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?