Is it mathematically valid to take the limit of an **equation** as opposed to an expression?

Question

Wolfram Alpha seems to think it's okay to write this: $$\lim_{n \to \infty} (n=\frac{n^2}{n})=True$$ I understand what is meant, and also why it returns True, but is this a mathematically valid statement? If not, is there a more correct way to write the same thing? Thank you for your time.

Answer 1

It could be interpreting this as taking the limit of both sides of the equation, because then you get $\lim\limits_{n\rightarrow\infty}n=\lim\limits_{n\rightarrow\infty} \frac{n^2}{n}$, which is a true statement. However, I think in common usage, people would interpret something like this as an abuse of notation, which, despite the name, isn't necessarily a bad thing, but you do have to be careful to avoid ambiguity.