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Sure, $999\dots=1$. It also equals $\pi$, and $\frac00$. At least it would, if it existed (it would be true vacuously).

But decimal notation is defined such that you can only have a finite number of digits to the left of the decimal place (whereas you can have infinite decimals to the right). Therefore, you have a bad assumption: that $999\dots$ existed. See this other answerother answer for a different decimal notation where you can have infinite digits to the left of the decimal point.

Sure, $999\dots=1$. It also equals $\pi$, and $\frac00$. At least it would, if it existed (it would be true vacuously).

But decimal notation is defined such that you can only have a finite number of digits to the left of the decimal place (whereas you can have infinite decimals to the right). Therefore, you have a bad assumption: that $999\dots$ existed. See this other answer for a different decimal notation where you can have infinite digits to the left of the decimal point.

Sure, $999\dots=1$. It also equals $\pi$, and $\frac00$. At least it would, if it existed (it would be true vacuously).

But decimal notation is defined such that you can only have a finite number of digits to the left of the decimal place (whereas you can have infinite decimals to the right). Therefore, you have a bad assumption: that $999\dots$ existed. See this other answer for a different decimal notation where you can have infinite digits to the left of the decimal point.

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Christopher King
Christopher King
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Sure, $999\dots=1$. It also equals $\pi$, and $\frac00$. At least it would, if it existed (it would be true vacuously).

But decimal notation is defined such that you can only have a finite number of digits to the left of the decimal place (whereas you can have infinite decimals to the right). Therefore, you have a bad assumption: that $999\dots$ existed. See this other answer for a different decimal notation where you can have infinite digits to the left of the decimal point.