Tuesday, November 28, 2017

decimal expansion - Is $0.9999...$ an integer?




Just out of curiosity, since
$$\sum_{i>0}\frac{9\times10^{i-1}}{10^i}, \quad\text{ or }\quad 0.999\ldots=1,$$
Does that mean $0.999\ldots=1$, or in other words, that $0.999\ldots$ is an integer, by applying the transitive property?



Ty.


Answer



$0.999999\ldots$ is indeed $1$, which indeed is a natural number and therefore an integer.



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