CS2603 Applied Logic for Hardware and Software
Rex Page – University of Oklahoma
1
Lecture 13 — CS 2603
Applied Logic for Hardware and Software
The m
o
st
impor
tant th
ing you will learn
… th
is
y
ear
… next year
… o
r
the year after t
ha
t
Induction
the original blue-light special

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CS2603 Applied Logic for Hardware and Software
Rex Page – University of Oklahoma
2
Mathematical Induction
Principle of Induction
Starting point
9
Predicate P
9
Universe of discourse:
N
= {0, 1, 2, …}
Process
9
Prove: P(0)
9
Prove:
∀
n.(P(n)
→
P(n+1))
Conclusion:
∀
n. P(n)
P(0)
∀
n.(P(n)
→
P(n+1))
⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯
{Ind}
∀
n. P(n)
Induction
Induction is a tremendous bargain
You get: proofs for an infinite number of propositions
9
P(0), P(1), P(2), …
But, you only have to prove one of them: P(0)
Also, you have to prove the implication: P(n)
→
P(n+1)
9
That is, you prove P(n+1), but you get to assume
P(n)
blue
-li
g
h
t
s
pecial
a new inference rule
for our formal system