It ought to be common knowledge that you should answer only questions that you know an answer to. Well, sometimes mistakes can happen and the answer becomes erroneous. That usually happen because
1.) You were simply mistaken, the question turn out to be harder or more subtle that you originally thought.
2.) You misread or misunderstood the question.
3.) Your hand-waving is not logically valid, leading to false answer.
Even the best mathematicians are sometimes tainted by these mistakes. I've once seen a very high rep user answer an easy question on the continuity of some function wrongly because he was very tired and sleepy (that's what he claimed).
However, there some certain people that attempt to answer questions that they have no clue about. Examples are
1.) Trying to answer a question on integrability without even knowing the definition of Riemann or Lebesgue integral.
2.) Answering question about well-defined-ness of a function while not knowing when a function (on an equivalent class) can fail to be well-defined.
3.) Justifying a vague answer using some philosophical stance that no one seems to share.
4.) Having bad grasp of real analysis in general, leading to wrong ideas of concepts in calculus i.e. limit, differentiation and integration.
It seems that they never had a proper systematic education about the topic they were trying to answer and, instead, basing thier answer on factual facts that they don't fully understand. The problem is that this kind of people tend not to delete their answers even when they're downvoted into oblivion, and usually stay true to their faith even when people are explaining to them why they are wrong.
What is the best way to deal with this kind of people? It is true that the voting system is already there to screen off bad answers and it seems to be working quite well. However, I believe that this kind of behavior should be discouraged. Indeed, the previous 4 examples come from the same person. The page Help Center > Answering doesn't seem to have a clear policy on this so I am asking it here.