Question:
Between two rational numbers
(a) there is no rational number
(b) there is exactly one rational number
(c) there are infinitely many rational numbers
(d) there are only rational numbers and no irrational numbers
Solution:
(c) Between two rational numbers, there are infinitely many rational numbers.
e.g., $\frac{3}{5}$ and $\frac{4}{5}$ are two rational numbers, then $\frac{31}{50}, \frac{32}{50}, \frac{33}{50}, \frac{34}{50}, \frac{35}{50}, \ldots$ are infinite rational numbers between them.
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