Soogsx Leaks: Don't Let Fear Hold You Back - Postcolonial Perspectives
MSN: Handyman reveals shockingly easy trick to avoid costly toilet leaks: 'Please don't ever stop giving tips and tricks' Handyman reveals shockingly easy trick to avoid costly toilet leaks: 'Please don't ever stop giving tips and tricks' InvestmentNews: 'Independence Stories': Don't let fear of the unknown hold you back 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.
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Key Insights
The verb let means “allow”, “permit”, “not prevent or forbid”, “pass, go or come” and it's used with an object and the bare infinitive. Are you going to let me drive or not? Don't let h... Thus you don't need to always change each Let's/Let us with a "replacement" however we will presume you do, so we could replace let us with We want to see x and y. AOL: Ladies, let’s talk about bladder leaks as you age … because nobody does Ladies, let’s talk about bladder leaks as you age … because nobody does