Question

What is the difference between an open interval and a closed interval?

Answer 1

Hint: In mathematics, a real interval is a set of real numbers that contains all real numbers lying between any two numbers of the set. The intervals of real numbers can be categorized into eleven different types: empty, degenerate, open, closed, left-closed right open, left-open right closed, left open, left closed, right open, right closed, unbounded at both ends.

Complete step by step answer:
An open interval is a type of interval that does not include its end points. We indicate open intervals by parentheses. For example, \[\left( {0,100} \right)\], is an open interval set. It means any number greater than \[0\] and less than \[100\]. Here, we exclude both the end points that are \[0,100\].
Mathematically,
\[\left( {0,100} \right) = \left\{ {x|0 < x < 100} \right\}\]
A closed interval is a type of interval that includes its end points also. We represent a closed interval by square brackets. For example, \[\left[ {0,100} \right]\], is a closed interval. It means any number greater than or equal to zero and less than or equal to hundred.
Mathematically,
\[\left[ {0,100} \right] = \left\{ {x|0 \leqslant x \leqslant 100} \right\}\]

Note:Bounded intervals are bounded sets, which means that their diameter, i.e the absolute difference between the end points is finite. The diameter is also called the length, size, width, measure, or range. The centre of bounded intervals with endpoints \[a,b\] is \[\left( {\dfrac{{a + b}}{2}} \right)\], and its radius is equal to \[\dfrac{{|a - b|}}{2}\]. These concepts are not defined for the empty or the unbounded sets. The size of unbounded intervals is usually defined to be infinity whereas the size of the empty interval may be defined as zero.