The binary octet structure used to form IP addresses is quite robust; each single octet has 256 possible permutations, and each IP address has four octets. This adds up quite quickly. The total number of possible IP addresses in the world is roughly 4.3 billion. Of these 4.3 billion addresses, several are restricted from normal use for a variety of reasons. For example, the IP address 0.0.0.0 is always used to represent the default network, while 255.255.255.255 is used to identify broadcasts, which are messages that get sent to every computer in a single network. Several other IP addresses are restricted as well, but for the most part, you can feel safe that you and your neighbor won't ever have overlapping IP addresses.
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