Question

Which option below demonstrates the correct notation for a continuous set of all numbers between 5 and 6, not including 5, but including 6?

Answer 1

The set is (5, 6]

Explanation:

Ok, let's see the different possibles notations to describe sets.

If we want to describe a discrete set, we use {}

Like in the set:

{1, 2, 3}

That set only contains the numbers 1, 2, and 3.

If we want to describe a continuous set that does not include the extremes, we use ()

For example:

(1, 3)

Contains all the numbers between 1 and 3, but does not include 1 and 3.

If we want to include the extremes, we need to use []

[1, 3]

This set is all the numbers between 1 and 3, including the values 1 and 3.

And we can mix these last two notations, so if we want a set that includes all the numbers between 5 and 6, not including 5 but including 6, we need to write:

(5, 6]