SmartmanApps

Juxtaposition is key to the bullshit you made up

Terms/Products is mathematical fact, as is The Distributive Law. Maths textbooks never use the word "juxtaposition".

You made a hundred comments in this thread about how 2*(8)2 is different from 2(8)2

That's right. 1/2(8)²=1/256, 1/2x8²=32, same difference as 8/2(1+3)=1 but 8/2x(1+3)=16

Here is a Maths textbook saying, you’re fucking wrong

Nope! It doesn't say that 1/a(b+c)=1/ax(b+c). You're making a false equivalence argument

Here’s another:

Question about solving an equation and not about solving an expression. False equivalence again.

You have harassed a dozen people specifically to insist that 6(ab)2 does not equal 6a2b2

Nope! I have never said that, which is why you're unable to quote me saying that. I said 6(a+b)² doesn't equal 6x(a+b)², same difference as 8/2(1+3)=1 but 8/2x(1+3)=16

You’ve sassed me specifically to say a variable can be zero, so 6(a+b) can be 6(a+0) can just be 6(a).

That's right

There is no out for you

Got no idea what you're talking about

This is what you’ve been saying

Yes

you’re just fucking wrong

No, you've come up with nothing other than False Equivalence arguments. You're taking an equation with exponents and no division, and trying to say the same rules apply to an expression with division and no exponents, even though we know that exponent rule is a special case anyway, even if there was an exponent in the expression, which there isn't. 🙄

about algebra, for children

For teenagers, who are taught The Distributive Law in Year 7

Then why doesn’t the juxtaposition of mc precede the square?

For starters stop calling it "juxtaposition" - it's a Product/Term. Second, as I already told you, c²=cc, so I don't know why you're still going on about it. I have no idea what your point is.

In your chosen book

You know I've quoted dozens of books, right?

you can’t say shit about it

Again I have no idea what you're talking about.

expands 6(ab)3 to 6(ab)(ab)(ab)

Ah, ok, NOW I see where you're getting confused. 6ab²=6abb, but 6(ab)²=6abab. Now spot the difference between 6ab and 6(a+b). Spoiler alert - the latter is a Factorised Term, where separate Terms have been Factorised into 1 term, the former isn't. 2 different scenario's, 2 different rules relating to Brackets, the former being a special case to differentiate between 6ab² and 6a²b²=6(ab)²

P.S.

is like arguing 1+2 is different from 2+1 because 8/1+2 is different from 8/2+1

this is correct - 2+1 is different from 1+2, but (1+2) is identically equal to (2+1) (notice how Brackets affect how it's evaluated? 😂) - but I had no idea what you meant by "throwing other numbers on there", so, again, I have no idea what your point is

But you understand E=mc2 does not mean E=(mxc)2

I already answered, and I have no idea what your point is.

This is you acknowledging that distribution and juxtaposition are only multiplication

Nope. It's me acknowledging they are both BRACKETS 🙄

E=mcc=(mxcxc) <== BRACKETS

a(b+c)=(ab+ac) <== BRACKETS

and only precede

everything 😂

Please find a calculator that gives a result different to 128 for the expression 2(3+5)². Should be easy, no?

Please find a Maths textbook that backs that up as being the correct answer. i.e. Exponents before Brackets. Should be easy, no? 🤣

This is your own source - and it says, juxtaposition is just multiplication

inside brackets. Don't leave out the inside brackets that they have specifically said you must use - "Parentheses must be introduced"! 🤣 BTW, this is a 19th Century textbook, from before they started calling them PRODUCTS 🙄

E=mc2 is E=(mc)2

No, it means E=mc² is E=mcc=(mxcxc)

Throwing other numbers on there

I have no idea what you're talking about 🙄

You realize a calculator doesn’t need to be a dedicated hardware, right?

You realise the calculator manufacturers have much more riding on their calculators being correct, right? 😂

Windows calculator, MacOS calculator, Android calculator, and all web-based calculators count as well.

Nope. Programmed by... programmers, who aren't earning any money from the calculator, and put the corresponding amount of effort into it.

You have no clue what you’re talking about.

says someone who just claimed that e-calcs count as much as actual, buy from a store, calculators 🤣

Alpha is a commercial product (with a free-tier as is usual nowadays)

Also well known to give wrong answers

uses the same engine as Mathematica, which is used extensively in industry, academic institutions

Nope! Academia warns against using it

None of your sources has exponents in them

In other words, you're admitting to trying to deflect from what's in Maths textbooks! 😂

that’s very convenient for your mistake of mixing up juxtaposition and your invented rule

It's the same rule, duh! Here it is in a textbook from more than 100 years ago when everything was still in brackets...

We've since then dropped the brackets from Factors which are a single Term. i.e. (a)(b+c) is now a(b+c), and (a)(b) is now ab. BTW would you like to explain how "my invented rule" appears in a textbook from more than 100 years ago? 🤣

Btw, ask yourself this as well: why would your invented interpretation of distributive law be necessary at all?

It's not invented, it's required as the reverse rule to Factorising, duh 😂 And I don't need to ask myself - as usual, all you have to do is look in Maths textbooks for the reason 😂

It brings no benefit to the table at all.

Being able to reverse the process of Factorising brings no benefit to the table?? 🤣

Juxtaposition arguably does

It's the same thing duh 🤣 ab=(a)(b), a(b+c)=(a)(b+c) notice how they are the same thing, expanding BRACKETS?? 🤣

Maybe you've forgotten about FOIL...

Now, think carefully about this, what happens when b=0, and what happens when d=0, you got it yet?? 🤣

because it allows shorter notation

AKA Factorised Terms and Products 😂

your invention doesn’t.

Again, explain how "my invention" appears in textbooks that are more than 100 years old. I'll wait 🤣

because it’s the only correct answer

Have you noticed yet that everything you think is correct is actually wrong as per Maths textbooks?? 🤣

I’ll consider your argument defeated

says person who has been comprehensively defeated by Maths textbooks and is now trying to deflect away from that 🤣

ignore further engagement from your part

I'll take that as an admission that you're wrong then, having been unable to debunk any Maths textbooks. See ya

Here you go

Yep, that's an old Casio model, Mr. "All modern calculators", proving yet again that you can't back up your own statements 😂

Please post a source that gives a different answer to this expression, I’ll wait.

No need to wait - just scroll back through this thread and look at all the sources I already posted 🙄

for big monetized products that’s no longer the case

You know none of the calculators you're referring to are commercial right? They're all free to use, and that tells you how much effort was put into them. The only e-calc I've ever seen give a correct answer is MathGPT, which is indeed commercial now (I tried it before it went commercial), so we have a commercial e-calc giving the correct answer, and all the free ones giving the wrong answer 😂

I’m in the software industry myself

So am I in case you didn't notice 😂

you have multiple downvotes in many posts

I've never seen more than 2 on any, Mr. Needs To Exaggerate Because Has No Actual Evidence Of Being Right 😂

you’re reading them wrong

says the person who is actually reading them wrong, who is unable to cite any example of me reading it wrong

clearly says a number next to a bracket means the content of the bracket must be multiplied with said number

the content of the bracket - you just quoted that yourself and still completely missed what that means 😂

Nowhere there does anybody speak of distribution taking precedence over other operations

BRACKETS has precedence over everything 😂 So here we have an example of you reading it wrong

nowhere in all sources I can find does it say so

And can you find any source which says Multiplication takes precedence over Brackets? No. Another example of you reading it wrong

Wonder why all screenshots you post use convoluted wording

They don't use "convoluted wording"! 🤣

"the contents OF THE BRACKETS should be multiplied"

"everything IN THE BRACKET should be multiplied by that number"

Yet another example of you reading it wrong 😂

wonder why you pop up everywhere arguing the same thing and keep getting downvoted?

The only person downvoting me is the person replying, whereas the others are getting downvoted by others as well 🙄

At some point you need to understand that if one old-ass calculator

My brand new Casio calculator gives the same answer! 😂 They all do now, except for Texas Instruments - the only one stubbornly still doing it wrongly

selective reading of cherry picked passages

Sure, I'm "cherry picking" the sections of textbooks about Distribution. Do you want me to post something random about a different topic? 😂 BTW, noted that you haven't come up with any textbooks that agree with you

all the proof you have

And it is indeed proof.

when all modern calculators

Agree with me (except for Texas Instruments)

algebra solvers

Written by programmers who have forgotten the rules of Maths, and as pointed out by many people in forums.

maybe it’s time to reconsider

And yet, here you are not reconsidering 🙄

Juxtaposition taking precedence over other multiplications I can understand

Because BRACKETS - ab=(axb) BY DEFINITION 😂

it’s an arguable point

And is also the exact same rule 🙄

Distribution being a mandatory step

There's a reason it's called The Distributive Law

taking precedence over even exponents is just silly

BRACKETS taking precedence over Exponents is "silly"?? 🤣🤣🤣

and unfortunately wrong

BRACKETS taking precedence over Exponents is "unfortunately wrong"?? 🤣🤣🤣

What I say to that is I’ve met plenty of teachers who are wrong about things in their own fields,

You think they're wrong you mean, person who is saying Brackets before Exponents is "wrong" 🤣🤣🤣

people defining the rules of all those algebra solvers aren’t the programmers,

Yes they are! That's why they give wrong answers 😂 I told one he was wrong and he went and fixed it, being the one who had programmed it that way 🙄

as you’d know if you looked a bit into product development.

I know they are because I have spoken directly to them 😂 Maybe try asking some yourself, before making completely wrong statements

It’s domain experts

No it isn't, as proven by personal experience. You know who uses domain experts? calculator manufacturers. 😂 They have considerably more riding on it being right or not.

who also define tests and receive feedback on the software’s performance and errors

You know there's a whole bunch of programmers who don't bother even defining tests to begin with, right??

I’m sure (lol) you’ve sent feedback to them

Yep!

they probably looked at it and decided you’re wrong

Except for the ones who did change it. The ones who claimed I was wrong, quoted Google - who have also been told they're wrong by many people -and not Maths textbooks 🙄

As well all have.

says person who did nothing of the sort, and lied about such things as "all modern calculators " being against me (they aren't, if you had actually tried some), Exponents having precedence over Brackets, etc.

Dude you’re not even hitting the right reply buttons anymore

Yes I am

Is that what you do when you’re drunk?

Is that why you think I'm hitting the wrong buttons?

It’d explain leading with ‘nope! I’ve said exactly what you accused me of.’

I have no idea what you're talking about. Maybe stop drinking

You keep pretending distribution is different from multiplication

No pretending - is is different - it's why you get different answers to 8/2(1+3) (Distribution) and 8/2x(1+3) (Multiplication) 😂

B 8/2(1+3)=8/(2+6)=8/8

E

DM 8/8=1

AS

B 8/2x(1+3)=8/2x4

E

DM 8/2x4=4x4=16

AS

That’s not Multiplication, it’s Distribution, a(b+c)=(ab+ac), a(b)=(axb).

That's right.

And then posting images that explicitly say the contents of the brackets should be multiplied

The "contents OF THE BRACKETS", done in the BRACKETS step , not the MULTIPLICATION step - there you go quoting proof that I'm correct! 😂

Or that they can be simplified first.

That's right, you can simplify then DISTRIBUTE, both part of the BRACKETS step, and your point is?

B 8/2(1+3)=8/2(4)=8/(2x4)=8/8

E

DM 8/8=1 <== same answer

AS

I am not playing dueling-sources with you

No, because you haven't got any 😂

your own sources call bullshit on what you keep hassling strangers about

says person failing to give a single example of that EVER happenning 😂

I'll take that as an admission of being wrong then. Thanks for playing

You’ve harassed a dozen people to say only 53+514

Nope! I've said a(b+c)=(ab+ac) is correct.

to the point you think 2(3+5)2 isn’t 2*82

You mean I know that, because it disobeys The Distributive Law 🙄 The expression you're looking for is 2x(3+5)², which is indeed not subject to Distribution, since the 2 is not next to the brackets.

If you’d stuck to one dogmatic answer

Instead I've stuck to one actual law of Maths, a(b+c)=(ab+ac).

But you’ve concisely proven

The Distributive Law, including c=0 🙄 Not sure why you would think c=0 is somehow an exception from a law

the harassment is the point

No, the rules of Maths is the point

when you can’t do algebra right

Says person who thinks c=0 is somehow an exception that isn't allowed,🙄but can't cite any textbook which says that

I think I know what you're missing - perhaps intentionally 🙄 - in a(b+c), c can be equal to 0. It can be any number, not just positive and negative, leaving us with a(b)=(axb), which is also what I've been saying all along (not sure how you missed it, other than to deliberately ignore it)

And what do you do with and and the b and then the a and the c?

BTW, there's no "the a and the b" and "the a and the c", there's ab and ac, which need to be added. If a=2, b=3, and c=4, we have 2(3+4)=(6+8)=14