Question

how many rational number are there between 2.5 and 3

Answer 1

there infinity of numbers in between 2.5 and 3

Answer 2

2.5. but wait! there’s more! You can generate infinitely many rational numbers between 2 and 3.

an=an−1+2−n;a0=2an=an−1+2−n;a0=2

2,52,114,238,4716,9532...2,52,114,238,4716,9532...

2,2.5,2.75,2.875,2.9375,2.96875...2,2.5,2.75,2.875,2.9375,2.96875...

This entire infinite series is made up of rational numbers between 2 and 3!