Any number that can be found on the number line, including all rational and irrational numbers. Real numbers can be positive, negative, or zero, and include integers, fractions, and numbers like π and √2.
The term 'real' emerged in the 17th century to distinguish these numbers from 'imaginary' numbers when complex numbers were being developed. 'Real' emphasizes that these numbers correspond to actual quantities that can be measured on a continuous scale.
Real numbers fill the number line so completely that between any two real numbers, there are infinitely many others - yet this 'completeness' wasn't rigorously defined until the 19th century! This led to profound insights about infinity and the foundations of calculus.
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