When exactly did we sign up for a discreet math course `-`
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.
—
Mike
