· Portal  Help Search Members Calendar 
Welcome Guest ( Log In  Register )  Resend Validation Email 
Welcome to Did You Know? 
algebraic topology 
Posted: 15:10 Friday 30 March 2007

Renaissance Group: Friends Posts: 143 Member No.: 14 Joined: 20 Feb 2007 

JaneFairfax 
Posted: 20:38 Thursday 05 February 2009

The Enlightenment Group: Moderators Posts: 673 Member No.: 20 Joined: 03 Mar 2007 
Did you know? Cauchy sequences of rational numbers can be added and multiplied term by term, and the results are also Cauchy sequences of rataional numbers. Indeed, under these operations, the set of all Cauchy sequences or rational numbers forms a commutative ring with zero element 
algebraic topology 
Posted: 10:41 Friday 06 February 2009

Renaissance Group: Friends Posts: 143 Member No.: 14 Joined: 20 Feb 2007 
Did you know? The elements of are equivalence classes of the equivalence relation ~ defined on by 
JaneFairfax 
Posted: 14:01 Friday 06 February 2009

The Enlightenment Group: Moderators Posts: 673 Member No.: 20 Joined: 03 Mar 2007 
Did you know? Cauchy sequences of rational numbers provide one of two principal methods of constructing the real numbers from the rational numbers. The other method, which I read about in A Survey of Modern Algebra by Garrett Birkhoff and Saunders MacLane a long time ago, is by means of Dedekind cuts. 
algebraic topology 
Posted: 16:34 Friday 06 February 2009

Renaissance Group: Friends Posts: 143 Member No.: 14 Joined: 20 Feb 2007 
Did you know? The construction of the reals from the rationals (whether by Cauchy sequences or by Dedekind cuts) involves the creation of a complete ordered field. 
JaneFairfax 
Posted: 18:12 Friday 06 February 2009

The Enlightenment Group: Moderators Posts: 673 Member No.: 20 Joined: 03 Mar 2007 
Did you know? Birkhoff & MacLane’s book also gives a proof of the result that any two complete ordered fields are isomorphic. 
algebraic topology 
Posted: 01:11 Wednesday 11 February 2009

Renaissance Group: Friends Posts: 143 Member No.: 14 Joined: 20 Feb 2007 
Did you know? Cauchy sequences are named after the French mathematician Augustin Louis Cauchy. 
JaneFairfax 
Posted: 16:30 Wednesday 11 February 2009

The Enlightenment Group: Moderators Posts: 673 Member No.: 20 Joined: 03 Mar 2007 
Did you know? Dedekind cuts are named after the German mathematician Richard Dedekind. 