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B Looking for internet famous math prob on dist law.

  1. Apr 3, 2016 #1
    A few years ago it was a big thing where high school basic math definition stumped a lot of pro mathematicians.

    The prob from memory involved order of operations. Could be wrong but I think it was getting the correct answer to;

    a(b+c) for specific values of a,b,c. All integers and no tricks.

    Some maths profs argued for their answer some changed but the only answer was it was not a well defined question. Few conceded the other guy was right, or how they were wrong.

    Sorry I can't define the actual problem but it started a math educator war. Hope my vague definition triggers someone's memory.
  2. jcsd
  3. Apr 3, 2016 #2
    OK pretty sure this is the problem although the numbers are irrelevant.


    What is the solution to 6÷2(1+2)=?: Professor of …:
  4. Apr 3, 2016 #3
    I'm gonna doubt that this stumped any pro mathematician
  5. Apr 3, 2016 #4
  6. Apr 3, 2016 #5
    That is correct. That means that the calculators were programmed incorrectly. They were programmed incorrectly because when typical students type in 6÷2(1+2) they often mean the incorrect thing.

    The PEMDAs do work and they do give a clear answer.
  7. Apr 3, 2016 #6
  8. Apr 3, 2016 #7
    Position 2 is crap. Find me some mathbooks that define "implied multiplication". You won't find it. I have never even heard of "implied multiplication" before this problem came around. Go ahead, search in Rudin, Bloch, Landau, or any other math book that rigorously defines numbers and their operations. Nowhere will you see that "juxtaposition" in any way behaves as position 2 tells us.
  9. Apr 3, 2016 #8
    Still a good discussion topic for students tho.

  10. Apr 3, 2016 #9


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    The problem stems from some people assume that
    1. ##a/bc## is equal to ##\frac{a}{bc}## instead of ##\frac{ac}{b}##, or
    2. people who think "implicit multiplication" (i.e. mathematical dot) and "explicit multiplication" (i.e. times symbol) are different. This is nonsense, there is only one multiplication of real numbers.
  11. Apr 3, 2016 #10
    Not really. It's completely irrelevant to mathematics. It's a stupid convention. Besides, nobody uses ÷ to denote division anymore.
  12. Apr 3, 2016 #11
    If you want a good discussion topic for students, then talk to them about the value of ##0^0##. For this, both sides actually do have a good point.
  13. Apr 3, 2016 #12


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    There is also "Is zero a natural number?"
  14. Apr 3, 2016 #13
    Or ##0\cdot \infty##, where the convention that it equals 0 sometimes makes a lot of things easier in some parts of math (measure theory).
  15. Apr 3, 2016 #14
    Great discussion topics, will do some work. Thanks.
    What about this one;


    Sorry can't make it nested.
  16. Apr 3, 2016 #15


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  17. Apr 3, 2016 #16
    Or ##\sqrt{2\sqrt{2\sqrt{2\sqrt{2\sqrt{....}}}}}##.

    Or the truly amazing

    [tex]\pi = \frac{4}{1+ \frac{1^2}{3 + \frac{2^2}{5+\frac{3^2}{...}}}}[/tex]
  18. Apr 3, 2016 #17
    And if you really want to upset the class:

  19. Apr 3, 2016 #18
    Interesting until I got to this and my heart sank;

    "The Lambert W relation cannot be expressed in terms of elementary functions"
  20. Apr 3, 2016 #19
    That doesn't mean anything. Why do you think the sine function is any more natural than the Lambert W function? We only know a limited number of exact values for the sine function too.
  21. Apr 3, 2016 #20
    On a simple note the correct answer to this finite problem?

  22. Apr 3, 2016 #21
    I think the sine function is more natural cos it is more natural;

    tide comes in, tide goes out therfore sine.

  23. Apr 3, 2016 #22
    Like expected, my computer gave an overflow error.
  24. Apr 3, 2016 #23
    So it's only natural because you can find an application of it in nature?
  25. Apr 3, 2016 #24
    By definition of the word natural your comment is trivial.
  26. Apr 3, 2016 #25
    OK. But then (all from wiki)

    So the Lambert W function is natural too.
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