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Mathematics
Calculus
How do you define unboundedness in Euclidean space?
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[QUOTE="member 587159, post: 6230781"] Boundedness is a metric concept, open sets is a topological concept so you shouldn't try to define boundedness via topological properties. Why don't you take the negation of the definition of boundedness Spivak provides? Thus, a set ##A## is unbounded if it is not contained in a rectangle. I.e., for every rectangle ##D## we have that ##A \not\subseteq D##, or equivalently for every rectangle ##D##, there is ##a \in A \setminus D##. Another fun characteristation of boundedness in this context: A set ##A## is unbounded if this set contains a sequence of elements ##(a_n)_n## such that ##\Vert a_n \Vert \to \infty##. On an unrelated note: what is your background on calculus/real analysis? This book my Spivak is hard to read if you don't have the proper background. [/QUOTE]
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Mathematics
Calculus
How do you define unboundedness in Euclidean space?
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