What is the value of $\displaystyle \sum_{i=0}^{4}1_Q(2^{\frac{i}{2}})$ where $\displaystyle 1_Q(x)$ is the indicator function for the set of rational numbers.

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- Oct 13th 2008, 10:44 AMjpatrieIndicator Function Question
What is the value of $\displaystyle \sum_{i=0}^{4}1_Q(2^{\frac{i}{2}})$ where $\displaystyle 1_Q(x)$ is the indicator function for the set of rational numbers.

- Oct 13th 2008, 10:51 AMPlato
What do you think this sum equals

$\displaystyle I_Q (2^0 ) + I_Q (2^{\frac{1}

{2}} ) + I_Q (2^1 ) + I_Q (2^{\frac{3}

{2}} ) + I_Q (2^2 )=?$ - Oct 13th 2008, 10:56 AMjpatrie
so

$\displaystyle 1+\sqrt2+2+\sqrt{2^3}+4$ ? - Oct 13th 2008, 11:25 AMPlato