What is the difference between set notation and interval notation?
As the question states - it's just a different notation to express the same thing.
When you represent a set with set notation, you look for a characteristic that identifies the elements of your set. For example, if you want to describe the set of all number greater than
Which you read as "All the real number
On the other hand, if you want to represent the set with interval notation, you need to know the upper and lower bound of the set, or possibly the upper and lower bound of all the intervals that compose the set.
For example, if your set is composed by all the numbers smaller than
This same set can be written in set notation:
Finally, note that if the characterization of the set is rather complex, the set notation becomes preferable to the interval one, which would require a great number of intervals in the union. In some other cases, it could be literally impossible to write a set in interval notation, for example is you consider only irrational numbers, you write
but you can't write is as union of intervals.
See explanation below
Imagine we have to express
In this notation we define the characteristics of all
Interval notation is other way to say the same but assuming that