Numerical answer
The five sentences below, labelled 1-5, can be arranged in a logical order to form a coherent paragraph. Enter the correct order as a five-digit number (e.g., 42135).
1. The concept of zero as a number in its own right, rather than merely a placeholder, emerged independently in ancient India by around the fifth century CE.
2. Babylonian and Mayan systems, for instance, used a placeholder symbol to indicate an empty position in a numeral, such as distinguishing 305 from 35.
3. Indian mathematicians, notably Brahmagupta, went further, treating zero as a number that could be added, subtracted, and multiplied according to explicit rules.
4. Earlier civilizations had recognized the need for something like zero long before this, but usually only as a placeholder within a positional numeral system.
5. This conceptual leap — from zero as an absent quantity to zero as a quantity itself — later travelled via Arab scholars into medieval Europe, where it transformed the practice of arithmetic.
1. The concept of zero as a number in its own right, rather than merely a placeholder, emerged independently in ancient India by around the fifth century CE.
2. Babylonian and Mayan systems, for instance, used a placeholder symbol to indicate an empty position in a numeral, such as distinguishing 305 from 35.
3. Indian mathematicians, notably Brahmagupta, went further, treating zero as a number that could be added, subtracted, and multiplied according to explicit rules.
4. Earlier civilizations had recognized the need for something like zero long before this, but usually only as a placeholder within a positional numeral system.
5. This conceptual leap — from zero as an absent quantity to zero as a quantity itself — later travelled via Arab scholars into medieval Europe, where it transformed the practice of arithmetic.
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Answer: 42135
Sentence 4 introduces earlier, placeholder-only uses of zero. Sentence 2 gives concrete examples of this (Babylonian, Mayan). Sentence 1 then contrasts this with India's independent conceptual leap to zero as a true number ('emerged independently'). Sentence 3 elaborates that leap with Brahmagupta's specific contribution, and sentence 5 concludes by tracing the idea's later spread to Europe. This gives the order 4-2-1-3-5.
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