Complex base numeral systems?

I am only in precalc but I am doing work with complex forces and I think that using a complex base numeral system would simplify much of my work, and i'm just interested in the topic.

http://arxiv.org/PS_cache/arxiv/pdf/...712.1309v3.pdf

I am having trouble following what is going on in the paper. My problems start at Definition 1. I dont understand what surjective/pseudoinjective mean, I dont know what the backwards E, the sideways union, the upsidedown A, the epsilon, the backwards epsilon, or for that matter the mu represent. I realize that I am in over my head, but what better way to learn right?

Also, why are certain boxes shaded in the integer part picture, and what do the Z^x's and stuff represent, im having trouble following.

If anybody has the time I would appreciate the help, but I understand if nobody wants to take on the difficult task of explaining something this complex to someone with such little foundation to work with.

-GTO