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| Main Author: | |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2508.10750 |
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Table of Contents:
- We present an explicit bijection between finite-decimal real numbers and natural numbers ($\mathbb{N} = \{1, 2, 3, ...\}$) using a systematic 4-tuple parametrization with closed-form mathematical formulas for enumeration. Our enumeration system provides complete indexing of all real numbers with terminating decimal representations through the parametrization $(\text{sign}, N_1, N_2, N_3)$. Both forward and inverse mappings execute in O(1) constant time, achieved through closed-form lexicographic positioning formulas that eliminate enumeration loops. The system uses exact decimal arithmetic throughout, ensuring perfect accuracy across all representable numbers. This bijective correspondence demonstrates that finite-decimal real numbers can be systematically enumerated and indexed with optimal constant-time computational efficiency.