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zli034
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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.
because it includes -1, don't think it is an open set.
zli034 said: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.
Office_Shredder said:Is the question: Is [tex] [-1, \infty)[/tex] an open set?
Or is the question: Does [tex] [-1, \infty)[/tex] contain an open set?
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.g_edgar said:It is not an open set. But it contains the open set (4, 7) for example.
An open set is a subset of a mathematical space that does not contain any of its boundary points. In other words, all points within an open set are considered to be "interior" points.
To determine if a set is open, you can use the definition of an open set: if every point within the set has a neighborhood that is also contained within the set, then the set is considered open.
An open set does not contain any of its boundary points, while a closed set contains all of its boundary points. Additionally, a set can be both open and closed, known as a clopen set.
Yes, a set can be both open and closed. This type of set is known as a clopen set and is a property of certain mathematical spaces, such as topological spaces.
Open sets are important in mathematics because they allow for the definition of continuity and convergence, which are fundamental concepts in analysis and topology. They also play a key role in the definition of differentiable functions and the study of topological properties of spaces.