
Re: Foundations of real numbers
Posted:
Oct 12, 2012 9:40 AM


For the beginning of a subject, sometimes the choices made are limited.
For example: I can imagine* a textbook that begins by postulating a complete ordered field R. (Complete in the order sense.) Then constructing, within R, the set N or natural numbers. Sometime later defining "sequence" as a function with domain N. And only still later defining "Cauchy" sequence. So, for this arrangement the least upper bound axiom makes perfect sense.
* Perhaps called CALCULUS, written by M. Spivak ...
 G. A. Edgar http://www.math.ohiostate.edu/~edgar/

