give an example of a bounded set in R in which neither of the bounds belongs to the set.
Answer (1)
30th Nov, 2019
Consider an open set (a,b) where a, b are any two Real Numbers.
Then this open set (a, b) is bounded below by a but a does not lie in the interval. Also this set is bounded above by b but b does not lie in the set.
This is the general case.
If you want a particular case, then consider an open set (3, 4) and its bounds does not lie in the set.
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