# Is this contains an open set?

1. Apr 9, 2010

### 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.

2. Apr 9, 2010

### SW VandeCarr

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.

Last edited: Apr 9, 2010
3. Apr 9, 2010

### Office_Shredder

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

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

4. Apr 10, 2010

### zli034

What's the difference?

5. Apr 10, 2010

### g_edgar

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

6. Apr 10, 2010

### SW VandeCarr

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.

Last edited: Apr 10, 2010