Is it acceptable to write "the function $f_n$ is cts for every $n \in \mathbb{N}$"?

Question

When I have a sequence of functions $f_n$, $n \in \mathbb{N}$, is it OK or acceptable to write

"The function $f_n$ is continuous for every $n \in \mathbb{N}$"

meaning

"For every $n \in \mathbb{N}$, the function $f_n$ is continuous"?

Thank you.

Answer 1

When writing with symbols, the quantifiers ("for every natural $n$" / "$\forall n\in\Bbb N$") has to come before using the $n$ for something like referring to the functions $f_n$. When writing in English, it's common to let it come after, as long as it's still part of the same sentence.

Answer 2

You should be okay in doing this provided 1. it's true (with justification?) and 2. it's clear from the context of your writing what the domain is of these functions.