On Mon, Jul 21, 2014 at 09:47:34PM +0900, Paul S. wrote: > On 7/21/2014 午後 09:31, Michael Conlen wrote: > >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. > > When exactly did we sign up for a discreet math course `-`
We probably shouldn't talk about it in public. - Matt "A discrete math course, on the other hand..."
