True or false: how many rationals lie between two rationals

Exercise and reference answers

Questions

1. Statement is true

   Yes

   Statement

   Between any two rational numbers there are countless others.

2. Statement is true

   Yes

   Statement

   The mean of two rationals lies between them.

3. Statement is true

   No

   Statement

   Only a finite number of rationals lie between two rationals.

4. Statement is true

   Yes

   Statement

   Taking means repeatedly keeps producing new rationals in between.

5. Statement is true

   No

   Statement

   Two rationals can be adjacent with nothing in between.

Explanation