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