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Thread: quotient values

  1. #1
    Super Member
    Aug 2009

    quotient values

    given that g: real number ->real number and for all x which are quotient numbers, g(x) =o. show that g is 0 function.

    what i did was i tried to divide the real line into small intervals of quotient values.
    and tried to say that by intermediate value thm, all values have to be 0..but i dont think that works right?
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  2. #2
    Senior Member Tinyboss's Avatar
    Jul 2008
    It's false without any additional assumptions. I'm guessing that g is supposed to be continuous in this exercise. The general fact is that two continuous functions which agree on a dense subset are the same function (at least when the codomain is a reasonable space, which R certainly is).

    Here's a hint for showing it in this particular case: suppose g(x) is nonzero for some x. Then...hmm...I don't think I can say anything further without giving it all away. Use continuity.
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