Last Updated：2025/12/31
Sentence
Mathematical
induction
is
often
compared
to
the
behavior
of
dominos.
The
dominos
are
stood
up
on
edge
close
to
each
other
in
a
long
row.
When
one
is
knocked
over,
it
hits
the
next
one
(analogous
to
n
in
S
implies
n
+
1
in
S),
which
in
turn
hits
the
next,
etc.
If
then
we
hit
the
first
(0
in
S),
then
they
will
all
eventually
fall
(S
is
all
of
ℕ).
In
Variation
1
above,
we
start
by
knocking
over
the
kth
domino,
so
that
it
and
all
subsequent
ones
eventually
fall.
Quizzes for review
Mathematical induction is often compared to the behavior of dominos. The dominos are stood up on edge close to each other in a long row. When one is knocked over, it hits the next one (analogous to n in S implies n + 1 in S), which in turn hits the next, etc. If then we hit the first (0 in S), then they will all eventually fall (S is all of ℕ). In Variation 1 above, we start by knocking over the kth domino, so that it and all subsequent ones eventually fall.
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