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While fixing my notation in a research article, I want to write something like this:

Let A be a line and (let) B (be) a plane.

Question: Do I have to write the second let and be or can I omit one or both of them?

(The context is a research article in mathematics, if this should matter. In fact, I do not talk about lines and planes there, but use these terms here in the hope to make the phrase more accessible to non-mathematicians.)

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No, you do not need to have the second "let." That is simply redundant. However, you do need the second "be."

In reality, you are just writing out in words what we would normally write in symbols. On a math paper, I would write something like:

Let x = 27, y = 30, and z = 2

2x - yz = 2(27) - (30)(2) = -6

So in words, I get:

Let x be 27, y be 30, and z be 2.

We don't need the repeated "let."

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  • I'd argue that we don't really need any other be but the first. In fact, I always read "Let x = 27, y = 30, and z = 2" aloud as "Let x be 27, y 30, and z 2. I remember that we have a similar ELL question related to this kind of ellipsis. I'll add a link to the question if I can find it.
    – Damkerng T.
    Commented Nov 14, 2015 at 22:21
  • @DamkerngT. Interesting. Sure, definitely link me to it. I haver never thought of it that way, nor have I heard any teacher or professor read it that way.
    – Alex K
    Commented Nov 14, 2015 at 22:30
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    I couldn't find that ELL question, even though I'm pretty sure we have it! :-( However, I found a couple examples in Google Books: (e) (i) Let X be a group, Y a subgroup of X and h : Y --> C a positive definite function; 12.5.8 Corollary. Let X be a variety, Y a prevariety, Z a subset of Y and u, v be morphisms from Y to X such that u(y) - v(y) for all y <element-of-symbol> Z
    – Damkerng T.
    Commented Nov 14, 2015 at 22:47
  • @DamkerngT. ah. I see what you're talking about. Yes, "___ a _____" does seem to be a valid construction. I think that works for typecasting, but I don't think that would work for values. "Let x be 27, y a 30, and z a 2." Or maybe it does. Either way, nice find
    – Alex K
    Commented Nov 15, 2015 at 0:48
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    @DamkerngT. Are the authors of the books you are citing native English speakers? The second reference is written by two mathematicians working in France. I do not know if they are native English speakers. In French I think one would write "Soit A une droite et (soit) B un plan" if I am not mistaken. So there is no analogue of the "be" there. I do not know if Fremlin is a native English speaker. I am asking this question here, because I am mainly hoping for an answer with an explanation rather than examples of the use (but I do appreciate your references).
    – skew41
    Commented Nov 15, 2015 at 10:31

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