Is it encouraged for users to delete answers with no upvotes, I understand we are encouraged to delete answers with negative votes by the reputation system, but what about answers with 0 votes? I suppose we should delete them whenever they are posted on a question that already has upvoted answers, and leave them up on unanswered question, is this correct?
Generally, I advise against deleting answers merely based on their score. Even the automatic processes do not do that: they take other factors into consideration.
I have a few negatively scored answers (some at -4) that I wouldn't consider deleting; and a bunch of positively scored answers that I deleted. It depends on what's in the answer, and how it relates to the question and possibly other answers. Not the score.
"A critic is a man who knows the way but cannot drive the car" - K.Tynan
So unless someone point out the fault in your answer, no votes or downvotes should not make you delete it. Sometimes I like to elaborate on answers from very basics which most people will avoid but it might help some "not so bright" student to understand it. It doesn't mean answer is bad, it is just for that person who after browsing internet for an hour will stumble upon my answer and will be satisfied.