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School math notation - x for multiplication or a variable?

  1. Dec 1, 2017 #21

    I like Serena

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    I did the exact same thing! ... and then I switched back when I started writing both ##\times## and ##x##.
    To be fair, I still tend to write ##x## as a cross in regular handwriting, but I definitely use the other form in math and physics.
     
  2. Dec 1, 2017 #22
    Yessss!!!
     
  3. Dec 1, 2017 #23

    I like Serena

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    For the record, there's plenty more symbols that cause confusion.
    ##a## and ##\alpha##,
    ##I##, ##l##, and ##1##,
    ##O## and ##0##.
    The challenge is to make them all look different.
     
  4. Dec 1, 2017 #24

    fresh_42

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    And if one has functions ##f,g## then what is this: ##fg=f \cdot g## or ##fg = f \circ g## or sometimes even ##fg= g \circ f##.
     
  5. Dec 1, 2017 #25

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    Indeed. And another favorite of mine, is f(x+1) or a(x+1) a function call or a multiplication?
    And for the record, we can also have ##f\cdot g=f \circ g## or ##f\cdot g=g \circ f## in abstract algebra.
     
  6. Dec 1, 2017 #26
    So, to sum the things up, I got the following advices:

    • abandon ##\times## and use ##\cdot## as soon as algebra is introduced
    • use some special curved way to write ##\times## meaning ##x## ( "with slightly curved ends on the upper left to lower right line" )
    • for the variable, just write curved ##x##, not cross
    • for multiplication, make ##\times## sign very small
    And... I got a confirmation that the usage of ##\times## sign for multiplication does cause problems. At least for some people.
     
  7. Dec 1, 2017 #27

    fresh_42

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    • and make the multiplication x very small
     
  8. Dec 1, 2017 #28

    I like Serena

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    Or as $ 1 000 001,99 eliminating the ambiguity, which is my personal preference.
     
  9. Dec 1, 2017 #29

    Mark44

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    The ##\times## symbol doesn't ordinarily cause problems, as it is reasonably distinct from ##x##. There are times (pun not intended) where the ##\times## symbol is preferable, such is in writing numbers in scientific notation -- e.g., Avogadro's number, ##6.022 \times 10^{23}## or the normalized form of binary fractions ##1.011 \times 2^5##.
     
  10. Dec 1, 2017 #30

    Mark44

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    I seriously doubt that the difference in how commas and periods are used as number separators made it into anyone's top 100 reasons for wanting to leave the EU. From my perspective, on the "other side of the pond," the reasons went a lot deeper. I won't elaborate, as this would be 1) off-topic and 2) heading off into politics.
     
  11. Dec 1, 2017 #31

    berkeman

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    Or vector cross products?

    Apologies if this has been mentioned already in the thread (I got some vertigo when the discussion veered into comma space), but just use the star character * for multiplication. It's pretty unambiguous for basic math, IMO.

    The "x" symbol has too many meanings to overload it with multiplication, IMO.

    http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/imgmag/fqvb.gif
    fqvb.gif
     
  12. Dec 1, 2017 #32

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    Can we please please make that ##\vec F=q\vec v \times \vec B##?
    I'm getting some vertigo myself for seeing an ##x## variable between vectors. :eek:
     
  13. Dec 1, 2017 #33

    berkeman

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    Let me call Hyperphysics....

    Oh, nuts, I misplaced their number... o0) :smile:
     
  14. Dec 1, 2017 #34

    berkeman

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    or *
     
  15. Dec 1, 2017 #35

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    From the context it's clear of course that it's a cross product, so in the end there is no ambiguity.
    Still, I'm not impressed with the Hyperphysics people, since they are apparently sloppy with their symbols.
    It's like seeing spelling mistakes in a curriculum vitae. ;)

    Oh, and btw, this cross product is multiplication - just for 3D vectors.
    It's just that we distinguish the center dot for the dot product, even though that is not proper multiplication (since its result is not a vector breaking closure).
     
    Last edited: Dec 1, 2017
  16. Dec 1, 2017 #36

    Mark44

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    Absolutely! The hyperphysics person isn't up to speed on math symbols like ##\times## versus letters ##x##.
     
  17. Dec 5, 2017 #37
    I was trained as an engineer in the US in the 1980s. The biggest issue I had with metric units is that all your conversion factors are power of 10 - you just had to shift the decimal. This is surprisingly easy to do. With imperial units we had so many bizarre conversion factors that it was actually easier to get the correct answer. 30 years later and I still remember 6.72x10^-4 lb Cp/ft sec for calculating Reynolds numbers.
     

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  18. Dec 6, 2017 #38
    To a certain extent we all develop tricks to cope with possible ambiguity. It keeps getting worse in math, as math pirates symbols from multiple alphabets, and often from weird fonts.

    My adaptations: I cross my sevens to make it clear that they aren't 1's. But I cross my z's so they are clearly not twos.
    Instead of the italic x used in many texts, I use a script x from my handwriting in 2nd grade.

    Being sloppy, a dot got lost or sometimes converted to a decimal point. I ended up using a tiny circle

    Most of the time being adjacent is enough to determine multiplication.

    In computing most languages use asterisk for multiplication, and double asterisk for exponents.
     
  19. Dec 6, 2017 #39

    symbolipoint

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    I stopped using "x" of whatever form, for indicating the multiplication operation. This started upon beginning of study of Algebra 1, and continued onward. Less confusion when communicating in written form for yourself and other people. Like you said, the dot, raised to midlevel, will show multiplication, unless someone misreads this as a decimal point, which probably does happen. We also have parentheses to separate plain number factors from each other.
     
  20. Dec 12, 2017 at 3:10 PM #40

    Mister T

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    When students start learning algebra they are taught that juxtaposition means multiplication, so there is no need for the cross or the raised dot. It's also common for a conscientious teacher to be aware of this difficulty and write ##x## for the letter instead of the cross used for multiplication. The cross continues to be used in scientific notation, but there its meaning is clear from the context.

    I picked up this habit and it wasn't until grad school that I realized I could drop it and simply write x instead of ##x##.
     
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