# "Let A be a set, [let] B [be] a group"

Let A be a set.

This is easy. But what about introducing several things in that manner?

1. Let A be a set, B be a group, and C be a number.
2. Let A be a set, let B be a group, and let C be a number.
3. Let A be a set, B be a group, and let C be a number.
4. Let A be a set, B a group, and C a number.

Which is the most correct one?

As Benjamin Wade comments, 4) is the most concise. 1) and 2) are long-winded but consistent in their presentation of the premises, and 3) is inconsistent (and hence has the least desirable wording).

I think that "Let A be a set, let B be a group, and let C be a number." is the most formal phrasing. Since this is a mathematically formal usage, I think that would be preferred, but I don't think any of the phrases you presented are wrong, and "Let A be a set, B a group, and C a number." is shorter and more succinct.

On a separate note, we have a sister site for Math you might consult.

The first form is the most appropriate one:

Let A be a set, B be a group, and C be a number.

• .............Why? May 23, 2014 at 11:07
• Mathematics books support this form . Remember clearly using it while solving the questions. May 23, 2014 at 11:33
• Mathematics books and articles also adopt other forms. It's rare that a balanced answer is given if one relies solely on venerating a particular style one has encountered. May 23, 2014 at 14:33