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A Set in a Metric Space $(X,d)$ is bounded if it has a Finite diameter, i.e., there is an $R<\infty$ such that $d(x,y)\leq R$ for all $x,y\in X$. A Set in $\Bbb{R}^n$ is bounded if it is contained inside some Ball ${x_1}^2+\ldots+{x_n}^2\leq R^2$ of Finite Radius $R$ (Adams 1994).

See also Bound, Finite


Adams, R. A. Calculus: A Complete Course. Reading, MA: Addison-Wesley, p. 707, 1994.

© 1996-9 Eric W. Weisstein