Is it correct to write the whole number $2$ as a mixed fraction $1 \dfrac{1}{1}$ or $2 \dfrac{0}{1}$? So if we start from writing $2$ as an improper fraction, and use the same procedure for any improper fraction to covert it to a mixed number, we'll get $2\dfrac{0}{1}$. Which makes sense, and it can be reverted back to $2$.
\begin{align}
2\rightarrow\dfrac{2}{1}\rightarrow 2\dfrac{0}{1}
\end{align}
But from playing around with this, I also found that there's another mixed number that can be evaluated to $2$. Starting from $1+\dfrac{1}{1}$
$$1+\dfrac{1}{1}\rightarrow1\dfrac{1}{1}\rightarrow\dfrac{2}{1}\rightarrow2$$
So, $2$ can be represented as either $2\dfrac01$ or $1\dfrac11$.
Are both these correct?

I would just write $2$, and reserve the use of mixed fractions for non-integers. Both your options look strange and unusual, but I don't think either of them is wrong.
