2015/03/14 by Weiss, Ittay
#00A05 #FOS: Mathematics #History and Overview (math.HO)
paper · doi:10.48550/arxiv.1503.04348
We present a detailed and elementary construction of the real numbers from the rational numbers a la Bourbaki. The real numbers are defined to be the set of all minimal Cauchy filters in ℚ (where the Cauchy condition is defined in terms of the absolute value function on ℚ) and are proven directly, without employing any of the techniques of uniform spaces, to form a complete ordered field. The construction can be seen as a variant of Bachmann's construction by means of nested rational intervals, allowing for a canonical choice of representatives.