Operator notation for arbitrary fields

Question

I'm trying to come up with a bijection between $\mathbb{R}$ and a complete totally ordered field $F$. Bearing in mind that $F$ is arbitrary, is it still OK to use operators such as $+$, $-$, $\cdot$, $/$ and $\sum$ on elements of $F$, and have it be understood from context that these are supposed to be $F$'s operators?

Answer 1

Provided that it's clear from context whenever you write $x+y$ which field $x$ and $y$ come from, then it's clear which field $+$ belongs to, so it's fine. (And similar for other operators.)