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August 17

"Suppose given" mathematically idiomatic English?

"Suppose given a positive $\epsilon$ ." A little thought shows that this is a grammatical English sentence, but would it be idiomatic in mathematics writing? Also, what is the parallel construction in French? I thought it was "Étant donné", but see this is not so. Tito Omburo (talk) 12:56, 17 August 2024 (UTC)[reply]

It sounds Victorian to me. The more usual phrasing would just be given without the suppose. --Trovatore (talk) 18:50, 17 August 2024 (UTC)[reply]

Without the imperative verb "suppose", it is no longer a complete sentence. Tito Omburo (talk) 00:19, 18 August 2024 (UTC)[reply]

Just "Given a positive

\epsilon

" should be followed by a main clause, as in "Given a positive

\epsilon

, find

M

such that

x>M

implies

f(x)<\epsilon .

" In that case, "Étant donné" is just fine, like here: "Étant donné un nombre positif rationnel

\varepsilon ,

..."

To me, "Suppose given a positive

\epsilon .

" sounds more ungrammatical than Victorian. Still old-school but sounding more grammatical (to me): "Let a positive

\epsilon

be given." In French, "Soit donné ..."; see here: "Soit donné un nombre positif (arbitrairement grand) h." Better still in English: "Let

\epsilon

be a positive number." --Lambiam 20:25, 17 August 2024 (UTC)[reply]

Yes, soit donné is what I was thinking of. Here "suppose" is a verb in imperative mood, and the condition we are supposing is that a positive epsilon [be given]. It's a construction that arises sometimes in mathematics writing, and I think it's grammatical. Tito Omburo (talk) 00:19, 18 August 2024 (UTC)[reply]

Do you think the following is grammatical:

"Suppose present a parent."

? --Lambiam 01:17, 18 August 2024 (UTC)[reply]

Why not? Tito Omburo (talk) 01:20, 18 August 2024 (UTC)[reply]

Why language is as it is is generally an unanswerable question. (Why is morous not an English word? porosity → porous, so why not morosity → morous?) The object of verbs like imagine and suppose is normally a noun phrase (Imagine a spherical cow.) or a clause (Suppose [that] $a$ is prime.). It can also be a subject + an infinitive (Suppose $a$ to be prime.). CGEL Chapter 4 §5.4 writes that to be can be omitted with a reflexive object (as in Suppose yourself away from home.^[1]), So then we have Suppose + object + predicate. In mathematical writing we find this also with other objects (as in Suppose $a$ prime to $b$ , and $a-b$ an odd number.^[2]). Constructions of the form Suppose + predicate + object, with object and predicate swapped, do not fit any of these forms. --Lambiam 07:52, 18 August 2024 (UTC)[reply]

My linguistic intuition is that both these constructions (suppose given ε and suppose present a parent) are — grammatical-ish, in the sense that in some contexts I would accept them (though find them a bit strained and unnatural) and in others I would reject them. --Trovatore (talk) 22:34, 18 August 2024 (UTC)[reply]

I suppose it could be OK in a construction like: "Suppose, given a positive $\epsilon$ , that all negative $\epsilon$ s of lower absolute value divide the original value with a remainder no greater than the square root of the log of $\epsilon$ to base 6". But a grammarian would require the commas around the parenthetic phrase. -- Jack of Oz ^{[pleasantries]} 22:40, 17 August 2024 (UTC)[reply]

It doesn't read like a complete sentence to me. It's missing something. For example, "Suppose one is given a positive

\epsilon

." would be a complete sentence, as would "Suppose a positive

\epsilon

is given." and also "Suppose

\epsilon

is positive." XOR'easter (talk) 22:29, 21 August 2024 (UTC)[reply]

I would go for one of "Given a positive number ⁠

\epsilon

⁠, ..." (part of a sentence); "Let ⁠

\epsilon

⁠ be a positive number...." (complete sentence); or "Suppose ⁠

\epsilon

⁠ is a positive number...." (complete sentence). The original proposal "suppose given" is ungrammatical. –jacobolus (t) 00:56, 22 August 2024 (UTC)[reply]

Whether or not it is grammatical, it is certainly not idiomatic 21st century mathematical English. 100.36.106.199 (talk) 01:59, 22 August 2024 (UTC)[reply]

Really? Is Robin Hartshorne not a 21st century mathematician? Tito Omburo (talk) 02:02, 22 August 2024 (UTC)[reply]

I know you are but what am I? 100.36.106.199 (talk) 02:07, 22 August 2024 (UTC)[reply]

Also, Jacob Lurie. Griffiths and Harris. Saunders Mac Lane. Vladimir Arnold. J-P Serre. Nick Katz. All seem to use this construction. Also one can find it in the English translations of Bourbaki. Tito Omburo (talk) 02:14, 22 August 2024 (UTC)[reply]

It's more widely attested than I would have expected, but its use seems confined to rather pure mathematics. To exaggerate a bit, it seems to be employed by people who learned how to write by reading English translations of Bourbaki. I'm scratching my head trying to think of other examples of an imperative-passive combination. It just feels unnatural — at odds with my sensibilities as a native speaker of (American) English. No one says Suppose eaten the dinner or Suppose murdered a body. I don't think the construction is grammatical when evaluated against English overall. Instead, it's a peculiarity of a certain sociolect. It might even be a one-off idiom rather than an example of a more general grammatical rule: just a two-word combination that speakers of the Bourbaki sociolect drop into their speech, rather like how some people end a theorem with "Q.E.D." without importing all the rules of Latin. I'd avoid it in any writing not targeted to a very niche audience. XOR'easter (talk) 04:46, 22 August 2024 (UTC)[reply]

I think this is basically right, as it feels like something loaned by the French. Tito Omburo (talk) 10:00, 22 August 2024 (UTC)[reply]

It's one thing for certain mathematicians to use odd expressions that are familiar within their particular closed club, but it's another for them to express themselves effectively to the world at large. And that is true of any field of human endeavour. The very fact that we're trying to work this query out means they have not been effective in their communication. One can find attestations for just about anything, but, for the most part, so what? -- Jack of Oz ^{[pleasantries]} 20:25, 23 August 2024 (UTC)[reply]

Well my question was to what extent this is idiomatic in mathematics writing. Tito Omburo (talk) 20:33, 23 August 2024 (UTC)[reply]

Are you sure that what you're interested in is getting other people's opinions on this question? It seems rather like you have a point of view about it and you are hoping others will support it. 100.36.106.199 (talk) 21:13, 24 August 2024 (UTC)[reply]

Well, I'm certainly interested in references one way or another on this topic. But the basic vibe I have gotten is that "this is ungrammatical" (when I have already stipulated that it is), or "this isn't used in mathematics writing" (when it very obviously is, very widely). Uneducated opinions aren't really worth much. Tito Omburo (talk) 21:17, 24 August 2024 (UTC)[reply]

"Uneducated" Is this a problem with English not being your first language, or just a straightforward WP:NPA violation? 100.36.106.199 (talk) 19:31, 25 August 2024 (UTC)[reply]

Do you have some concrete examples with links? This phrasing reads to me like the general type of abbreviation of full sentences by ungrammatical fragments (in this case, an ordinary construction along the lines of "suppose we are given" is getting its middle chomped out) which is relatively common on blackboards along with replacing words by symbols, etc. I'd expect to sometimes find it in lecture notes but rarely in textbooks written by native speakers. But maybe I just don't have my finger on the pulse of some modern mathematical writing. –jacobolus (t) 05:13, 22 August 2024 (UTC)[reply]

Lurie's Higher Algebra is filled with examples [3]. For example, on page 26, "Suppose given a diagram X f → Y g → Z h → X[1] in the homotopy category hC." Tito Omburo (talk) 09:46, 22 August 2024 (UTC)[reply]

He more commonly seems to use "Suppose we are given ..." or "suppose X is given ..." (among other similar constructions, altogether many hundreds of examples), but there are indeed 7 examples near the top of the abbreviated ungrammatical "suppose given" version. If this book were ever published the copyeditor would hopefully fix those. –jacobolus (t) 02:40, 24 August 2024 (UTC)[reply]

I picked this example because it is freely available. But Hartshorne's Algebriac geometry is in its eighth corrected printinting, and still has numerous examples of the construction which you contend is ungrammatical. Likewise Katz and Mazur Arithmetic moduli of elliptic curves. Serge Lang's Algebra, Fundamentals of differential geometry, Complex analysis, SL(2,R), Topics in the cohomology of groups, and Cyclotomic fields. Arnold's Ordinary differential equations, and Mathematical methods of classical physics. MacLane and Moerdijk's Sheaves in geometry and logic. A lot of these are very standard and popular textbooks. Tito Omburo (talk) 16:42, 24 August 2024 (UTC)[reply]

I think Hartshorn just loves dropping verbs or where possible both subjects and verbs from his sentences. It's a very "straight from the chalkboard" style. His book is full of heavily abbreviated "sentences" like "Suppose given X,Y schemes over S ...". In my opinion these are ungrammatical as English prose, but fine as doodled abbreviations. YMMV. –jacobolus (t) 17:09, 24 August 2024 (UTC)[reply]