*If* you had read more than 2 sentences of it, you would discover that you *cannot* use axb to show *the product*, only ab 🙄

a*b2 is ab2

No it isn’t 😂 1/axb²=b²/a. 1/ab²=1/ab². Welcome to why we teach students about Terms 🙄

No textbook you’re grasping for contains your made-up exception

Law is the word you’re looking for, and I posted dozens of them here in this post which you keep ignoring Mr. Ostrich

They all show what I’m rubbing your nose in. You’re just full of shit.

Nope, they all show you are full of shit Mr. Ostrich. See previous link

Multiplying two things makes them one term

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