Is this contains an open set?


by zli034
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zli034
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#1
Apr9-10, 07:37 PM
P: 103
On the number line R, does [-1,[tex]\infty[/tex]) contain an open set?

because it includes -1, don't think it is an open set.
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SW VandeCarr
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#2
Apr9-10, 08:39 PM
P: 2,490
Quote Quote by zli034 View Post
On the number line R, does [-1,[tex]\infty[/tex]) contain an open set?

because it includes -1, don't think it is an open set.
It's a half open interval that you've shown. If you define a set {[tex][-1,\infty)[/tex]} then it contains at least one half open subset.
Office_Shredder
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#3
Apr9-10, 09:01 PM
Mentor
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Is the question: Is [tex] [-1, \infty)[/tex] an open set?

Or is the question: Does [tex] [-1, \infty)[/tex] contain an open set?

zli034
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#4
Apr10-10, 08:23 AM
P: 103

Is this contains an open set?


Quote Quote by Office_Shredder View Post
Is the question: Is [tex] [-1, \infty)[/tex] an open set?

Or is the question: Does [tex] [-1, \infty)[/tex] contain an open set?
What's the difference?
g_edgar
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#5
Apr10-10, 12:17 PM
P: 608
It is not an open set. But it contains the open set (4, 7) for example.
SW VandeCarr
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#6
Apr10-10, 05:16 PM
P: 2,490
Quote Quote by g_edgar View Post
It is not an open set. But it contains the open set (4, 7) for example.
I guess I'm not understanding the OP's question. Any non zero interval on the reals "contains" every possible combination: [a,b],(a,b),(a,b],[a,b). Any such interval has a bijective mapping to the entire set of reals, so of course the interval [-1,[tex]\infty)[/tex] "contains" open sets.

EDIT: Perhaps I'm mistaken, but in terms of open and closed sets or subsets, I'm considering the actual membership of a given set to be dependent on the specification (choice) of that set. Therefore I could specify that every subset of C:C subset of R be closed.


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