Exponential Set

This set should be called Factorial Set of order 2, in line with the updated definition of Mirror Set;
http://a-theory-of-nothingness.blogspot.com/2006/11/mirror-set-rev-1.html

E0=,
E1=EE0=E={,}={}
E2=EE1={,{}}={{},}
E3=EE2={,{},{,{}}}
E4=EE3={,{},{,{}},{,{},{,{}}}}
...
En=EE(n-1)

Where E is a reflection operator. It gathers the past under one roof. Although it has multiple content, it also has an overall duality like HSet. ESet looks like e^z since the self similarity in breadth. HSet is self similar in depth, for example H3={,{,{,{}}}}. Self similarity of exponential function is evident from differentiation, (d/dz)e^z=e^z. Taylor's expansion of e^z is an iterated process, like ESet.

The identity (E0=,) is a bit strange but my hand was forced by 0!=1. But it also makes some sense since the seperator is defined first. (E0=) is even stranger.

The number of states;

SE0=0!=1
SE1=1!0!=1
SE2=2!1!0!=2
SE3=3!2!1!0!=12
SE4=4!3!2!1!0!=288
SE5=5!4!3!2!1!0!=34560
SE6=6!5!4!3!2!1!0!=24883200
...
SEn=n!(n-1)!(n-2)!...2!1!0!

Self similarity also shows up in the state calculation. The factorial is calculated to depth 2.

Note the curious 'nineness' of 4-6;

2+8+8=18=2*9
3+4+5+6+0=18=2*9
2+4+8+8+3+2+0+0=27=3*9