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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.

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Probably yes, but please, don't use the one you wrote here. A symbol should be as simple as possible. You could use something like $\sim_k$. It is not a problem to use symbols similar to some used in other places, as long as you define them well and don't use two symbols which are too similar in the same paper (to avoid confusion). –  Daniel Robert-Nicoud Feb 6 '13 at 21:44
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2 Answers 2

up vote 2 down vote accepted

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.

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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.

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