A set-builder notation describes or defines the elements of a set instead of listing the elements. For example, the set { 1, 2, 3, 4, 5, 6, 7, 8, 9 } list the elements.
The same set could be described as { x/x is a counting number less than 10 } in set-builder notation.
We read the set { x / x is a counting number less than 10 } as the set of all x such that x is a counting number less than 10.
When the set is written as { 1, 2, 3, 4, 5, 6, 7, 8, 9 } , we call it the roster method.
You can list all even numbers between 10 and 20 inside curly braces separated by a comma. Again, this is called the roster notation.
However, could you use the roster notation to list all the prime numbers? See now when it is a good idea to use the set-builder notation.
Some sets are big or have many elements, so it is more convenient to use set-builder notation as opposed to listing all the elements which is not practical when doing math.
For example, instead of making a list of all counting numbers smaller than 1000, it is more convenient to write { x / x is a counting number less than 100 }
It is also very useful to use a set-builder notation to describe the domain of a function.
If f(x) = 2 / (x-5), the domain of f is {x / x is not equal to 5}
1) x > 9
Unless otherwise stated, you should always assume that a given set consists of real numbers.
Therefore, x > 9 can be written as { x / x > 9, is a real number }
2) The set of all integers that are all multiples of five.
{x / x = 5n, n is an integer }
3) { -6, -5, -4, -3, -2, ... }
{ x / x ≥ -6, x is an integer }4) The set of all even numbers
{x / x = 2n, n is an integer }
5) The set of all odd numbers
{x / x = 2n + 1, n is an integer }
Mar 29, 23 10:19 AM
Mar 15, 23 07:45 AM