Re: How is this collection called?

From: Mikito Harakiri <>
Date: Wed, 31 Mar 2004 11:05:25 -0800
Message-ID: <ANEac.32$>

"Paul" <> wrote in message "Paul" <> wrote in message
> Define a*b as "a U {b}" (where U is set union)
> Then a*(b*c) = aU{bU{c}} != (a*b)*c = aU{b}U{c}.
> But if you think in terms of physical boxes, imagine a small box
> inside a medium box, which in turn is inside a large box. For these
> things you could say the small box "is-in" the large one, even though
> it isn't directly inside.
> I think it's just the same (isomorphic to) as the tree example?

It is isomorphic indeed to a tree operation, but this is a different tree operation (and different tree structure?)

In case of binary trees with labeled ordered children the tree composition operation a*b is building a larger tree that has root connected to 2 branches a and b:

+--- a
+--- b

You, however, refer to a [nonbinary] tree with unordered children with composition being defined as attaching subtree b to the root of a (at level 1):

...<the rest of a>

In the first case the * operation could be defined commutative (unordered children) or not, but in your case

a*b != b*a

always. Received on Wed Mar 31 2004 - 21:05:25 CEST

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