1

Math proves often start with "let". For example:

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?

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3

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).

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2

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.

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2

The first form is the most appropriate one:

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

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3
  • 1
    .............Why?
    – Edwin Ashworth
    May 23 '14 at 11:07
  • Mathematics books support this form . Remember clearly using it while solving the questions.
    – Veronica Diamond
    May 23 '14 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.
    – Edwin Ashworth
    May 23 '14 at 14:33

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