Question: Is it in the spirit of Stack Exchange to always make a sincere attempt to interpret the OP's intentions? I believe it is.

Precision is important in maths, and where questions are imprecise it will often be helpful to address that imprecision. However I frequently see answers or comments which pick some logical fallacy or inaccuracy within a question, then to declare the question answered on the basis of it, while making apparently minimal attempt to interpret what the OP intended.

I think it's important to interpret the OP's intentions and to address the question they *intend* to ask, rather than some technicality. We will all have seen perhaps the stupidest example of this, in which the next number in some sequence is proposed by some method which can generate infinitely many candidates all having equal claim.

I am in favour of such stupidity attracting a waterfall of downvotes from the community.

Answer: 
I think it can be helpful, **in a comment**, to point out that the question, as read literally, has a trivial answer. This may help the asker to understand what assumptions or requirements may be missing. 

For instance, given the question:

> 
> Does there exist a topological space $X$ such that every continuous $f : X \to \mathbb{R}$ is constant?
> 
> 
> 

I might comment:

> 
> Yes, you could take $X$ to be a single point, or equip $X$ with the indiscrete topology. Perhaps you meant to require that $X$ should contain at least two points and be Hausdorff?
> 
> 
> 

But I would not post it as an answer; I would not claim that it answers the question; and I would not upvote such answers.
I think that sincere attempt is part of what a good answer requires.

I frequently think I know what the OP intended even though it's not what the question says. If the question is otherwise reasonable (shows effort, ...) I may answer (or comment), beginning

> 
> I think you mean ... if so
> 
> 
> 

sometimes, with just a hint when I think I can help the OP solve the problem her/himself.

When this strategy succeeds it helps everyone: the OP learns and the moderators have less work managing the close queue.

I (too) dislike (snarky) answers that are correct because they rely on the literal but clearly unintended meaning of the question.