Indicator Function Question

**jpatrie** · October 13th 2008, 10:44 AM

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.

**Plato** · October 13th 2008, 10:51 AM

What do you think this sum equals
$I_Q (2^0 ) + I_Q (2^{\frac{1}<br /> {2}} ) + I_Q (2^1 ) + I_Q (2^{\frac{3}<br /> {2}} ) + I_Q (2^2 )=?$

**jpatrie** · October 13th 2008, 10:56 AM

so

$1+\sqrt2+2+\sqrt{2^3}+4$ ?

**Plato** · October 13th 2008, 11:25 AM

Originally Posted by jpatrie

$1+\sqrt2+2+\sqrt{2^3}+4$ ?

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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