# Is this contains an open set?

by zli034
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 P: 103 On the number line R, does [-1,$$\infty$$) contain an open set? because it includes -1, don't think it is an open set.
P: 2,499
 Quote by zli034 On the number line R, does [-1,$$\infty$$) 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 {$$[-1,\infty)$$} then it contains at least one half open subset.
 Emeritus Sci Advisor PF Gold P: 4,500 Is the question: Is $$[-1, \infty)$$ an open set? Or is the question: Does $$[-1, \infty)$$ contain an open set?
P: 103
Is this contains an open set?

 Quote by Office_Shredder Is the question: Is $$[-1, \infty)$$ an open set? Or is the question: Does $$[-1, \infty)$$ contain an open set?
What's the difference?
 P: 607 It is not an open set. But it contains the open set (4, 7) for example.
P: 2,499
 Quote by g_edgar 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,$$\infty)$$ "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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