Let’s is the english cohortative word, meaning “let us” in an exhortation of the group including the speaker to do something. Lets is the third person singular present tense form of the verb let meaning. Aug 29, 2013i find the distinction that macmillan makes between not to mention and the supposedly synonymous let alone and still/much/even less useful:
The phrases let alone and still/much/even less. Jun 14, 2011i notice that "let alone" is used in sentences that have a comma. Feb 23, 2016in "let's get started", the starting point is in view and "let's get going", you are on the starting point already.
I think that "let a be a set, let b be a group, and let c be a number." is the most formal phrasing. Otherwise, know that a basic search will turn up let us in innumerable journal articles, official proclamations, formal invitations,. Jan 12, 2016don't let's forget the 1943 noel coward song "don't let's be beastly to the germans".
If we un-contract, it becomes "do not let us be beastly to the germans" which is perfectly acceptable. Oct 3, 2011"let us go/let us pray" is a special verb construction of the type let, imperative+us,accusative+bare infinitive.
