# Is it correct to say "Be m a number...", instead of "Let m be a number..." in math and elsewhere?

I know declaring things with 'be' is common in older texts. Is it grammatically sound using it in this context? It doesn't have to be in math, but that is where I saw it once and have been writing it ever since.

Here some more examples:

• "Be ε a sufficiently small positive number."
• "Assume, by way of contradiction, that f(x) = 0 has multiple solutions; be a and b any of two them."
• "Be x = 10 and y = 14.:
• "Be A the altitude and θ the angle of elevation."
• "Be x, y and z the coordinates of this vector."
• "Be it ever so humble, there's no place like home" means Even if it is humble, not let it be. And "Let x=10" is a fixed form in math, so inventing others will make it look like an outsider wrote it. Commented Dec 24, 2023 at 1:30
• Could you say where you saw these things? There is an older usage of the subjunctive, no longer seen today, to write "if m be a number..." But I've never seen "Be m a number." This looks a lot like what you'd see in French or German, though.
– Dave
Commented Dec 24, 2023 at 3:13
• @YosefBaskin that doesn't however mean that "be X" can't mean "let X be." For example, "hallowed be thy name" or "now therefore be it resolved...." Commented Dec 24, 2023 at 16:04
• Hello. Great question, but could you please add examples of "declaring things with 'be' in older texts"?
– Stef
Commented Dec 24, 2023 at 20:09
• "I know its used a lot in the Qur'an" You mean, it's used in a lot of translations of the Qur'an. Commented Dec 24, 2023 at 20:13

No, constructions like “Be m an integer” and others with be are not at all idiomatic in mathematical discourse. What you will find is things like “Let m be an integer,” “Suppose m is an integer,” and “Assume m is an integer.”

• I would insert the word "modern" between "mathematical" and "discourse" in your first sentence (the construction is archaic, and was once considered acceptable---it no longer is). (+1) Commented Dec 25, 2023 at 18:07
• @XanderHenderson: Agreed, except that we actually put "modern" before "mathematical", not after it. (See books.google.com/ngrams/… .) Commented Dec 26, 2023 at 10:17
• @ruakh That's just me being dyslexic. Of course, you are correct (the line break on my screen messed with my head). Commented Dec 26, 2023 at 13:25

Is it grammatically sound using it in this context?

No. Grammar guidance changes. This use of "to be" in the present subjunctive to indicate irrealis - a theoretical or possible state of an object - died out about 400 years ago, but is fossilised in some phrases, sayings, quotations, etc.

*Be ε a sufficiently small positive number -> If ε is a sufficiently small positive number

*Be x, y and z the coordinates of this vector. -> If x, y and z are the coordinates of this vector.

Religious texts and speech is a different matter, apparently deities do not speak Modern English and their acolytes mimic them.

• I would not read any of the given examples as the beginning of an if/then statement. Rather, they are assumptions, which, in normal mathematical exposition, would be more along the lines of "Let $\varepsilon$ be sufficiently small..." or "Assume that $x$, $y$, and $z$ are the coordinates...". These are statements meant to instantiate some kind of object, not to introduce a conditional (at least, that is how it reads to my ear). Commented Dec 25, 2023 at 18:10
• I'm sure they are an "if statement" - compare "Were I a millionaire, I would buy a palace." = "If I were a millionaire, I would buy a palace." and "Had I £1 million, I would buy a palace." = "If I had I £1 million, I would buy a palace.". That said, the OP has given no real context and Let and if carry much the same meaning. Commented Dec 25, 2023 at 18:19
• I am conveying to you how I read that language, as a trained mathematician. As you say, there is context missing, but all of these appear to be examples of instantiation, not conditionals. You are free to ignore me, but your interpretation does not sound right to my mathematically trained ear. Commented Dec 25, 2023 at 18:24

It's archaic, but with that in mind it is arguably correct. Only arguably so, however: most native speakers would probably (as you see here) call it incorrect, because they aren't well versed in early modern English. The subjunctive mood is all but gone from the present-day language.

It will certainly make your readers stumble, and that is unlikely to be your goal. You are probably well advised to stick to the idiomatic "let X be" or "assume X is," etc.

Also, the construction "be X" meaning "whether X be true" or "even though X be true" is probably closer to most people's minds, as in the example mentioned in a comment "be it ever so humble, there's no place like home." Reading your second example, I would think you're going in that direction, which would be wrong.

Another factor: you can read "let x = 10" as "let X equal ten," which is an idiomatic English sentence, but in the subjunctive mood it should be "be X 10" (or more obscurely "equal X 10"). Seeing "be x = 10" I'm a bit confused as to what words I should pronounce, but "be X 10" is rather cryptic.

• I think it also sounds wrong because Be can be used in the imperative: Be of good cheer; Death, be not proud. Commented Dec 24, 2023 at 18:41
• @AndrewLazarus Sounds like you're arguing that it sounds correct ;-) When we write "Let x be a number..." we want the imperative. We use "Let ... be" instead of "Be ..." specifically because there is no third-person imperative in English, and the "let" construction is as close as we can get to third-person imperative.
– Stef
Commented Dec 24, 2023 at 20:07
• @Stef But imperative "let X be ten" is addressed to the reader: second person imperative of "let" in tbe sense of "allow." When "be" is used as the second person imperative, it is an instruction to the listener to adopt some state ("be happy"), which it decidedly is not in a construction such as "be it now enacted...." Commented Dec 25, 2023 at 1:34
• @phoog Yes? I agree that there doesn't exist a third-person imperative in English and consequently that neither "let X be 10" nor "be X 10" are third-person imperative, since there is no such thing. Other that that I am not sure I understood your comment.
– Stef
Commented Dec 25, 2023 at 11:27
• Just because it was once correct, when early modern English was the spoken dialect, it doesn't mean it's correct now. Commented Dec 25, 2023 at 22:51