Open Set

The strategy below will be to build up to an example of an Open Set.

Let A={0,1,2,3}

The set A is finite. It consists of 4 integers on a number line. Let’s change it to being 0, 3 and all real values between 0 and 3.

B = [0,3]

The set B contains an infinite number of values on the number line between 0 and 3, and it also includes 0 and 3. Notice the [] notation.

C= (0,3)

Notice that the notation has changed. The set C has an infinite number of points between 0 and 3 but it does not include either 0 or 3.

This brings up an interesting result–we can’t answer the question “what is the smallest number in this set” and we can’t answer the question “what is the largest answer in this set?”

We can’t get to 0 but if you choose a nonzero positive value, we can get closer to zero than that number you picked. Let’s look at one way this can be done with algebra.

Let the nonzero positive value you picked, be the value ‘x’. We can get closer than that to zero with our value ‘y’ calculated below: