Is there a particular word in English for a string of two inequalities which together give both a lower and an upper bound for a certain quantity? French has encadrement for things like this, as in
Pour tout réel x, on a l’encadrement
$latex x-\frac{x^2}{2}\leq \cos(x)\leq x-\frac{x^2}{2}+\frac{x^4}{24},$
This is often quite convenient — of course, one can say “we have the following inequalities…”, but the extra information is useful to have, and it helps avoiding too many repetitions.
Note: The OED only lists encadré as an English word, as a technical term in crystallography:
A crystal is named encadré, when it has facets which form kinds of squares around the planes of a more simple form already existing in the same species, R. Jameson, A treatise on the external characters of minerals, 1805.
