Talk:Real Number Ordering is Compatible with Multiplication

I believe this page should be removed and replaced by a redirect to Definition:Real Number Axioms. See Axiom RO2. (We need a redirect as many pages refer to this page.)

In any event, the property certainly does not follow from any property of the rational numbers. KarlFrei (talk) 02:21, 19 September 2018 (EDT)


 * If the justification is wrong, we rewrite the proof --prime mover (talk) 04:47, 19 September 2018 (EDT)


 * Perhaps I was unclear. I believe that there is nothing to show, as this is an axiom for the real numbers. See Definition:Real Number Axioms. This is the reason this page should be turned into a redirect. KarlFrei (talk) 04:50, 19 September 2018 (EDT)


 * It is only an axiom of the real numbers if we declare them axiomatic. If we derive the properties of the real numbers by defining the reals as the set of limits of Cauchy sequences on the rationals (having defined the rationals via the integers and natural numbers from ZF or ZFC, they are not axiomatic but are derived. That is the reason for the existence of this page. --prime mover (talk) 06:59, 19 September 2018 (EDT)


 * Ah I see. Thank you! KarlFrei (talk) 07:16, 19 September 2018 (EDT)