Drexel dragonThe Math ForumDonate to the Math Forum



Search All of the Math Forum:

Views expressed in these public forums are not endorsed by Drexel University or The Math Forum.


Math Forum » Discussions » sci.math.* » sci.math

Topic: You know you've made it in mathematics when...
Replies: 27   Last Post: Feb 19, 1998 4:16 AM

Advanced Search

Back to Topic List Back to Topic List Jump to Tree View Jump to Tree View   Messages: [ Previous | Next ]
Lee Lady

Posts: 24
Registered: 12/12/04
Re: Quick proof of the Well-Ordering Property
Posted: Feb 17, 1998 2:17 PM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply



In article <34E95F44.5FE6@pitt.edu>,
Michael David Cochran <mdcst22@pitt.edu> wrote:
>Does anyone have a fast proof of the Well-Ordering Property? The
>Well-Ordering Property states that every nonempty set of positive
>integers contains a smallest member.


Since the set S is non-empty, it contains at least one element. Choose
one. For convenience, call it n. Now if n is not itself the smallest
element in S, then the smallest element would be smaller than n. Hence
without loss of generality we may replace S by the subset of S
consisting of integers in S less than or equal to n. But there are
only finitely many positive integers less than or equal to n. (In
fact, there are only n of them!) Therefore, without loss of generality
we may suppose that S is finite. But clearly every finite set of
integers (or real numbers for that matter) has a smallest element.

If you can read pdf (Adobe Acrobat) files, you might be interested in a
rather extended discussion of some related matters in my lengthy article
on the Division Algorithm: www.math.Hawaii.Edu/~lee/courses/Division.pdf.
(Versions of the article in dvi format and postscript format are also
available.)

--
Trying to understand learning by studying schooling
is rather like trying to understand sexuality by studying bordellos.
-- Mary Catherine Bateson, Peripheral Visions
lady@Hawaii.Edu






Date Subject Author
2/14/98
Read You know you've made it in mathematics when...
Dave Rusin
2/15/98
Read Re: You know you've made it in mathematics when...
Richard Carr
2/15/98
Read Re: You know you've made it in mathematics when...
Jeff Erickson
2/15/98
Read Re: You know you've made it in mathematics when...
Fickdichhh
2/15/98
Read Re: You know you've made it in mathematics when...
Jos Horikx
2/15/98
Read Re: You know you've made it in mathematics when...
Dave Rusin
2/17/98
Read Quick proof of the Well-Ordering Property
Michael David Cochran
2/17/98
Read Re: Quick proof of the Well-Ordering Property
Robin Chapman
2/17/98
Read Re: Quick proof of the Well-Ordering Property
Lee Lady
2/17/98
Read Re: Quick proof of the Well-Ordering Property
Moshe Shulman
2/18/98
Read Re: Quick proof of the Well-Ordering Property
Adam Meikle
2/18/98
Read Re: Quick proof of the Well-Ordering Property
Moshe Shulman
2/17/98
Read Re: Quick proof of the Well-Ordering Property
Torkel Franzen
2/19/98
Read Re: Quick proof of the Well-Ordering Property
Bill Dubuque
2/15/98
Read Re: You know you've made it in mathematics when...
Michail Brzitwa
2/16/98
Read Re: You know you've made it in mathematics when...
Brian Howie
2/16/98
Read Re: You know you've made it in mathematics when...
Matthew P Wiener
2/16/98
Read Re: You know you've made it in mathematics when...
Allen Adler
2/17/98
Read Re: You know you've made it in mathematics when...
Ilias Kastanas
2/17/98
Read Re: You know you've made it in mathematics when...
Matthew P Wiener
2/17/98
Read Re: You know you've made it in mathematics when...
ariskin@mps.org
2/17/98
Read Re: You know you've made it in mathematics when...
William C Waterhouse
2/16/98
Read Re: You know you've made it in mathematics when...
Dave Rusin
2/16/98
Read Re: You know you've made it in mathematics when...
Lee Rudolph
2/16/98
Read Re: You know you've made it in mathematics when...
Allen Adler
2/17/98
Read Re: You know you've made it in mathematics when...
Matthew P Wiener
2/17/98
Read Re: You know you've made it in mathematics when...
Kjell Fredrik Rogstad Pettersen
2/17/98
Read Re: You know you've made it in mathematics when...
Michael Weiss

Point your RSS reader here for a feed of the latest messages in this topic.

[Privacy Policy] [Terms of Use]

© Drexel University 1994-2014. All Rights Reserved.
The Math Forum is a research and educational enterprise of the Drexel University School of Education.