Does the Interval [-1,∞) Include Any Open Sets?

[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.

 

[SW VandeCarr]

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.

 

[Office_Shredder]

Is the question: Is [-1, \infty) an open set?

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

 

[zli034]

Is the question: Is [-1, \infty) an open set?

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

What's the difference?

 

[g_edgar]

It is not an open set. But it contains the open set (4, 7) for example.

 

[SW VandeCarr]

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.