tsirel said:Probably you mean not a finite combination, but the union of an infinite sequence, like
[tex](a,b) = [a+1,b-1] \cup [a-0.5,b+0.5] \cup\dots[/tex]
CompuChip said:It's not, and it's not open either. But I kind of hoped you would see how to write (-inf, a] as a union of closed sets. And I don't think a finite combination is possible, since any finite union or intersection of closed sets is closed, right?
An open interval is defined as a set of numbers that includes all the values between two given numbers, but does not include the endpoints. In contrast, a closed interval includes the endpoints as well.
The notation for open and closed intervals was established to clearly distinguish between the two types of intervals. The use of parentheses for open intervals indicates that the endpoints are not included, while the use of brackets for closed intervals indicates that the endpoints are included.
To determine if an interval is open or closed, you must look at the notation used to represent the interval. If the interval is written as (a,b), it is open. If it is written as [a,b], it is closed.
Yes, it is possible to convert open intervals to closed intervals and vice versa. This is done by changing the notation used to represent the interval. For example, the open interval (a,b) can be converted to a closed interval by changing it to [a,b]. Similarly, the closed interval [a,b] can be converted to an open interval by changing it to (a,b).
Open and closed intervals are commonly used in mathematics to represent ranges of values. They are often used in calculus to denote the domain of a function or to represent a solution set. They are also used in set theory and are an important concept in understanding the continuity of functions.