Science Forum - Dedekind Cuts Make Dedekind cuts of the ordered set of rationals, and note that, as one of the resulting subsets is open at the cut, then that set will contain the http://thescienceforum.com/Dedekind-cuts-684t.php
Dedekind Cut - Need Help With Proof 2 posts 1 author(p is a positive rational number x is a Dedekind cut) - Eq(qex ~ p +q e x) First note that a Dedekind cut is not all of the rationals -this http://www.mathkb.com/Uwe/Forum.aspx/math-logic/3955/Dedekind-cut-need-help-with
Information 2 posts 1 author - Last post Oct 10show that {r IN Q r^3 2} is a dedekind cut. {r in Q r^3 2} = {r in Q r ( 2^(1/3))} i) http://www.mymathforum.com/viewtopic.php?f=22&t=16303
Extractions: Skip to main content Help Contact Us Trusted archives for scholarship The JSTOR site requires that your browser allows JSTOR ( http://www.jstor.org ) to set and modify cookies. JSTOR uses cookies to maintain information that will enable access to the archive and improve the response time and performance of the system. Any personal information, other than what is voluntarily submitted, is not extracted in this process, and we do not use cookies to identify what other websites or pages you have visited. JSTOR is part of ITHAKA, a not-for-profit organization helping the academic community use digital technologies to preserve the scholarly record and to advance research and teaching in sustainable ways.
Dedekind, Richard Apr 2, 2008 While teaching calculus for the first time at the ETH Zürich Polytechnic, Dedekind came up with the notion now called a Dedekind cut (in http://www.newworldencyclopedia.org/entry/Richard_Dedekind
Extractions: Jump to: navigation search Previous (Richard Daley) Next (Richard Felton Outcault) Richard Dedekind Julius Wilhelm Richard Dedekind (October 6, 1831 – February 12, 1916) was one of the major German mathematicians in the late nineteenth century who did important work in abstract algebra, algebraic number theory, and laid the foundations for the concept of the real numbers. He was one of the few mathematicians who understood the importance of set theory developed by Cantor Dedekind argued that the numbers system can be independently developed from geometrical notations and that they are grounded in and derived from a certain inherent creative capacity of the mind, which were some of those issues debated by Bolzano, Cantor Frege , and Hilbert. Dedekind was the youngest of four children of Julius Levin Ulrich Dedekind. He was born, lived most of his life, and died in Braunschweig (often called "Brunswick" in English). In 1848, he entered the Collegium Carolinum in Braunschweig, where his father was an administrator, obtaining a solid grounding in mathematics. In 1850, he entered the University of Göttingen. Dedekind studied number theory under Moritz Stern. Gauss was still teaching, although mostly at an elementary level, and Dedekind became his last student. Dedekind received his doctorate in 1852, for a thesis titled
