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