# Notation for “should be equal to”

Suppose I have some (possibly complicated) expression depending on one or more parameters, and a value which this expression should have for the solution I'm interested in. How do you write that, in particular if you want to distinguish it from a simple equals sign used to denote equivalence as a result of algebraic transformations.

Example:

So you have $f(x)=ax^2+bx+c$ and are looking for extremal values. You do that by finding zeros of the derivative: $$\frac{\mathrm df}{\mathrm dx}=2ax+b\;\langle\text{your symbol here}\rangle\;0$$ You can solve the above expression for $x$ to find the extremum.

I'll post the notation I've been using so far as an answer, but please post additional answers if some other notation is used in your field. I've also been using my notation in several answers here on MSE, so these might serve as more verbose examples: 1, 2, 3.

• Usually I just write out "Want to show" Sep 10 '14 at 15:27

## 2 Answers

One notation which I've been using myself, and which I've seen others use around me, is writing this as $a\overset!=b$. It might be read as something like “$a$ shall be (made) equal to $b$”.

The exclamation point indicates an imperative, a need for action, a goal. This is opposed to plain $a=b$ (“$a$ is equal to $b$.”) which indicates a fact, and also opposed to $a\overset?=b$ (“Is $a$ equal to $b$?”) which indicates a question, check or predicate. I believe that punctuation in English sentences is very close to these semantic distinctions, so I consider the use of these punctuation marks fairly appropriate.

However, I was very surprised that $\overset?=$ has its own Unicode code point (≟, U+225F, “questioned equal to”) but $\overset!=$ apparently is not available as a Unicode code point (unless I missed it). So perhaps my use is not as wide-spread as I had assumed. Please upvote this answer if you would use the same notation, and if there are enough upvotes, then perhaps we should request a code point for this glyph eventually.

• I can confirm. $\overset{!}{=}$ is the only sign I have ever seen for this use. Sep 10 '14 at 15:24
• I have seen =? before and I use it too. Sep 10 '14 at 15:27
• I was wondering about $\overset{!}{=}$, since I just saw it in the book "Physics from Symmetry" imgur.com/a/i9jhE Jun 12 '17 at 2:42
• You can type $\overset !=$ with \overset ! = for the people who came here to see how to type this (like me). Mar 11 '21 at 12:58

I use $a \stackrel{\text{set}}=b$ to indicate that we are about to solve the equation.

For instance $f'(x)\stackrel{\text{set}}=0$.