Denseness property

The rational numbers are dense on the set of real numbers. The irrational numbers are also dense on the set of real numbers. This means that they are packed so crowded on the number line that we cannot identify two numbers right "next to" each other. If we take any two rational numbers, we can always find a rational number between them. In fact, there are infinitely many rational numbers between them!

Example: find a rational number between 3/8 and 3/5

Question: are the whole numbers dense on the set of real numbers? Why or why not?