


Exercise
41. Naming sets using normal form 
By definition, a set's normal form is the one that lists the set's
pcs in the most compact "ascending" (clockwise) order. Here,
to review, are the steps for finding a set’s normal form.
 List the pc content of the segment, eliminating all repetitions.
 Arrange the pc integers in "ascending" (clockwise) orders.
Remember: there are always as many possible "ascending" orders
as the set has pcs.
 Choose the most compact of the "ascending" orders.
Do this by subtracting the first integer from the last. The one whose
overall interval span is smallest is the set’s normal form.
With some sets, two or more orders tie for overall compactness. If so,
 Choose the set that is most compact towards the left. Measure the
intervals from first to secondlast pc. Still tied? Measure from first
to thirdlast pc, to fourthlast, and so on, until one set wins in compactness.
With sets of great interval regularity, no amount of measuring will
break the compactness tie. In such a case
 Choose the order that begins with the lowest number.
The following exercise has five parts, ae. In parts ad, you’ll
be guided through the steps for finding the normal forms of four sets.
In part e, you’re on your own for four more sets (though answers
and comments are available).
Begin the exercise.

Page last modified 27
July 2001 / GRT


