Shape

182 II Seeing How It Works
and the four squares (planes)
Maximal elements are discrete, but discrete elements may not be maximal, as these
squares show
Boundary elements can’t overlap.
(The equivalence relation I have in mind for sets of basic elements is this. Let the
set S be included in the set T when every basic element embedded in a basic element
in S has a basic element embedded in it that’s also embedded in a basic element in T.
Then the sets S and T are equivalent if and only if each is included in the other. Inclusion
is the same as the part relation below, without maximal elements. That accounts
for all of the complication. The smallest set in the equivalence class determined by S
contains only maximal elements. The set of seven lines
is equivalent to the set of ten lines
And the four lines in the set
are maximal. In all three cases, the same square