SmartmanApps

My dude sit in a university lecture for math majors

You know I have a Masters in Maths, right? 🤣

Your school books arent gospel

Proofs are, and these things are very easy to prove 🙄

Wikipedia

isn't a Maths textbook 🙄 far out, did you learn English from Wikipedia too? You sure seem to have trouble understanding the words Maths textbook

You don’t trust Wikipedia?

The site that you just quoted which is proven wrong by Maths textbooks, THAT Wikipedia?? 🤣🤣🤣

you’ve yet to explain why notations like prefix and postfix dont need these “rules”.

Umm, they do need the rules! 😂

how could they only apply to certain notations?

They don't, they apply to all notations 🙄

Do you teach classes like this? “That’s not a product, it’s a multiplication”

Yep! And if you read more than 2 sentences out of the textbook you would know why 🙄

those are the same thing.

Says person who only read 2 sentences out of a whole chapter 🙄

Shouldn’t you, as a teacher, be explaining the difference, if you say there is one?

Yep, and it's right there in the textbook! 🙄

I’m starting to believe you don’t think they’re is one

So you think if a=2 and b=3, then...

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

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

Are somehow the same answer?? 😂 Which one is it then? 1/6 or 3/2?? 😂

You could argue that “product” refers to the result of the multiplication rather than the operation

Yep by definition!

there’s no sense in which the formula “a × b” does not refer to the result of multiplying a and b

There's no sense in which it does refer to the result you mean. The result of axb is ab. If a=2, b=3, axb=ab. 2x3=6, axb=2x3, ab=6

you don’t bother to even make such an argument

Says someone revealing that they haven't read a word I've said 🙄

you’re not actuality smart enough to understand the words you’re using

says someone who has just proven they haven't been reading them 🙄

It’s interesting, isn’t it, that you never provide any reference to your textbooks to back up these strange interpretations

Yes I did, and you only read 2 sentences out of it 😂

Where in your textbook does it say explicitly that ab is not a multiplication

Read on dude, read on, like I have been telling you the whole time. Oh wait, that would prove you were wrong. Oh, I wonder why you haven't read it... 🙄

It doesn’t, does it?

The page that you only read one sentence from 🙄

You’re keen to cite textbooks any time you can, but here you can’t

I already did and you only read 2 sentences out of it 🙄

You complain that people don’t read enough of the textbook, yet they read more than you ever refer to

says person who has repeatedly proven they've only read 2 sentences 🙄

In the other thread I said I wouldn’t continue unless you demonstrated your good faith by admitting to a simple verifiable fact that you got wrong

And I pointed out that in fact you got it wrong, and Mr. Hypocrite has failed to admit it 🙄

provide an actual textbook example where any of the disputed claims you make are explicitly made

Same one I already told you and you only read 2 sentences out of a whole chapter

there should be some textbook somewhere which says that mathematics would not work with different orders of operations

It's easy enough to prove yourself, like I did. Go ahead and try it out and let me know how you go.

you’ve never found a textbook which says anything like this

No, I was able to prove it myself 🙄

only things like “mathematicians have agreed”

Because it was proven 🙄

where’s your textbook which says that “a × b is not a term”?

Same textbook that you only read 2 sentences from

Where is the textbook that says 5(17) requires distribution?

It tells you tight there on the same page that you must remove all brackets, 🙄 which you also haven't admitted to being wrong about yet, surprise, surprise, surprise

Where’s your textbook which says “ab is a product, not multiplication”?

Same one you only read 2 sentences from

there is a textbook reference saying “ab means the same as a × b”,

And you stopped reading at that point didn't even finish the page, never mind the chapter 🙄 Just started making false claims (contradicted by same textbook) that "means" means "equals", instead of realising they have explicitly not said equals 🙄

so your mental contortions are not more authoritative

Says person who made the mental contortion that "means" means "equals" instead of reading the rest of the page

your ability to interpret maths textbooks is poor

says person who only read 2 sentences out of a whole chapter 🙄

we can have a productive discussion

when you decide to read more than 2 sentences 🙄

My prediction: you’ll present some implicit references

Wrong, as usual

try to argue they mean what you want

says person trying to argue that "means" means "equals" 🙄

You have declined to admit to a simple error you made

Not me, must be you! 😂

that early calculators lacked a stack,

They didn't 🙄

that basic four function calculators all did and still do

Have a stack, yes. I have one and it quite happily says that 2+3x4=14, something it can't do without putting "2+" on the stack while it does the 3x4 first 🙄

There’s no point having a discussion with someone so stubborn that they can’t admit a single mistake.

says someone too stubborn to admit making a mistake 🙄

I’m not sure whether you’re trying to wind people up or just a bit dim

Neither. I'm the one doing fact-checks with actual, you know, facts, like my simple calculator having a stack and correctly evaluating 2+3x4=14. It's the one I had in Primary school. The one in the first manual works the exact same way

this conversation is like trying to explain something to a particularly stuck-up dog

So maybe start listening to what I've been trying to tell you then. 🙄 It's all there in textbooks, if you just decide to read more than 2 sentences out of them.

The real tragedy is that you claim to be out there teaching kids this overcomplicated and false drivel.

Facts, as per the syllabus and Maths textbooks. Again, you need to read more than 2 sentences to discover that 🙄

only if you show that you’re not just a troll.

says person who has thus far refused to read more than 2 sentences out of the textbook 🙄

You can do that by admitting that you were wrong to say that all calculators have stacks

I wasn't wrong 🙄 The first manual that was linked to proved it. If you don't press the +/= button before the multiply then it will put the first part on the stack and evaluate the multiplication first, something it doesn't do if you press the +/= first to make it evaluate what you have typed in so far. 🙄 Every calculator will evaluate what you have typed in so far if you press the equals button, as pointed out in the first manual

because I showed you two examples

The first of which had a stack 🙄 the second of which was a chain calculator, designed to work that way. You're the one being dishonest

you were wrong

No I wasn't

that this screenshot

Which is a 1912 textbook. It also calls Factorising "Collections", and The Distributive Law "The Law of Distribution", and Products "Multiplication". Guess what? The language has changed a little in the last 110 years 🙄

it’s from Advanced Algebra by J.V. Collins, pg 6

Yep, published in 1912

On page 3, the concept of juxtaposition is introduced

And we now call them Products. 🙄 You can see them being called that in Modern Algebra, which was published in 1965. In fact, in Lennes' infamous 1917 letter, he used the word Product (but didn't understand, as shown by his letter), so the language had already changed then

admitting to an error on your part

There was no error. The language has changed since 1912 🙄

you actually are capable of admitting error

Of course I am. Doesn't mean I'm going to "admit" to an error when there is none 🙄

Fuck where this started

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

P.S. show me where the squared is in...

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

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

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

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

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

Show me any textbook that gets the answers you insist on

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

Yes we could

No you can't! 😂

it’s a theoretical different notation

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

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

But it does breakdown if you treat ab as axb 🙄

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

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

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

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

for certain values of b

Got nothing to do with the values of b

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

says person still ignoring all these textbooks

pretend 2(8)2

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

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

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

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

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

ab means a*b

means, isn't equal

That’s why 1/ab=1/(a*b)

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

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

No you can't! 😂

because that distinction is only convention

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

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

says person still ignoring all these textbooks

You sneered about 1/ab five minutes ago

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

Troll

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

That’s convention for notation

Nope, still rules

not a distinction between a*b and ab

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

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

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

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

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

avoid these textbooks telling you

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

They are the same thing. They are one term

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

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

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

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

You poor thing…

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

You can’t keep your own horseshit straight

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

You insist they’re not the same. How?

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

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

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

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 🙄