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Limit on the edge of the domain
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[QUOTE="mathwonk, post: 6863673, member: 13785"] pasmith: Indeed it adds nothing if someone knows that you are quantifying x to lie in the domain, but you are assuming that someone will understand this implicitly because you have later written f(x). So I just suggest, for clarity, you make explicit what the domain of your universal quantifier is, i.e. I recommend putting "for all x in the domain of f" instead of just "for all x". I make this suggestion partly because I myself had trouble understanding clearly what you meant by your post. I.e. I at first took it for granted that your universal quantifier was "for all real x". Thus I assumed you meant the (omitted) statement "x is in the domain of f" to be understood in the conclusion of your implication, rather than the hypothesis. Mark44: I was trying to second your comment. Indeed everything always depends on the definitions, so it makes no sense to ask whether something is true without giving the definition one is using for the terms involved. Many of us tend to assume everyone is using the same conventions and definitions that we are, and I think this is the basis of most misunderstandings. Cheers! [/QUOTE]
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Limit on the edge of the domain
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