Hi. I was doing some work you may find useful. I was just recently introduced to p-adic... stuff? So, I'm sorry in advanced if I get my terminology off.

I was introduced to these because of something I was working on in binary that begged for more convenient notation (infinite divergent series in binary).... anyway, for clarity everything below is in base 2 besides the rationals which are in standard base 10. Ie ...111.0 = 1+2+4... etc. So I let x=...1010.0 X/2=...10101.0 Then added 1 to x get. x+1=...101011.0 Then x+(x/2) to get = (-1/3)+(-2/3)=-1 What I found out was that the results I found where contrary to p-adic notation. I "should" have gotten plus or minus 1/3, but instead got -1/3 and -2/3. I also got that -...111.0=0(note the negative). I should have gotten that -...111.0=1.

I suspect that these differences may be due to the "first prime" in p-adic being considered a zero, and not a 1, but I have no idea. Like I said, I was just recently lead to this, and have basically no undergraduate mathematical training, but I hope it helps. I suspect it may be related.