Domain of functional sequence

Question

may I ask you about domain of this functional sequence?

functional sequence is ln(1/n - x)

n is natural number from 1

I dont know if it is (-inf;0) or (-inf;0].

thanks a lot :)

Answer 1

Let $f_n(x)=\ln\left(\frac1n-x\right)$ and see whether $f_n(0)$ makes sense for all $n\in\Bbb Z^+$. Formally $f_n(0)=\ln\left(\frac1n\right)$; is that defined for all $n\in\Bbb Z^+$?