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

 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.

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I am a professor of mathematics at ETH Zürich since 2008.

10 thoughts on “Encadrement”

  1. Maybe you could say “we have the following bounds …” instead of “we have the following inequalities…”?

  2. “two-sided inequality” is nice, I hadn’t thought of that.

    As a further remark, although “encadrement” is quite frequent in French, I can’t think of a “named” mathematical result which refers to it (whereas there are many named inequalities).

  3. “Sandwich” is certainly a noun, even though I’ve never seen it used in this way in print. “Capture” could lend itself to the relevant transformational grammar. The very novelty of “sandwich” (as opposed to other over-used terms, such as “normal”, in other contexts) might recommend it.

  4. About “sandwich” (definitely a noun!), I meant that I find it difficult to imagine using it: “we have the following sandwich a<b<c” just sounds terrible to my ear…

  5. “We have the following sandwich….” has a kind of Conway-esque flavor to it. But if not, how about “bracketing”, “embrace”, “corral”?

  6. “bracket” or “bracketing” seems the best — I was going to mention it in another post today, after seeing it in my digital camera’s manual (as in “exposure bracket”).
    So here is the post I had prepared…

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