Abstract
To review our progress to date, we have rigorously constructed three fundamental number systems: the natural number system N, the integers Z, and the rationals Q 1. We defined the natural numbers using the five Peano axioms, and postulated that such a number system existed; this is plausible, since the natural numbers correspond to the very intuitive and fundamental notion of sequential counting. Using that number system one could then recursively define addition and multiplication, and verify that they obeyed the usual laws of algebra.
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© 2016 Springer Science+Business Media Singapore
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Tao, T. (2016). The real numbers. In: Analysis I. Texts and Readings in Mathematics, vol 37. Springer, Singapore. https://doi.org/10.1007/978-981-10-1789-6_5
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DOI: https://doi.org/10.1007/978-981-10-1789-6_5
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Online ISBN: 978-981-10-1789-6
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