As a rule, we don't use the passive voice with let. Moreover, there is a sense. Let s is the english cohortative word, meaning let us in an exhortation of the group including the speaker to do something.
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Allow or permit is normally used instead: 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. We were allowed to do whatever we.
I think that let a be a set, let b be a group, and let c be a number. is the most formal phrasing.
Lets is the third person. In let's get started, the starting point is in view and let's get going, you are on the starting point already. Since this is a mathematically formal usage, i think that.
