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Dense numbers

  1. Jul 4, 2015 #1
    Hello,

    Please, someone, explain what the // in the hint below stands for:

    "Show that the numbers of the form
    ±m√2/n
    for m, n ∈ N are dense."

    Hint:
    "To find a number in (x, y), find a rational in (x//√2, y//√2). Conclude from this that the set of
    all (irrational) numbers of the form ±m√2/n is dense."

    Thank you in advance.
     
  2. jcsd
  3. Jul 5, 2015 #2

    pasmith

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    Homework Helper

    I think it's a misprint for division, since if you take a rational in [itex](x/\sqrt{2},y/\sqrt{2})[/itex] and multiply it by [itex]\sqrt{2}[/itex] you indeed get a real number in [itex](x,y)[/itex].
     
  4. Jul 5, 2015 #3
    I suspected that, but I didn't want to go astray trying a wrong tack in case I was just ignorant of the symbol.

    Thank you very much, pasmith.
     
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