A number that can be expressed as the ratio of two integers p/q where q ≠ 0. This includes all integers, fractions, and terminating or repeating decimals.
From Latin 'rationalis' meaning 'of reason' or 'reasonable,' derived from 'ratio' meaning 'calculation' or 'proportion.' The term emphasizes that these numbers can be expressed as ratios, making them 'reasonable' or calculable in ancient mathematical thinking.
Rational numbers seemed to encompass all numbers until the Pythagoreans discovered that √2 couldn't be expressed as a fraction - a shocking discovery that shattered their belief in the rational nature of reality! This crisis led to the discovery of irrational numbers and revolutionized mathematics.
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