Creating a new math symbol?

Question

I am working on a lemma that uses equivalence classes and $\equiv_{k}$ indicates that two sets are congruent mod $k$. Example: with $k=4$ there are $24$ possible sets, of which I only want to consider $6$ sets as congruent. I have an algorithm to create the appropriate equivalence classes.

I wanted a way to indicate that the equivalence classes were calculated differently. Since I am working with square-roots, I came up with:
$$\sqrt{\equiv_k}$$

which means square-root equivalence mod $k$. ($k$ is the square-root.)

Is it acceptable to create a new symbol for a paper?

Edit: $$\equiv^{\prime}_{k}$$ How about this? My proof uses $k^{\prime}$ as a second divisor.

Answer 1

It is acceptable to create a new symbol although one should be as a default extremely hesitant to do so and extremely picky about the choice of symbol once one has decided to do so.

In your case I would suggest not using that symbol. I would suggest using $\equiv'$, $\equiv^\ast$, $\equiv_\ast$, $\sim$, $\simeq$, or any one of the many other symbols that already exist.

Answer 2

Also, make note, you might your new symbol to generalize to the opposite, i.e. $=$ vs. $\ne$. I strongly recommend using a standard symbol with some extra decoration as Jim suggests.