My apologies if my question is not appropriate for this forum. In mathematical writing, one often needs to let certain letters denote certain mathematical objects. For example:

"Let X be a number. Let Y be a set."

I am confident the following examples are correct ways to combine the above two sentences into one.

  • "Let X be a number; let Y be a set."
  • "Let X be a number, and let Y be a set."

However, I do not know if either of the following are correct.

  • "Let X be a number and Y be a set."
  • "Let X be a number and Y a set."

My question is this: which of the latter two are grammatically correct (or incorrect) and why?

closed as off-topic by Armen Ծիրունյան, MrHen, cornbread ninja 麵包忍者, Kristina Lopez, Hellion Oct 25 '13 at 15:11

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Both are fine, as Barrie said. What may be making you question your own judgment here is the novelty of the locution or the fact that you are talking about X’s and Y’s. Under these circumstances, if you’re wondering about grammaticality, it is often useful to preserve the grammatical form while switching to more familiar words. If you ask whether the following are grammatical, the answer is (hopefully) an obvious “yes”:

Let Mary eat bread and John drink chocolate.

Let Mary eat bread and John, chocolate.

And, if they are grammatical, then so are the sentences you gave.


Both are grammatical. The second has the advantage of being slightly shorter.

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