Day 231 · Aug 18

The History of Zero

Zero as a number – not just a placeholder – was developed in India by the 7th century, notably by Brahmagupta. He defined addition: a+0 = a; subtraction: a–0 = a; multiplication: a×0 = 0. He also struggled with division by zero, calling it ‘a fraction with zero as denominator’. Zero reached the Islamic world and then Europe via Fibonacci (1202). Without zero, our place‑value number system collapses. Zero also enables calculus (limits approach zero) and algebra (the additive identity). It took over 1,000 years to fully accept.

Why is division by zero undefined? Consider the limit 1/x as x → 0⁺ (positive) vs 0⁻ (negative). They diverge to +∞ and –∞ respectively – no single value.

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