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. 311-321. 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
This document was generated using the
LaTeX2HTML translator Version 2K.1beta (1.56)
Copyright © 1993, 1994, 1995, 1996,
Nikos Drakos,
Computer Based Learning Unit, University of Leeds.
Copyright © 1997, 1998, 1999,
Ross Moore,
Mathematics Department, Macquarie University, Sydney.
The command line arguments were:
latex2html ll2
The translation was initiated by Glowacki Martin / TU Wien Studenten Account Kopie on 2002-10-25
URL of this proof as currently expanded for referencing
and bookmarking purposes.
open all
close all
This HTML file was generated using the pf2html extension, version 0.03.
LaTeX2HTML + pf.sty (hypertext proofs).
Project homepage at http://www.dbai.tuwien.ac.at/proj/pf2html
Glowacki Martin / TU Wien Studenten Account Kopie
2002-10-25