> >"Never begin a science [or mathematics] tossup with a straightforward >definition of the answer." > >That's right, NEVER. Whoever wrote the "continuous" question may have >thought they were giving some obscure initial clue, but "the inverse >image of an open set is open" is the definition of continuous. Period. >Maybe you think basic point-set topology is advanced, but it isn't. >This is the definition anyone who knows anything about real >mathematics uses. Epsilon-delta stuff is ok for basic analysis, but >it's not the definition of continuous in full generality. Ok, I wasn't there, and I haven't seen the question, but from my point of view, this comment is ridiculous. Acfraud is lambasting NAQT for starting a question with a clue which the experts will know quickly while other people will still have a chance later by putting it in (sometimes advanced) calculus terms or in more basic terms at the end. Of course, the "inverse-image" definition is the most general one, but very few people meet it before their senior year as math majors, or even in grad school. I, for one, much prefer this to something with vague similies or ambiguous characterizations at the start, which happens much more frequently. Alex >The problem with giving a definition - which is possible in >mathematics questions to a larger degree than in other fields - in the >first clue is that, to do *anything* with a term, you need to know the >definition. This means that almost anyone with knowledge of a subject >is equally capable of answering the question at that point, and you >get a buzzer race. In practice, some may know anecdotal facts without >knowing the definition of a term, and so could potentially answer such >a question later, but in general, *if one knows anything about a >mathematical term, one knows the definition*.
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