Greek Philosophy
Irrational numbers are real numbers that cannot be expressed as a simple fraction, meaning they cannot be written as the ratio of two integers. These numbers have non-repeating, non-terminating decimal expansions, which sets them apart from rational numbers. In the context of Pythagorean philosophy, irrational numbers challenge the Pythagoreans' belief in the ultimate harmony and completeness of numerical relationships, highlighting the complexities of mathematics and reality.
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