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Discussing continuity of a function

  1. Jan 13, 2009 #1
    1. The problem statement, all variables and given/known data

    Discuss the continuity of the function f defined for all x belongs to [0,1] by f(x)=x if x is rational and f(x)=x^2 is x is irrational.

    2. Relevant equations

    3. The attempt at a solution

    I have no idea how to begin this question.....some help would be great thanks!
  2. jcsd
  3. Jan 14, 2009 #2
    Maybe you should try checking some points. Is f continuous at 0? How about sqrt(2)?
  4. Jan 14, 2009 #3


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    Staff Emeritus
    Science Advisor

    You will need to know
    1) The definition of "continuous at a point".
    2) The fact that there exist rational numbers in any interval, no matter how small.
    3) The fact theat there exist irrational numbers in any interval, no matter how small.
    The last two should help you find the limit, or determine if it does not exist, at any point.
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