I'm not sure if this is the appropriate section ... on that note

I recently came upon the topic of p-adic fields, and it got me thinking.

Is this correct:

$\displaystyle \sum_{i=0}^{\infty}9*10^i + 1 = \sum_{i=0}^{\infty}0*10^i = 0$

Is there anything about this on the net that I could read?