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💡𝚂𝗆𝖺𝗋𝗍𝗆𝖺𝗇 𝙰𝗉𝗉𝗌📱

@ SmartmanApps @programming.dev

Posts
26
Comments
418
Joined
3 yr. ago

  • Math is not a democracy

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  • having an agreed-upon convention absolutely matters for arriving at expected computational outcomes,

    Proven rules actually

    we call it a convention

    No we don't - the order of operations rules

    it’s not a “correct” vs “incorrect” principle of mathematics

    The rules most definitely are

    It’s just a rule we agreed upon to allow consistent results

    proven rules which are true whether you agree to it or not! 😂

    any good math educator will be clear on this

    Yep

    If you know the PEMDAS convention already, that’s good, since it’s by far the most common today

    No it isn't.

    But if you don’t yet, don’t worry

    As long as you know the rules then that's all that matters

  • Math is not a democracy

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  • You’ve completely not understood that order of operations is an arbitrary convention

    No, you've completely not understood that they are universal rules of Maths

    How did you decide to expand the definition of multiplication before evaluating the addition? Convention

    The definition of Multiplication as being repeated addition

    You can’t write 2 + 2 ÷ 2 like this

    Yes you can

    so how are you gonna decide whether to decide to divide or add first?

    The rules of Maths, which says Division must be before Addition

  • Math is not a democracy

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  • PEMDAS isn’t obvious to “common people”?

    Everyone is taught the rules of Maths

    If “×” means “groups of,”

    It means repeated addition actually

    “2+2×4” means “two plus two groups of four”

    No, it means 2+2+2+2+2

    Sure the order of operations could be arbitrarily different

    No they can't

    I feel like we settled on that order because it simply makes more sense intuitively

    It's because Multiplication is defined as repeated addition, so if you don't do it before addition you get wrong answers

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  • Your obviously is only a convention

    Nope. Rules of Maths

    it would have to have different order or parentheses or both.

    Neither. Multiplication is always before Addition, hence "obviously"

    Of course everything in math is convention

    Nope. The vast majority of it is proven rules

    2+(2*4) is more obvious to common people

    Weird then how many people were able to get this right without brackets for centuries before we started using brackets in Maths (which we've only had for 300 years)

  • Math is not a democracy

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  • The order of operations is different between conventional written maths, calculators, reverse polish notation, python, etc.

    The notation might be different, but the rules are universal

  • Math is not a democracy

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  • it’s just about convention aka how to communicate math

    They're rules actually.

    The author didn’t make themselves clear enough

    Yes they did, someone screwed up the answers, just like in this book...

    misunderstand what calculation they mean

    There's only 1 possible answer to it.

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  • That’s normal for multiple choice

    No it isn't.

    sometimes all the answers are correct

    Not in multiple choice they aren't. At best you might have "D) All of the above" if there's genuinely more than 1 answer

    We can assume

    Someone screwed up somewhere, and there will be lots of complaints from students. Despite it being "you only had 1 job", proofreaders still miss things sometimes...

  • Math is not a democracy

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  • different places teach different conventions

    But they all teach the same rules

    some places say that PEDMAS is a very strict order

    Which is totally fine and works

    Other places say that it is PE D|M A|S,

    Which is also totally fine and works

    even in this post, say it’s PEMDAS

    Also totally fine and works

    it’s simply a matter of if the people talking agree on the convention to use

    No-one has to agree on any convention - they can use whatever they want and as long as they obey the rules it will work

    can’t agree on

    Educated people agree that which convention you use doesn't matter.

  • Math is not a democracy

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  • Nothing about math is real

    You spelt "everything" wrong

    Every single thing about it is abstract

    Representing something real underneath in every case - 1+1=2 can refer to apples, eggs, cardboard boxes, anything at all.

  • Math is not a democracy

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  • PEMDAS isn’t even real

    Yes it is

    It’s something we made up

    No it isn't. They are proven rules of Maths arising from the definitions of the operators to begin with.

    Creating fake problems by inserting ambiguity is ridiculous

    There's no ambiguity in the order of operations rules

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  • Then you’re just a crank who lies to thirteen-year-olds about some bullshit you made up.

    Weird then that's in in Maths textbooks isn't it 😂

    Both 2(8+0)2 and 2(8*1)2

    Says another person who can't tell the difference between a(b+c) and a(bc) 🙄

    Nobody but you has this problem

    Knowing how to read Maths textbooks is a problem?? 😂 I can assure you that all my students have this same "problem"

    Real math doesn’t work differently based on how you got there

    It does if you have different expressions, such as 8/2(1+3) and 8/2x(1+3)

    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

    Different expressions, different order of evaluation, same rules of Maths (both following BEDMAS here) resulting in the different evaluations of the different expressions 🙄

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  • We can see the Acrobat window in those scans you found online.

    ...and the ones that came with the textbook, and not in the photo's 😂

    You think 2(8)2 is 128 if that’s simplified from 2(8+0)2… but 256 if it’s simplified from 2(8*1)2. In short: no

    says person who can't tell the difference between a(b+c) and a(bc) 😂

    I think you’re about fifteen years old. You had an unpleasant teacher who belittled you, and you’ve identified with the aggressor. Your whole online persona is posturing to always be smarterer than everybody else

    #EveryAccusationIsAConfession

    Wolfram fucking Alpha is wrong about basic algebra

    Which is an established fact

    Faced with a contradiction that requires you to insist (8*1) ≠ (8+0)

    again says person who can't tell the difference between a(b+c) and a(bc) 😂

    The word you should be looking for is, “oops.”

    yet again says person who can't tell the difference between a(b+c) and a(bc) 😂

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  • Don’t move the goalposts

    I didn't. You're the one who has been desperately trying to make a False Equivalence argument between a(b+c) and a(bc)² 🙄

    I’ve posted textbooks showing that “solving brackets” only applies to the inside,

    No you haven't. A college refresher isn't a Maths textbook, and I already pointed out to you that they don't mention The Distributive Law at all, unlike, you know, high school Maths textbooks 🙄

    distribution is part of multiplication

    And the high school Maths textbooks I posted prove you are wrong about that 🙄

    and optional

    And the high school Maths textbooks I posted prove you are wrong about that too, 🙄 unless you think "optional" is a valid interpretation of what "must" means 😂

    You’ve said yourself your magic rule is taught in highschool,

    Yep

    so a refresher course in college would never ignore it

    And yet you proved that they did in fact forget about it 🙄

    Now instead of giving weak excuses

    they say to person who has been backed up by every textbook they posted so far 😂

    provide your part of the proof.

    Just scroll back dude - they're all still there, like here for example.

    And I’m not talking about multiplication

    Well that'll be a nice change then 😂

    I want to see anywhere where a distribution is given precedence over an exponent

    Because you are hell bent on making a False Equivalence argument between a(b+c) and a(bc)². I don't care dude. there is no exponent in the meme. I'll take that as an admission that you are wrong about a(b+c) then.

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  • PDFs found online

    Nope! If you looked more carefully you'll find some of them are photo's and scans. You also seem to be forgetting that every modern textbook comes with a PDF as well 🙄

    From which you are ignoring counterexamples using a(b+c)n. Fraud

    says the actual fraud who keeps ignoring that there is no exponent in a(b+c) 😂

    Go ahead and tell me how you would explain what 3(x+y) means without referring to Multiplication?

    Your own spammed screenshots say 3 gets multiplied

    So in other words, you weren't able to. Also, it doesn't say that - well done on missing the point for a third time in a row 😂

    There is no special case

    So you think 2(3x4x5)=(2x3x2x4x2x5) is totally fine? BWAHAHAHAHAHAHAAHA 😂😂😂

    You made it up

    Weird then that it's in Maths textbooks isn't it, that 2(3x4x5) is in fact only equal to 2(60)? 😂

    does it just mean 8?

    says person showing they don't know the difference in meaning between "means" and "equals" 😂

    so 2(8+0)2 is the same as 2(8)2

    Yep.

    The latter is the next step in simplifying the former

    Yep.

    You’ve admitted simplifying first is valid

    Yep.

    when your nose was rubbed in your own found PDFs doing exactly that

    Nope! When you finally discovered that they were both valid, even though only a couple of textbooks I posted specifically said to Distribute first. We in fact teach students to simplify before Distributing - less working out, less mistakes with signs.

    You don’t have an opinion

    That's right, just facts, as per Maths textbooks 😂

    You make no claim, anymore

    a(b+c)=(ab+ac), same thing I've been saying the whole time

    All you have left are derision and emojis

    and facts

    You’ve admitted 2(8*1)2 means 2(8)(8)

    Nope! Never said anything of the sort, liar. I have said the whole time that Multiplication is a special case, to which you claimed there was no special case.

    insist that’s different from 2(8)2 because…

    No Multiplication. It's not complicated 🙄

    You cannot explain it even now

    I already did. Not my fault you don't understand the difference between Addition and Multiplication 😂

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  • Your bullshit hit max comment depth.

    That's hilarious that you're calling textbooks "bullshit" 🤣🤣🤣 BTW there's nothing preventing you from addressing comments made in a different post to the one you're replying to, 🙄 and yet, yet again, you didn't. Did you work out yet why we don't write (a+b)c? It's all in the post you're avoiding.

    So when you said 2(8)2 is 256, you were wrong

    Nope. 2(8*1)² has a Multiplication inside the Brackets, so The Distributive Law does not apply, 2(8)² doesn't have Multiplication in it, so The Distributive Law does apply. As I've already said repeatedly, if you wanted 2x8², then you could've just written 2x8². If you've written 2(8) rather then 2x8, then you are saying this is a Product, not a Multiplication.

    Otherwise - walk me through how 2(8*1)2, 2(8+0)2, and 2(8)2 aren’t equal, alleged math teacher.

    I already did multiple times. The first one has Multiplication in it, the other two don't. Multiplication (and Division) is the special case where The Distributive Law does not apply, because you cannot Distribute over Multiplication, only Addition (and Subtraction)

    alleged math teacher.

    who mysteriously owns dozens of Maths textbooks, many of which quoted in the post you're avoiding 😂

    None of them have said a(b+c)=ax(b+c)

    “3(x+y) means 3*(x+y).”

    Yep, doesn't say equals, exactly as I said 🙄 Congratulations on missing the point a second time in a row. You wanna go for three?

    “It depends on what the definition of is, is,”

    You think "means" and "equals" are the same word?? BWAHAHAHAHAHAHA! 🤣🤣🤣 You know the language has to get dumbed down to Year 7 level, right? And you're still missing the point, right? 😂 Go ahead and tell me how you would explain what 3(x+y) means without referring to Multiplication? I'll wait. BTW I'll point out yet again That the questions on Page 282, answers on Page 577, prove I am the one interpreting this right. Maths teacher understands Maths textbook language better than someone who isn't a Maths teacher. Who woulda thought?? 😂

    says someone definitely not trapped in a contradiction

    Yep, I'm definitely not trapped in a contradiction. 🤣🤣🤣 Look at the questions on Page 282, answers on Page 577, and then ask yourself what you think they meant when they said means, 😂and not equals. There is definitely a specific reason they did not say equals

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  • Firstly, it's hilarious that you've gone back to a previous comment, thus ignoring the dozen textbook references I posted 😂

    That would mean 2(8*1)2 is 128

    That's right, because we don't Distribute over Multiplication (and Division), only Addition and Subtraction (it's right there in the Property's name - The Distributive Property of Multiplication over Addition). Welcome to you proving why a(bc)² is a special case 😂 I've been telling you this whole time that a(b+c) and a(bc) aren't the same, and you finally stumbled on why they aren't the same 😂

    You are the one saying it’s not 2a2b2,

    No I'm not. I never said that, liar. I've been telling you the whole time that it is a special case 🙄 (upon which you claimed there was no special case)

    because you think it’s 22a2b2,

    No I don't. That's why you can't quote me ever saying that 🙄

    exponents are where you are blatantly full of shit

    and there are no exponents in a(b+c) and all this stuff about exponents is you being blatantly full of shit 🙄

    Source: your ass.

    No, this meme

    Notice that there are no exponents? 😂

    Every published example disagrees

    says person who came back to this post to avoid this post which is full of published examples that agree with me - weird that 😂

    that up-to-date Maths textbook must be wrong

    And I also pointed out why that was wrong here. i.e. the post that you have avoided replying to 😂

    You alone are correct on this accursed Earth

    No, all textbooks as well, except those which are using the old-fashioned and wrong syntax of (a+b)c, not to mention most calculators as well (only Texas Instruments is still doing it wrongly).

    Page 31 of the PDF… right

    Before the pages I already posted in the post that you are avoiding replying to 😂

    where you’ve dishonestly twisted the “expanding brackets” text. Next page: “3(x+y) means 3*(x+y).”

    means not equals, Mr. Person Who Is Actually Dishonestly Twisting The Words, as proven by the exercises on Page 282, answers on Page 577, which are also in the post that you are avoiding replying to 😂

    Page 129 of that PDF, exercise 5, question 14: simplify 2(e4)2. The answer on PDF page 414 is 2e8

    That's right

    Your bullshit would say 4e8.

    Nope. Been telling you the whole time that is a special case, upon which you claimed there was no such special case 😂

    if you somehow need further proof of how this actually works

    No, I don't, it's still a False Equivalence argument 🙄 But if you wanna waste your time on an irrelevant point (which you seem determined to do), go ahead, don't let me stop you, but that's an admission that you are wrong about a(b+c)

    Damn dude, that’s five textbooks you chose saying you’re full of shit

    Nope! None of them have said a(b+c)=ax(b+c), they have all said a(b+c)=(ab+ac), which is why you're avoiding replying to the post of mine which quotes them all 🙄

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  • This is a college textbook, and that explains how to solve it

    It's a college refresher course on high school Maths. They also forgot to cover The Distributive Law, which is not unusual given college Professors don't actually teach high school Maths.

    Another example

    From the same refresher course 🙄

    Alternatively, here is another example

    Which also doesn't cover The Distributive Law, which isn't surprising given that chapter isn't even about order of operations! 😂

    In case you can’t find the correct part

    Still not about a(b+c). You lot are investing so much effort into such an obvious False Equivalence argument it's hilarious! 😂

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  • There is no special case

    So you're saying there no such rule as 2(ab)²=2a²b². Got it. you're admitting you're wrong then 😂

    You made it up by confusing yourself about “dismissing a bracket.”

    Says person who just claimed there's no such rule as the one they've been making the basis of their wrong claims 😂

    To everyone else in the world, brackets are just another term

    That's right. That's why you cannot separate the coefficient from it 😂

    Several of the textbooks I’ve linked will freely juxtapose brackets and variables before or after

    Several of your textbooks are outdated then

    because it makes no difference

    So is (2+3)-4 equal to -20 or 1? I'll wait

    And that’s as factorization.

    Wrong Factorisation. ab+ac=a(b+c)

    This Maths textbook you plainly didn’t read was published this decade

    And yet, is still wrong

    Still waiting on any book ever that demonstrates your special bullshit

    You were the one who just said there's no such special rule as 2(ab)²=2a²b² 😂

    7bx with b=(m+n) becomes

    7x(m+n)

    and it’s the same damn thing

    No, 7(m+n)x is invalid syntax due to ambiguity when x is negative.

    Splitting it like 7xm+7xn is no different from splitting (m+n)/7 into m/7+n/7

    That's right. I never said otherwise.

    Brackets only happen first because they have to be reduced to a single term

    They happen first because they already are a single Term...

    A bracket with one number is not “unsolved”

    Yes it is! If you haven't solved Brackets then you cannot progress onto Exponents.

    it’s one number

    Exactly! That's why you cannot separate the a from (b+c) - it's all ONE NUMBER 😂

    Squaring a bracket with one number is squaring that number.

    if it has been written as 2(ab)², not if it has been written a(b+c)². Also, again, there is no exponent in a(b+c), so that rule doesn't apply anyway 😂

    Hence: 6(ab)3

    6(ab)² <== note: not 6(a+b)², nor 6(a+b) for that matter. You're still desperately trying to make a False Equivalence argument 😂

    It has a (b-c) term

    No it doesn't. a(b-c) is one term

    The base of an exponent is whatever’s in the symbols of inclusion.

    And there's no exponent in a(b+c) 🙄

    See page 121 of 696

    See page 37

    Also see page 282 and answers on page 577. x(x-1) is one term, as taught on page 37

    In an expression such as 3a2,

    3a² <== note: not 3(a+b), which has no exponent 🙄 It's hilarious how much effort you're putting into such an obvious False Equivalence argument 😂

    You will never find a published example that makes an exception for distribution first

    BWAHAHAHAHAHAHAH! I see you haven't read ANY of the sources I've posted so far then 🤣

    refers to both 8x7 and 8(7) as “symbols of multiplication.”

    Yep, present tense and past tense, since 8(7) is a Product, a number, as per Pages 36 and 37, which you're still conveniently ignoring, despite me having posted it multiple times

    It’s just multiplication

    Nope. 8(7) is a Product, a single Term, as per Pages 36 and 37. You won't find them writing 8(7)=8x7 anywhere in the whole book, always 8(7)=56, because it's a number

    It’s not special, you crank

    Yes it is, as per the textbook you're quoting from! 🤣

    8(7) is a product identical to 8x7

    Nope! 8(7) is a number, as per the textbook you are - selectively - quoting from 😂 8(7) is one term, 8x7 is two terms, as per Page 37

    Squaring either factor only squares that factor

    Where there are multiple pronumeral factors and you need the brackets to specify which factors the square is applying to, which, again, none of which applies to a(b+c) anyway Mr. False Equivalence 😂

    Variables don’t work differently when you know what they are.

    They're not variables if you know what they are - they are constants, literally a number as per pages 36 and 37

    b=1 is not somehow an exception that isn’t allowed, remember?

    That's right. a(1+c)=(a+ac), and you're point is??

    There’s an exponent in 2(8)2

    and no Pronumerals, and 2(8) is a number as per pages 36 and 37. 🙄And if you had read those pages, you would find it also tells you why you cannot write 2(8) as 28 (in case it's not obvious). if you want 2x8², then you can just write 2x8² 🙄

    it concisely demonstrates to anyone who passed high school that you can’t do algebra

    says someone who is trying to say that a rule about exponents applies to expressions without exponents 🤣

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  • Solving brackets does not include forced distribution

    Yes it does! 😂

    Juxtaposition means multiplication,

    No, it doesn't. A Product is the result of Multiplication. If a=2 and b=3, axb=ab, 2x3=6, axb=2x3, ab=6. 3(x-y) is 1 term, 3x-3y is 2 terms...

    as such, 2(3+5)² is the same as 2*(3+5)²

    No it isn't. 2(3+5)² is 1 term, 2x(3+5)² is 2 terms

    so once the brackets result in 8

    They don't - you still have an undistributed coefficient, 2(8)

    they’re solved

    Not until you've Distributed and Simplified they aren't

    Distribution needs to happen if you want to remove the brackets

    if you want to remove the brackets, YES, that's what the Brackets step is for, duh! 😂 The textbook above says to Distribute first, then Simplify.

    while there are still multiple terms inside

    As in 2(8)=(2x8) and 2(3+5)=(6+10) is multiple Terms inside 😂

    it’s still a part of the multiplication

    Nope! The Brackets step, duh 😂 You cannot progress until all Brackets have been removed

    which has higher priority.

    It doesn't have a higher priority than Brackets! 🤣

    Your whole argument hangs on the misinterpretation of textbooks

    says person who can't cite any textbooks that agree with them, so their whole argument hangs on all Maths textbooks are wrong but can't say why, 😂 wrongly calls Products "Multiplication", and claimed that I invented a rule that is in an 1898 textbook! 🤣 And has also failed to come up with any alterative "interpretations" of "must" and "Brackets" that don't mean, you know, must and brackets 😂

    This is what it feels like to argue against Bible fanatics

    says the Bible fanatic, who in this case can't even show me what it says in The Bible (Maths textbooks) that agrees with them 😂

    provide me a solver that says 2(3+5)² is 256 and you’ve won, it’s so easy no?

    provide me a Maths textbook that says 8/2(1+3)=16 and you’ve won, it’s so easy no? 🤣

    And in the meantime, here's one saying it's 1, because x(x-1) is a single Term...

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  • Nobody has argued exponents should go before brackets

    You did! 😂 You said 2(3+5)²=2(8)²=2(64), which is doing the Exponent when there are still unsolved Brackets 😂

    I’m saying distribution being mandatory is an invented rule from your part

    You still haven't explained how it's in 19th Century textbooks if I "made it up"! 😂

    If you don't remember Roman Numerals either, that's 1898

    No wonder you can’t produce such a simple request.

    says person who still hasn't produced a single textbook that supports anything that they say, and it's such a simple request 😂