Proof that all natural numbers are interesting
Leslie Lamport
December 1, 1993
Abstract:
Theorem All natural numbers are interesting.
Assume: a natural number.
Prove: is interesting.

<1>1: A number is interesting if it is the smallest number not in
an interesting set.

Proof: By definition of interesting.

<1>2: Case:

Proof: By <1>1, since is the smallest natural number not in
.

<1>3: Case:

 is interesting

Proof: By <1>1, since case assumption <1>
implies that
is interesting.

<1>4Q.E.D.

Proof: Steps <1>2 and <1>3, assumption <0>,
and mathematical induction.


 1
 Leslie Lamport, 1993, How to write a proof. In
Global Analysis of Modern Mathematics, pp. 311321. Publish or
Perish, Houston, Texas, February 1993. A symposium in honor of
Richard Palais' sixtieth birthday (also published as SRC Research
Report 94).
http://research.microsoft.com/users/lamport/proofs/src94.ps.Z
Proof that all natural numbers are interesting
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