Difference between revisions of "Bounded"
(New page: Intuitively, a set is '''bounded''' if the distances between its points are all less than some finite real number (the ''bound''). Formally, we say that a subset <math...) |
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Latest revision as of 17:37, 15 February 2008
Intuitively, a set is bounded if the distances between its points are all less than some finite real number (the bound). Formally, we say that a subset 
of a metric space 
(such as the standard Euclidean plane, 
with distance 
), is bounded if for some 
there exists some 
such that for all 
, 
.
Note that if a set is bounded, the choice of 
is immaterial if are willing to change the bound: we have by the triangle inequality that 
for all .
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