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Math Help - Indicator Function Question

  1. #1
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    Indicator Function Question

    What is the value of \sum_{i=0}^{4}1_Q(2^{\frac{i}{2}}) where 1_Q(x) is the indicator function for the set of rational numbers.
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  2. #2
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    What do you think this sum equals
    I_Q (2^0 ) + I_Q (2^{\frac{1}<br />
{2}} ) + I_Q (2^1 ) + I_Q (2^{\frac{3}<br />
{2}} ) + I_Q (2^2 )=?
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  3. #3
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    so

    1+\sqrt2+2+\sqrt{2^3}+4 ?
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  4. #4
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    Quote Originally Posted by jpatrie View Post
    1+\sqrt2+2+\sqrt{2^3}+4 ?
    No indeed.
    Do you know what an indicator function is? Often it is called a characteristic function.
    I_Q (x) = \left\{ {\begin{array}{rl}<br />
   1 & {x \in Q}  \\   0 & {x \notin Q}  \\ \end{array} } \right.
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