# Solve for ? - undetermined inequality symbol

So I was solving a problem in Rudin (chapter 3 #16, to be specific) and I realized how convenient it would be to have a symbol that represented an undetermined equivalence relationship. As an example I will use the symbol $\sim$.

$\mathbf{Example}$. Suppose we have an expression $A$ that we want to relate to $B$. We then set $$A \sim B$$ and perform an algebraic operation to obtain $A'$ and $B'$. If this operation involved multiplying both sides by a negative number, we change $\sim$ to $\sim'$. So suppose it did; then we have $$A' \sim' B'.$$ Lets perform another algebraic operation, and suppose again that we multiplied by a negative number. Then $\sim'$ becomes $\sim$ (since inequalities are the same under two multiplications by negatives), and we obtain $A''$ and $B''$ and thus $$A'' \sim B''.$$ We can continue on in this fashion until we have have done $n$ operations. For simplicity let us suppose that at this point our equivalence relation is $\sim'$. Then $$A^{(n)} \sim' B^{(n)}.$$ Suppose further that we actually know that $A^{(n)} < B^{(n)}$. Then we can conclude $$A > B.$$ If instead we knew that $A^{(n)} = B^{(n)}$ we would have $A = B$, and if instead we knew that $A^{(n)} > B^{(n)}$ we would have $A < B$.

Does anyone know of a symbol such as this, and if so, are there interesting things to be said about essentially solving for equivalence relations?

• +1 I have had the same thought. I don't think any symbol has been designated, but I agree that it would be useful to have a standard one. – user142299 Aug 2 '14 at 1:44
• Perhaps $\overset?>$? – Akiva Weinberger Sep 19 '14 at 16:43

If I'm not sure whether the relationship is $<$, $=$, or $>$, I usually use a circled question mark. In LaTeX, type \textcircled{\scriptsize ?}.
I can't seem to do this in MathJax; perhaps the closest would be to type $\fbox{?}$ to get $\fbox{?}$.