00:01
Hi there, in this question, we have to show that the set s is equal to 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 is compact.
00:12
So, first let's see what is combat.
00:17
A set is said to be compact if every open cover of the set has a finite subcover.
00:24
But more than this thing, we can use a particular result here.
00:30
The result is called as hain -boril theorem, that is if ain, a is a subset of r, then a is compact if and only if a is closed and bounded.
00:41
So here it is enough to show that the given set s, the given set s, we have to show that, we have to show that s is closed and bounded.
00:59
So first let us see how s is closed.
01:05
For that we have another result that is every final.
01:08
Set is closed.
01:10
So we can see that here s is the set 1 .2, 3, 4, 4, 5, 6, 7, 7, 8, 9, 9, 10.
01:21
So the number of elements of s, that is cardinality of s is equal to 10 and that is less than infinity...