As of May 4 2007 the scripts will autodetect your timezone settings. Nothing here has to be changed, but there are a few things

## Tuesday, April 29, 2008

### The field of fractions of an integral domain

$V=\mathbb{Z}&space;\times&space;\mathbb{Z}&space;\backslash&space;\left\{0\right\}&space;\\&space;&space;R:&space;(a,b)\equiv&space;(c,d)&space;\Leftrightarrow&space;&space;ad=bc\\&space;&space;\\&space;&space;(a,b)&space;+&space;(c,d)&space;=&space;(ad&space;+&space;bc,&space;bd)\\&space;&space;(a,b)&space;\cdot&space;(c,d)&space;=&space;(ac,&space;bd)$

Create a set V of ordered pairs from {..., -2, -1, 0, 1, 2, ...} (integers) and {..., -2, -1, 1, 2, ...} (integers excluding 0). Elements of V are for example (3,1), (5,1) and (4,2).

Create an equivalence relation on elements of V. Two elements (a,b) and (c,d) are 'equivalent', 'belong to the same equivalence class' if ad=bc. For example (4,2) and (8,4) are equivalent while (4,1) and (8,4) are not.

Define addition '+' as (a,b) + (c,d) = (ad + bc, bd).

Define multiplication '.' as (a,b) . (c,d) = (ac, bd).

This is how the field of Rationals is formally constructed from the Integers.

## Welcome to The Bridge

Mathematics: is it the fabric of MEST?
This is my voyage
My continuous mission
To uncover hidden structures
To create new theorems and proofs
To boldly go where no man has gone before

(Raumpatrouille – Die phantastischen Abenteuer des Raumschiffes Orion, colloquially aka Raumpatrouille Orion was the first German science fiction television series. Its seven episodes were broadcast by ARD beginning September 17, 1966. The series has since acquired cult status in Germany. Broadcast six years before Star Trek first aired in West Germany (in 1972), it became a huge success.)