In literature, I read the following:
A typical relationship*, often appearing in the literature, is:
$$|-\nabla(\bar p+\rho g z)|\equiv \rho g J=q(\mu w+\rho Bq^m)$$
The nomenclature does not define the $\equiv$ symbol. I think it means "equivalent to" or "defined as". If it does mean that, what is its purpose? That is, what information would be lost (or error incurred) if the relationship* was written with an "equal to" sign $=$ in place of the "equivalent to" sign $\equiv$? E.g.,:
$$|-\nabla(\bar p+\rho g z)| = \rho g J=q(\mu w+\rho Bq^m)$$
*A secondary question: Is the use of the term "relationship" specific to this situation? I.e., can we not refer to the above as an "equation"?
Best Answer
Like $:=$ or $\overset{\text{def}}{=}$, $\equiv$ is indeed a moderately common way to distinguish a definition of the l.h.s. in terms of the r.h.s. from any other sort of equality relation ("equation", "relationship", "relation" are all completely interchangeable here).
The purpose is to clearly distinguish between equations, which can/need to be derived, and definitions, which are simply stated and need no proof. There are plenty of texts that do not use special notation for definitions, so this is clearly not universally considered to be necessary.