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💡𝚂𝗆𝖺𝗋𝗍𝗆𝖺𝗇 𝙰𝗉𝗉𝗌📱

@ SmartmanApps @programming.dev

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26
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418
Joined
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  • So is 3xy

    That's right

    That doesn’t mean 3xy2 is 9y2x2.

    That's right. It means 3abb=(3xaxbxb)

    The power only applies to the last element

    Factor yes, hence the special rule about Brackets and Exponents that only applies in that context

    like how (8)22 only squares the 2

    It doesn't do anything, being an invalid syntax to follow brackets immediately with a number. You can do ab, a(b), but not (a)b

    not (6ab)(6ab)(6ab)

    Yep, as opposed to 6(a+b), which is (6a+6b)

    3(x+1)2 for x=-2 is 3, not 9

    No it isn't. See previous point. Do we have an a(b+c), yes we do. Do we have an a(bc)²? No we don't.

    2(x-b)2 has a 2b2 term

    No, it has a a(b-c) term, squared

    shut the fuck up

    says someone still trying to make the special case of Exponents and Brackets apply to a Factorised Term when it doesn't. 😂 I'll take that as your admission of being wrong about a(b+c)=ax(b+c) then. Thanks for playing

    For a=8, b=1, that’s 2*(81)(8*1).

    Only if you had defined it as such to begin with, otherwise the Brackets Exponents rule doesn't apply if you started out with 2(8)², which is different to 2(8²) and 2(ab)²

    ..and there's still no exponent in a(b+c) anyway, Mr. False Equivalence

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  • a=8, b=1, it’s the same thing

    No it isn't! 😂 8 is a single numerical factor. ab is a Product of 2 algebraic factors.

    False equivalence is you arguing about brackets and exponents

    Nope. I was talking about 1/a(b+c) the whole time, as the reason the Distributive Law exists, until you lot decided to drag exponents into it in a False Equivalence argument. I even posted a textbook that showed more than a century ago they were still writing the first set of Brackets. i.e. 1/(a)(b+c). i.e. It's the FOIL rule, (a+b)(c+d)=(ac+ad+bc+bd) where b=0, and these days we don't write (a)(b+c) anymore, we just write a(b+c), which is already a single Term, same as (a+b)(c+d) is a single term, thus doesn't need the brackets around the a to show it's a single Term.

    3(x-y) is a single term...

    This entire thing is about your lone-fool campaign

    Hilarious that all Maths textbooks, Maths teachers, and most calculators agree with me then, isn't it 😂

    insist 2(8)2 doesn’t mean 2*82,

    Again, you lot were the ones who dragged exponents into it in a False Equivalence argument to 1/a(b+c)

    I found four examples, across two centuries

    None of which relate to the actual original argument about 1/a(b+c)=1/(ab+ac) and not (b+c)/a

    You can’t pivot to pretending this is a division syntax issue

    I'm not pivoting, that was the original argument. 😂 The most popular memes are 8/2(2+2) and 6/2(1+2), and in this case they removed the Division to throw a curve-ball in there (note the people who failed to notice the difference initially). We know a(b+c)=(ab+ac), because it has to work when it follows a Division, 1/a(b+c)=1/(ab+ac). It's the same reason that 1/a²=1/(axa), and not 1/axa=a/a=1. It's the reason for the brackets in (ab+ac) and (axa), hence why it's done in the Brackets step (not the MULTIPLY step). It's you lot trying to pivot to arguments about exponents, because you are desperately trying to separate the a from a(b+c), so that it can be ax(b+c), and thus fall to the Multiply step instead of the Brackets step, but you cannot find any textbooks that say a(b+c)=ax(b+c) - they all say a(b+c)=(ab+ac) - so you're trying this desperate False Equivalence argument to separate the a by dragging exponents into it and invoking the special Brackets rule which only applies in certain circumstances, none of which apply to a(b+c) 😂

    2(8)2 is (2*8)2.

    That's right

    are you just full of shit?

    says the person making False Equivalence arguments. 🙄 Let me know when you find a textbook that says a(b+c)=ax(b+c), otherwise I'll take that as an admission of being wrong that you keep avoiding the actual original point that a(b+c) is a single Term, as per Maths textbooks

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  • That’s you saying it

    No it isn't! 😂 Spot the difference 1/2(8)²=1/256 vs.

    6(ab)2 does not equal 6a2b2

    You are unambiguously saying a(b)c somehow means (ab)c=ac bc

    Nope. Never said that either 🙄

    except when you try to nuh-uh at anyone pointing out that’s what you said

    Because that isn't what I said. See previous point 😂

    Where the fuck did 256 come from if that’s not exactly what you’re doing?

    From 2(8)², which isn't the same thing as 2(ab)² 🙄 The thing you want it to mean is 2(8²)

    snipping about terms I am quoting from a textbook you posted,

    Because you're on a completely different page and making False Equivalence arguments.

    you wanna pretend 2(x-b)2 isn’t precisely what you insist you’re talking about?

    No idea what you're talking about, again. 2(x-b)2 is most certainly different to 2(xb)2, no pretense needed. you're sure hung up on making these False Equivalence arguments.

    Show me any book where the equations agree with you

    Easy. You could've started with that and saved all this trouble. (you also would've found this if you'd bothered to read my thread that I linked to)...

    Thus, x(x-1) is a single term which is entirely in the denominator, consistent with what is taught in the early chapters of the book, which I have posted screenshots of several times.

    I’ve posted four examples to the contrary

    You've posted 4 False Equivalence arguments 🙄 If you don't understand what that means, it means proving that ab=axb does not prove that 1/ab=1/axb. In the former there is multiplication only, in the latter there is Division, hence False Equivalence in trying to say what applies to Multiplication also applies to Division

    all you’ve got is

    Pointing out that you're making a False Equivalence argument. You're taking examples where the special Exponent rule of Brackets applies, and trying to say that applies to expressions with no Exponents. It doesn't. 🙄 The Distributive Law always applies. The special exponent rule with Brackets only applies in certain circumstances. I already said this several posts back, and you're pretending to not know it's a special case, and make a False Equivalence argument to an expression that doesn't even have any exponents in it 😂

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  • 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

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  • 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

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  • 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 😂

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  • 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? 🤣

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  • 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 🙄

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  • 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

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  • 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 😂

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  • 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.

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  • 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

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  • 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

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  • 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)

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  • 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

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  • The first textbook only gets 5(17) by not doing what the second textbook says to do with 5(3+14)

    Because the first textbook is illustrating do brackets from the inside out, which the second textbook isn't doing (it only has one set of brackets, not nested brackets like the first one). They even tell you that right before the example. They still are both Distributing. You're also ignoring that they actually wrote 5[3+(14)], so they are resolving the inner brackets first, exactly as they said they were doing. 🙄 The 5 is outside the outermost brackets, and so they Distribute when they reach the outermost brackets. This is so not complicated - I don't know why you struggle with it so much 🙄

    First image says ‘always simplify inside,’ and shows that

    And then says to Distribute, and shows that 🙄 "A number next to anything in brackets means the contents of the brackets should be multiplied".

    Second image says ‘everything inside must be multiplied,’ and shows that

    Yep, that's right, same as I've been telling you the whole time 😂

    You’re such an incompetent troll that you proved yourself wrong within the same post

    Ah, no, you did, again - you even just quoted that the second one also says to Distribute! BWAHAHAHAHAHAHAHA! 😂 I'll remember that you just called yourself an incompetent troll going forward. 😂

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  • I’ve read everything you’ve posted

    You've read every textbook, and looked at the calculator answer? Yeah nah, you clearly haven't.

    you’re interpreting the texts in such a way that they support your flawed argument

    Says person who can't come up with any textbooks that support their argument. 😂 BTW if you had looked at the calculator, you would've seen it does it exactly as I have described - 6/2(1+2)=6/2(3)=6/(2x3)=6/6=1, not, you know, 6/2(1+2)=3(3)=9, which is your flawed argument

    conveniently ignoring what they’re actually saying, such as “if” statements

    Says person ignoring this "if" statement which says you literally must distribute if you want to remove the brackets.

    Even this textbook that you yourself posted goes against what you’re saying

    No it doesn't! 😂

    Notice something?

    Yes, you ignored the Distribution in the last step 😂 I have no idea what you think is significant about the first 2 steps, other than you were trying to draw attention away from the Distribution in the last step

    Here's another one (different authors) that does the same thing, which you would've seen if you had actually read all the textbooks I posted, but they explicitly spell out what they're doing as they're doing it...

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  • 5(17) means they didn’t distribute 5(3+14) into 53+514

    That's right, they Distributed the 5(17) into (5x17), and your point is?

    These textbooks unambiguously disagree

    With you, yes, and your point is?

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  • Or it was some random teacher

    Yeah, maybe. My Year 7 students, who have come fresh to me from Year 6, use BEDMAS, and I teach BEDMAS for consistency (I also think it's a better acronym anyway - think of a massive 4-poster bed to ingrain the idea of BED-MAS)...

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  • Like how the 5 in the first image isn’t?

    BWAHAHAHAHAHA! And how exactly do you think they got from 5(17) to 85 without distributing?? 🤣 Spoiler alert, this is what they actually did...

    5(17)=(5x17)=85

    They do that throughout the book, because they think it's so trivial to get from 5(17) to 85, that if you don't know how to do it without writing (5x17) first, then you have deeper problems than just not knowing how to Distribute 😂