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From Latin dominus (“lord, head of household”), akin to Italian don, Sicilian don, Spanish don; from domus (“house”). Doublet of dom, domine, dominie and dominus. As a rule, we don't use the passive voice with "let".
Understanding the Context
"Allow" or "permit" is normally used instead: We were allowed to do whatever we wanted. We were permitted to drive the vehicle. 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.
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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. 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. Wish.com is a serious player in the world of online marketplaces, and is well known for offering an eclectic and often amusing mix of cheap, quirky items for sale online. But don't be fooled - our research has shown that some of the products it sells can vary from misleading to downright dangerous.
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