1 TB. - Calculus

Question

Intervals: What is meant by an open interval in R? What is meant by a closed interval in R? Is every interval either open or closed? 

Step-by-Step Solution

Answer

An open interval does not include its endpoints, and a closed interval includes its endpoints.

Not every interval is either open or closed.

Step 1: Given information

Determine the open and closed interval in R? Is every interval either open or closed? 

Step 2: Definition of the closed and open interval.

An open interval does not contain endpoints.

Parentheses represent open intervals. For example, $(0,3)$. Here 0 and 3 are not in the interval.

A closed interval contains the endpoint of the interval and is indicated by the square brackets.

For example $[0,3]$. Here the endpoints 0 and 3 are in interval.

Interval can be a half-open interval that includes only one of its endpoints.

So, not every interval is either open or closed.