- #1
Mr Davis 97
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With regard to the real number system, what is the importance of the Archimedean property and the property that the rationals are dense in ##\mathbb{R}## (which is a consequence of the Archimedean property)?
Related to this, what is the most general structure for which the Archimedean property holds? Is it an ordered field? If so, then why do analysis courses go through the procedure of proving it using the least upper bound property, when it can be proved in a more general way, without reference to the peculiarities of the real number system?
Related to this, what is the most general structure for which the Archimedean property holds? Is it an ordered field? If so, then why do analysis courses go through the procedure of proving it using the least upper bound property, when it can be proved in a more general way, without reference to the peculiarities of the real number system?