EDIT: Nevermind about the "fraction" part. What I mean is a number whose last digit repeats infinitely.

The function \(\displaystyle f(x)=\frac{1}{x}\) is not defined at x=0.

What is the proper way to express numbers with an infinitely repeating last digit as the area under this function?

Taking a shot at it, if I take as an example the number \(\displaystyle 8\overline{33333}\) I would say...

\(\displaystyle \lim_{b \to 0 }\; \int_{b}^{1}\frac{1}{x}\; dx=8\overline{33333}\)

Is this correct? Is there a less ugly way to do it?

Thanks

The function \(\displaystyle f(x)=\frac{1}{x}\) is not defined at x=0.

What is the proper way to express numbers with an infinitely repeating last digit as the area under this function?

Taking a shot at it, if I take as an example the number \(\displaystyle 8\overline{33333}\) I would say...

\(\displaystyle \lim_{b \to 0 }\; \int_{b}^{1}\frac{1}{x}\; dx=8\overline{33333}\)

Is this correct? Is there a less ugly way to do it?

Thanks

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