SkipCaptcha, Automoderated users, edit
3,266
edits
Changes
Jump to navigation
Jump to search
Line 1:
Line 1: + +
Article needs work!
Previously someone had written that Dedekind cuts called the concepts of real numbers into question, and that Dedekind cuts relied on the use of the axiom of choice. I've never heard such an insanely wrong description of Dedekind cuts, so I removed the statement. Dedekind cuts most certainly do NOT rely on choice in their description. Moreover, the purpose behind Dedekind cuts is that they allow one to construct the real numbers out of the rationals. So far from calling the existence of the reals into question, Dedekind put the definition of the reals onto solid ground.--[[User:Mathoreilly|Mathoreilly]] 11:02, 2 July 2008 (EDT)
Previously someone had written that Dedekind cuts called the concepts of real numbers into question, and that Dedekind cuts relied on the use of the axiom of choice. I've never heard such an insanely wrong description of Dedekind cuts, so I removed the statement. Dedekind cuts most certainly do NOT rely on choice in their description. Moreover, the purpose behind Dedekind cuts is that they allow one to construct the real numbers out of the rationals. So far from calling the existence of the reals into question, Dedekind put the definition of the reals onto solid ground.--[[User:Mathoreilly|Mathoreilly]] 11:02, 2 July 2008 (EDT)
I agree. Any mathematician who was concerned about Dedekind cuts relying on the axiom of choice was just wrong. They have nothing to do with AC. Nor did they "undercut the assumption of the continuity of the real line". They put the continuity on a firm basis. Nor did they create gaps. They filled them. [[User:SamHB|SamHB]] 22:30, 20 August 2008 (EDT)