Don't Let the Media Distort the Rubi Rose Leaked Reality - Postcolonial Perspectives
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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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. If you distort a statement, fact, or idea, you report or represent it in an untrue way. The media distorts reality; categorises people as all good or all bad. [VERB noun] The minister has said his remarks at the weekend have been distorted. [VERB noun] Leaked documents suggest President Trump will use his first White House Correspondents’ Dinner appearance as a platform to target media outlets critical of him.
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