From Hull AWE
Several errors have occurred with the use of the verb 'to let'.
- Let, in such constructions as 'Let me', or 'Let him do it', is, in form, an imperative verb with an Object. (in terms of usage, it is felt to be politer than a plain instruction delivered as a simple base form verb. 'Let me do that' is a polite way of offering to do something for someone else.)
- A personal pronoun that follows let should be in the objective form: "Let
you and Iagree" is an error for 'you and me', who are the people being allowed, or encouraged, to agree.
- 'Let us' is the nearest English has to a 1st person imperative. It is in the plural, and so the suggestion should always include the person being addressed. In spoken English, that will include the person to whom the speaker is talking, whether one or a group. In academic writing, the writer is inviting the reader, usually to share some assumptions.
- "Let us assume that ..." implies that in order to continue the main discussion, the text will now pass over another matter, perhaps because it is of limited relevance, perhaps because it is a controversial subject that cannot be dealt with in the short space, for example, of an undergraduate assignment.
- "Let us now turn to ..." is a form of sign-posting a writer's argument: it suggests 'Now this text has finished [for its essay] with the previous topic , and the text is moving on to the topic of ...'
- In Maths and related subjects it is conventional to define (or assign) symbols such as x and y etc by using the words "Let x = [the numerical value of the quantity in question]." So assumptions are made: 'Let d = [or be] the distance travelled, and t be the time elapsed. Then the velocity v = d/t.'
- The phrase let alone is another formal imperative, which actually gives no orders. It means 'not to mention'. It is useful in academic writing, as it allows a writer, paradoxically, to mention a detail that will not be covered (~ 'I want to show that I know something I haven't got space to write about'.)
- Let's should not be used in academic English, where the more formal Let us is to be preferred, however stuffy it may feel to young writers.
Let's usis "absurd" (Burchfield's Fowler), and should be shunned. (It is simply redundant verbiage, and says 'let us us' - which is indeed absurd.)
- As a kind of substitute or polite imperative, the use of let is old, and the need for it is high enough. It should be used, even in academic writing - but not in the contracted form - wherever it is useful.