As a rule, we don't use the passive voice with "let". "Allow" or "permit" is normally used instead: We were allowed to do whatever we wanted. We were permitted to drive the vehicle.

Understanding the Context

Accordi... 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.

Key Insights

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Final Thoughts

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