Which of the following is a closed statement? Question 16 options: A) z is a positive number. B) x is an odd number. C) 30 is an
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Answer:
a) Suppose that F is ordered in ascending order: . Then, the complement of F can be written as
which is the union of a finite number of open intervals, then is an open set. Thus, F is a closed subset of the real numbers.
b) Take an arbitrary element of F, let us say . Now, choose a real number
such that
there are not other element of F, because
is less that the minimum distance between
and its neighbors.
In case that we only consider
, and if
we only consider
.
Then, all points of F are isolated.
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