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Is there a way to write $f(c)=2^{\lfloor \frac{c}{10} \rfloor}c$ without using the floor function?

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@JasperLoy $f(c) = 2^{\lfloor\frac{c}{10}\rfloor}c$ – mirai Oct 27 '12 at 17:03
@JasperLoy It's a variable then. I've updated the question. – mirai Oct 29 '12 at 3:15

Perhaps you are looking for $f(c)=\sum_{k=-\infty}^{\infty}2^kc\chi_{[10k,10(k+1))}(c)$ where $\chi_E$ is the characteristic function of $E$ that sends an element to $1$ if it is in $E$ and to $0$ otherwise.

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