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Sullivan

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[Apr. 14th, 2006|02:13 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."
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