# Section 1.4: Problem 3 Solution

Working problems is a crucial part of learning mathematics. No one can learn... merely by poring over the definitions, theorems, and examples that are worked out in the text. One must work part of it out for oneself. To provide that opportunity is the purpose of the exercises.

James R. Munkres

We can generalize the discussion in this section by requiring of
only that it be a class of relations on
.
is defined as before, except that
is now a construction sequence provided that for each
we have either
or
for some
and some
all less than
. Give the correct definition of
and show that
.

is the intersection of all inductive sets
such that
and if
and
for some
, then
.

is inductive, therefore,
.

And for any construction sequence
, by ordinary induction, each
, therefore,
.