The Internet

Seth Breidbart once described The Internet as

"the largest equivalence class in the reflexive, transitive, symmetric closure of the relationship 'can be reached by an IP packet from'."

While most people don't look at it from a mathematic perspective, The Internet is, in practical terms, the collection of tier 1 networks which peer with one another and comprise the default-free zone (or 'DFZ'), and the waterfall of networks which peer with them or purchase transit to them; in short, if you pitch a packet over the wall with a public IP address as its destination, and you are connected to The Internet somehow, that packet should get there, and reply packets should get back to you.