Enlightnement came from a somewhat unexpected source (the manual for my digital camera), and a comment on the earlier post also suggested it: what may be the most natural English rendering of the French encadrement is “bracket”, or “bracketing”.

Indeed, it seems the term “bracket” is used in photography for the operation of taking simultaneously (or as nearly so as possible) three pictures, one with a given selected exposure, and two with higher and lower settings, so that the amateur photographer can then select which is best.

The ever-helpful OED confirms that this is a good choice: we find for Bracket, n., 5(b)

The (specified) distance between a pair of shots fired, one beyond the target and one short of it, in order to find the range for artillery; chiefly in the phrase to establish a bracket.

The quotations that go with this sense are convincing (if somewhat martial); here is the first one:

1899 Daily News 6 Dec. 5/7 At first I fire at 3100 yards, and if I find that my shot is short I fire a second round, say at 3300, in order to go beyond the object. If I see that my shot does go over I am satisfied that I have established what is called ‘a long bracket’, that is to say, I have found two ranges, 200 yards apart, between which the object must lie… I..fire another shot to shorten the distance within which I can then know that the target must be. This we call, on the same principle as the other, ‘a short bracket’.

There is then a further sense 5(c) with similar meaning:

A group bracketed together as of equal standing in some graded system, as income bracket: a class of persons grouped according to income.

And then, finally, bracketing is defined as “The action of furnishing, coupling, uniting, with brackets”. Altogether, it seems one can quite correctly state, in demotic English, something like:

… and so we have the bracket

$x-\frac{x^2}{2}\leq \cos(x)\leq x-\frac{x^2}{2}+\frac{x^4}{24}$

(although, to my ear, the variant “we have the bracketing” seems better).