what are open and closed numbers
Open and closed numbers are terms commonly used in mathematics to describe intervals and boundaries.
1. Closed Numbers: A closed number refers to a number that includes its endpoints or boundaries. In other words, the range or set of values includes the starting and ending points. Closed intervals are often denoted using square brackets [ ].
For example, if we have the closed interval [1, 5], it means that the range includes all real numbers from 1 to 5, including 1 and 5 themselves.
2. Open Numbers: On the other hand, an open number refers to a range or set of values that does not include its endpoints or boundaries. Open intervals are typically denoted using parentheses ( ).
For instance, if we have the open interval (2, 7), it means that the range includes all real numbers between 2 and 7, but excludes 2 and 7 themselves.
To determine whether a number is open or closed, you need to look at the notation used and examine if the endpoints are included or excluded based on the brackets and parentheses used.
It is important to note that the concepts of open and closed numbers can also be applied to infinite intervals, where the range extends indefinitely in one or both directions. In this case, the appropriate symbols (∞ or -∞) are used to represent infinity. For example, (2, ∞) would indicate all real numbers greater than 2, but not including 2 or any negative numbers.