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Does juxtaposition always show multiplication?

  1. Jan 24, 2005 #1
    Hi everybody,
    I just want to make something clear: does juxtaposition always show multiplication? For example 2ab(c+d)e(pi)=2*a*b*(c+d)*e*(pi) ? Generally it applies to any multiplication as long as there are no confusions,despite the number of factors?(obviously 23 is not 2*3!) ?
    And one more thing: when we write
    ---- we mean (a+b):(c-d) ? In other worlds the fraction bar shows that
    everything that is above it, after it's calculated ,is divided with the final value of the expression under it, right? Is this always called a fraction?For example when a is irrational is it called a fraction? In any case every rule applied to fractions applies to this kind of "fraction" too? They are general rules of division?(example a a*c
    - = ----
    b b*c )
  2. jcsd
  3. Jan 24, 2005 #2


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    Hi, C0nfused:
    These are very important questions, because an unambiguous notation is absolutely essential in mathematics!

    Juxtaposition rule:
    You are right, but there are a couple of important exceptions:
    1) 23 should ALWAYS be read as "twenty-three", never "2 times 3".
    In general, juxtaposed digits are to be read in the "usual" manner we learn in school.
    The following is a really bad notation:
    2*a*3=2a3; the right hand side is plain awful; either keep the explicit left hand side, or rewrite it as 6a.

    2) Functions:
    If you have a function f of x, it is common to write the value as f(x).
    This does NOT mean f*x!!

    Parenthesis rule:
    Parentheses is one of the most important notational tools to get an unambiguous notation. Hence, study parenthesis conventions thouroughly!

    If you haven't access to a good formatting program, you should ALWAYS enclose complicated denominators and numerators in brackets.
    For example:
    (a+3b+45)/(d-14e+f) is unambiguous, whereas a+3b+45/d-14e+f not only invites confusion, but is plain wrong.
    The only explicit fraction in the last expression is 45/d, which is something completely different..

    And yes, we may call an expression a/b a fraction even if either a or b (or both) is irrational.

    Welcome to PF, by the way!
    Last edited: Jan 24, 2005
  4. Jan 26, 2005 #3
    Thank you arildno for your really helpful and accurate answer
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