$S = 1,1.1,0.9,1.01,cdots$
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$S = 1,1.1,0.9,1.01,cdots$
The following conclusions I drew from the set:
The set is bounded with $sup S = 1.1$ and $inf S = 0.9$, thus the bound is attained by the set.
The interior of the set is empty. The set is closed, and hence compact.
What will be the limit points of the set?
Also please verify the conclusions. Thank You.
calculus real-analysis elementary-set-theory supremum-and-infimum
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up vote
1
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$S = 1,1.1,0.9,1.01,cdots$
The following conclusions I drew from the set:
The set is bounded with $sup S = 1.1$ and $inf S = 0.9$, thus the bound is attained by the set.
The interior of the set is empty. The set is closed, and hence compact.
What will be the limit points of the set?
Also please verify the conclusions. Thank You.
calculus real-analysis elementary-set-theory supremum-and-infimum
add a comment |Â
up vote
1
down vote
favorite
up vote
1
down vote
favorite
$S = 1,1.1,0.9,1.01,cdots$
The following conclusions I drew from the set:
The set is bounded with $sup S = 1.1$ and $inf S = 0.9$, thus the bound is attained by the set.
The interior of the set is empty. The set is closed, and hence compact.
What will be the limit points of the set?
Also please verify the conclusions. Thank You.
calculus real-analysis elementary-set-theory supremum-and-infimum
$S = 1,1.1,0.9,1.01,cdots$
The following conclusions I drew from the set:
The set is bounded with $sup S = 1.1$ and $inf S = 0.9$, thus the bound is attained by the set.
The interior of the set is empty. The set is closed, and hence compact.
What will be the limit points of the set?
Also please verify the conclusions. Thank You.
calculus real-analysis elementary-set-theory supremum-and-infimum
calculus real-analysis elementary-set-theory supremum-and-infimum
asked Aug 30 at 4:27
user8795
5,36561843
5,36561843
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1 Answer
1
active
oldest
votes
up vote
0
down vote
accepted
All your conclusions are correct.
The only limit point of the set is $1$,since you are approaching from both sides.
All the other points are isolated points.
add a comment |Â
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
0
down vote
accepted
All your conclusions are correct.
The only limit point of the set is $1$,since you are approaching from both sides.
All the other points are isolated points.
add a comment |Â
up vote
0
down vote
accepted
All your conclusions are correct.
The only limit point of the set is $1$,since you are approaching from both sides.
All the other points are isolated points.
add a comment |Â
up vote
0
down vote
accepted
up vote
0
down vote
accepted
All your conclusions are correct.
The only limit point of the set is $1$,since you are approaching from both sides.
All the other points are isolated points.
All your conclusions are correct.
The only limit point of the set is $1$,since you are approaching from both sides.
All the other points are isolated points.
answered Aug 30 at 4:36
Mohammad Riazi-Kermani
31k41853
31k41853
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add a comment |Â
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