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💡𝚂𝗆𝖺𝗋𝗍𝗆𝖺𝗇 𝙰𝗉𝗉𝗌📱

@ SmartmanApps @programming.dev

Posts
26
Comments
418
Joined
3 yr. ago

  • A fake Facebook event disguised as a math problem has been one of its top posts for 6 months

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  • But +, -, *, and / are all binary operators?

    No, only multiply and divide are. 2+3 is really +2+3, but we don't write the first plus usually (on the other hand we do always write the minus if it starts with one).

    As far as I know, the only reason multiplication and division come first is that we’ve all agreed to it.

    No, they come first because you get wrong answers if you don't do them first. e.g. 2+3x4=14, not 20. All the rules of Maths exist to make sure you get correct answers. Multiplication is defined as repeated addition - 3x4=3+3+3+3 - hence wrong answers if you do the addition first (just changed the multiplicand, and hence the answer). Ditto for exponents, which are defined as repeated multiplication, a2=(axa). Order of operations is the process of reducing everything down to adds and subtracts on a number line. 32=3x3=3+3+3

  • A fake Facebook event disguised as a math problem has been one of its top posts for 6 months

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  • I’m defining the division operation, not the quotient

    Yep, the quotient is the result of Division. It's right there in the definition in Euler. Dividend / Divisor = Quotient <= no reference to multiplication anywhere

    Yes, the quotient is obtained by dividing… Now define dividing.

    You not able to read the direct quote from Euler defining Division? Doesn't mention Multiplication at all.

    The actual is the one I gave

    No, you gave an alternative (and also you gave no citation for it anyway - just something you made up by the look of it). The actual definition is in Euler.

    That’s why I said they are also defined based on a multiplication

    Again, emphasis on "alternative", not actual.

    implying the non-alternative one (understand, the actual one) was the one I gave

    The one you gave bears no resemblance at all to what is in Euler, nor was given with a citation.

    Feel free to send your entire Euler document rather than screenshotting the one part

    The name of the PDF is in the top-left. Not too observant I see

    you thought makes you right

    That's the one and only actual definition of Division. Not sure what you think is in the rest of the book, but he doesn't spend the whole time talking about Division, but feel free to go ahead and download the whole thing and read it from cover to cover to be sure! 😂

    Note, by the way, that Euler isn’t the only mathematician who contributed to the modern definitions in algebra and arithmetics.

    And none of the definitions you have given have come from a Mathematician. Saying "most professions", and the lack of a citation, was a dead giveaway! 😂

  • A fake Facebook event disguised as a math problem has been one of its top posts for 6 months

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  • Yes, it is

    No it isn't.

    The division of a by b in the set of real numbers and the set of rational numbers (which are, de facto, the default sets used in most professions) is defined as the multiplication of a by the multiplicative inverse of b

    No it isn't. The Quotient is defined as the number obtained when you divide the Dividend by the Divisor. Here it is straight out of Euler...

    Alternative definitions are also based on a multiplication

    Emphasis on "alternative", not actual.

  • A fake Facebook event disguised as a math problem has been one of its top posts for 6 months

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  • A fake Facebook event disguised as a math problem has been one of its top posts for 6 months

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  • Another common issue is thinking “parentheses go first”

    There's no "think" - it's an absolute rule.

    then beginning by solving the operation beside them

    a(b) isn't an operation - it's a Product. a(b)=(axb) per The Distributive Law.

    (mostly multiplication)

    NOT Multiplication, a Product/Term.

    The point being that what’s inside the parentheses goes first, not what’s beside them

    Nope, it's the WHOLE Bracketed Term. a/bxc=ac/b, but a/b( c )=a/(bxc). Inside is only a "rule" in Elementary School, when there isn't ANYTHING next to them (students aren't taught this until High School, in Algebra), and it's not even really a rule then, it's just that there isn't anything ELSE involved in the Brackets step than what is inside (since they're never given anything on the outside).

  • A fake Facebook event disguised as a math problem has been one of its top posts for 6 months

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  • Oh, but of course the statement changes if you add parentheses

    It sure does, but they don't seem to understand that.

  • A fake Facebook event disguised as a math problem has been one of its top posts for 6 months

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  • Except it does matter

    No it doesn't. You disobeying the rules and getting lots of wrong answers in your examples doesn't change that.

    I left some examples for another post with multiplication and division

    Which you did wrong.

    I’ll give you some addition and subtraction to see order matter with those operations as well

    And I'll show you it doesn't matter when you do it correctly

    Subtraction first: 1 + (2 - 3) + 4 1 + (-1) + 4 = 4

    Nope. Right answer for wrong reason - you only co-incidentally got the answer right. -3+1+2+4=-3+7=4

    Right to left: 1 + (2 - (3 + 4)) 1 + (2 - 7) 1 + (-5) = -4

    Nope. 4-3+2+1=1+2+1=3+1=4

    Edit: You can argue that, for example, the addition first could be (1 + 2) + (-3 + 4)

    Or you could just do it correctly in the first place, always obeying Left Associativity and never adding Brackets

    in my opinion that’s another ambiguous case

    There aren't ANY ambiguous cases. In every case it's equal to 4. If you didn't get 4, then you made a mistake and got a wrong answer.

  • A fake Facebook event disguised as a math problem has been one of its top posts for 6 months

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  • Addition first: 9-4=5

    Nope. Addition first is 9+3-1=12-1=11. You did 9-(1+3), incorrectly adding brackets and changing the answer (thus a wrong answer)

  • A fake Facebook event disguised as a math problem has been one of its top posts for 6 months

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  • The solution accepted anywhere but in the US school system range from “Bloody use parenthesis, then” over “Why is there more than one division in this formula why didn’t you re-arrange everything to be less confusing” to “50 Hertz, in base units, are 50s-1”.

    No, the solution is learn the rules of Maths. You can find them in Maths textbooks, even in U.S. Maths textbooks.

    so no actual mathematician, or other people using maths in earnest, use that kind of notation.

    Yes we do, and it's what we teach students to do.

  • A fake Facebook event disguised as a math problem has been one of its top posts for 6 months

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  • It’s so we don’t have to spam brackets everywhere

    No it isn't. The order of operations rules were around for several centuries before we even started using Brackets in Maths.

    ((((((9+2)-1)+6)-4)+7)-3)+5

    It was literally never written like that

    we only need parentheses when we want to deviate from the norm

    That has always been the case

  • A fake Facebook event disguised as a math problem has been one of its top posts for 6 months

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  • 100% with you. “Left to right” as far as I can tell only exists to make otherwise “unsolvable” problems a kind of official solution

    It's not a rule, it's a convention, and it exists so as to avoid making mistakes with signs, mistakes you made in almost every example you gave where you disobeyed left to right.

  • A fake Facebook event disguised as a math problem has been one of its top posts for 6 months

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  • until the ambiguity is removed

    There isn't any ambiguity.

    all those answers are correct

    No, only 1 answer is correct, and all the others are wrong.

    Until the author gives me clarity then that sentence has multiple meanings. With math

    Maths isn't English and doesn't have multiple meanings. It has rules. Obey the rules and you always get the right answer.

    it doesn’t click for people that the equation is incomplete.

    It isn't incomplete.

  • A fake Facebook event disguised as a math problem has been one of its top posts for 6 months

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  • I stand corrected

    No, you weren't. Most of their answers were wrong. You were right. See my reply. 4 is the only correct answer, and if you don't get 4 then you did something wrong, as they did repeatedly (kept adding brackets and thus changing the Associativity).

  • A fake Facebook event disguised as a math problem has been one of its top posts for 6 months

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  • Right to left:

    6 * (4 / (2 * (3 / 9)))

    Nope! 6 × 4 ÷ 2 × 3 ÷ 9 =4 right to left is 6 ÷ 9 x 3 ÷ 2 × 4 =4. You disobeyed the rule of Left Associativity, and your answer is wrong

    Multiplication first: (6 * 4) / (2 * 3) / 9

    Also nope. Multiplication first is 6 x 4 x 3 ÷ 2 ÷ 9 =4

    Left first: (24 / 6) / 9

    Still nope. 6 × 4 x 3 ÷ 2 ÷ 9 =4

    Right side first: 24 / (6 / 9)

    Still nope. 6 × 4 x 3 ÷ 9 ÷ 2 =4

    And finally division first: 6 * (4 / 2) * (3 / 9)

    And finally still nope. 6 ÷ 9 ÷ 2 x 4 x 3 =4

    Hint: note that I never once added any brackets. You did, hence your multiple wrong answers.

    It’s ambiguous which one of these is correct

    No it isn't. Only 4 is correct, as I have just shown repeatedly.

    Hence the best method we have for “correct” is left to right

    It's because students don't make mistakes with signs if you don't change the order. I just showed you can still get the correct answer with different orders, but you have to make sure you obey Left Associativity at every step.

  • A fake Facebook event disguised as a math problem has been one of its top posts for 6 months

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  • The issue normally with these “trick” questions

    There's no "trick" - it's a straight-out test of Maths knowledge.

    the ambiguous nature of that division sign

    Nothing ambiguous about it. The Term on the left divided by the Term on the right.

    A common mistake is to think division is prioritised above multiplication

    It's not a mistake. You can do them in any order you want.

    when it actually has the same priority

    Which means you can do them in any order

  • A fake Facebook event disguised as a math problem has been one of its top posts for 6 months

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  • So order of operations is hard?

    Not for students it isn't. Adults who've forgotten the rules on the other hand...

  • A fake Facebook event disguised as a math problem has been one of its top posts for 6 months

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  • Hey, this is Presh Talwalkar

    Person who has forgotten about The Distributive Law and lied about 1917.

    Discussion of a brief history of this viral math problem

    Including lying about 1917

    Ultimately followed by brief discussion on the order of operations

    But forgets about Terms and The Distributive Law.

    And that’s the answer

    Now watch his other ones, where he screws it up royally. Dude has no idea how to handle brackets. Should be avoided at all costs.

  • A fake Facebook event disguised as a math problem has been one of its top posts for 6 months

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  • There’s no “whatever-the-fuck-your-country-calls-it”

    Yes there is. BEDMAS, BODMAS, and BIDMAS

    the US is the only country using it

    No they're not.

    at some point they’re dropping it

    No, at no point do the order of operations rules ever get dropped

    using multiplication by juxtaposition (2x + 4x2)

    They're called Terms/Products.

  • A fake Facebook event disguised as a math problem has been one of its top posts for 6 months

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  • Where I live, this would be considered juxtaposition

    Not just where you live, everywhere, in Maths textbooks. Adults forgetting the rules (and unqualified U.S. teachers not teaching what's in the textbooks) is another matter altogether.

  • A fake Facebook event disguised as a math problem has been one of its top posts for 6 months

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  • For me it’s the arguments when there is a parentheses but no operator (otherwise known as implied multiplication)

    No, it's known as Factorised Terms/Products, solved via The Distributive Law, a(b+c)=(ab+ac). "implied multiplication" is a made up rule by people who have forgotten the actual rules, and often they get it wrong (because, having wrongly called it "multiplication", they then wrongly give it the precedence of multiplication, not brackets).