On Jul 18, 2014, at 2:32 PM, Jay Ashworth <j...@baylink.com> wrote: > ----- Original Message ----- >> From: "Owen DeLong" <o...@delong.com> > >> But the part that will really bend your mind is when you realize that >> there is no such thing as "THE Internet". > > "The Internet as "the largest equivalence class in the reflexive, transitive, > symmetric closure of the relationship 'can be reached by an IP packet from'" > -- Seth Breidbart.
I happen to like this idea but since we are getting picky and equivalence classes are a mathematical structure 'can be reached by an IP packet from’ is not an equivalence relation. I will use ~ as the relation and say that x ~ y if x can be reached by an IP packet from y In particular symmetry does not hold. a ~ b implies that a can be reached by b but it does not hold that b ~ a; either because of NAT or firewall or an asymmetric routing fault. It’s also true that transitivity does not hold, a ~ b and b ~ c does not imply that a ~ c for similar reasons. Therefore, the hypothesis that ‘can be reached by an IP packet from’ partitions the set of computers into equivalence classes fails. Perhaps if A is the set of computers then “The Internet” is the largest subset of AxA, say B subset AxA, such for (a, b) in B the three relations hold and the relation partitions B into a single equivalence class. That really doesn’t have the same ring to it though does it. — Mike
