(no subject) 
[Apr. 14th, 200602:13 pm]
Sullivan

day 3: my father said this to me the other day, "your salvation lies in you mind."
I've started studing group theory. I cannot explain the full rediclousness of it, see passage below:
"Let X be a finite set and let Sx denote the set of all permutations of X onto itself:
Sx= { f: X>X  f is a bijection}
This set has the following properties:
1. if f, g belong to Sx, then fg (the composition of these permutations) also belongs to Sx. 2. if f,g,h belong to Sx, then (fg)h = f(gh).
3. the identity permutation I: X > X belongs to Sx
4. if f belongs to Sx the the inverse permutation f^1 also belongs to Sx.
The set Sx is called the symetric group of X. We shall usually take for the set of X a set of the form {1, 2, 3, ..., n}, in which case we shall denote the symmetric group by Sn, this group is also called the symmetric group on n letters." 

