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.
Is a point of this site to help to socialize mathematics? How great is our obligation to help those learning to express themselves with mathematical precision? There is a broad spectrum of compassion within the user community. Some obvious homework questions are answered immediately. Some closed immediately. Do we want to have a site that welcomes mathematical explorers, or do we want to enforce discipline and rigor?

Most of the responders have mathematical skills, and they are stripped of social tools when a question is stripped of tone and context when encoded to a string of letters. We are reduced to inference, to guessing. Some users think poorly formed questions should be rebuffed. They may argue that condoning such behavior enforces bad habits. Some users try to add value and provide help not just for the OP, but anyone who looks at the question later.

Do we want the site diluted - or polluted - with extraneous questions? Or do we want to embrace the community at large, and accept a need for maturation? The site rewards users for removing poorly received questions. Should the reward be increased? Should the trustees of the site be entrusted to cull low value material?

The countervailing currents swirl.