Question

What is the difference between set notation and interval notation?

Answer 1

Hint: The difference between set and interval is that an interval is a set that consists of all real numbers between a given pair of numbers. An endpoint of an interval is either of the two points that mark the end of the line segment.
From the above hint, we have had a clear picture regarding the difference between set and an interval.

Complete step-by-step solution:
Now let us note down the difference between the set notation and interval notation.
We can identify the fact that there is only the difference in the way they are represented. When we represent a set with set notation, we look for a characteristic that identifies the elements of our set.
For example, if we want to represent the set of all the numbers that are greater than 3 and less than 8, we write it as
$$\{x\in R\mid 3<x<8\}$$
The above is the set notation.
Now let us see the interval notation:
For a set to be notified in the interval notation, we should know the upper limit as well as the lower limit of all the intervals that compose the set.
For example, if our set is composed by all the numbers smaller than 2, or between 30 and 50, or greater than 120, we write the following union of intervals:
$$(-\mathrm{\infty },2)\cup (30,50)\cup (120,\mathrm{\infty })$$
This can also be notified in the set notation in the following way:
$$\{x\in R\mid x<2\text{ or }30<x<50\text{ or }x>120\}$$

Note:We can observe that characterization of a set is rather complicated. So we prefer the set notation to the interval ones because it requires set functions like unions to be used. In some cases, it would be impossible to note it which includes irrational numbers too.