Xref: utzoo rec.humor:10884 sci.misc:1144
Path: utzoo!mnetor!uunet!husc6!rutgers!iuvax!pur-ee!pur-phy!hal
From: hal@pur-phy (Hal Chambers)
Newsgroups: rec.humor,sci.misc
Subject: Re: Do You Have an Interesting Formula?
Message-ID: <1029@pur-phy>
Date: 24 Mar 88 12:28:41 GMT
References: <2933@slovax.UUCP> <3451@bnrmtv.UUCP> <9@dm.sei.cmu.edu> <238@scampi.UUCP>
Reply-To: hal@newton.physics.purdue.edu.UUCP (Hal Chambers)
Organization: Purdue Univ. Physics Dept., W. Lafayette, IN
Lines: 30

In article <238@scampi.UUCP> ramin@scampi.UUCP (Fubar Void) writes:
  >In article <9@dm.sei.cmu.edu>, ejh@sei.cmu.edu (Erik Hardy) writes:
  >> on a lighter note, what's the value of:
  >>
  >> 		-- cabin
  >> 		|	1
  >> 		|	-  dx?
  >> 		|	x
  >> 	       -- 1

 >I think it's more like:

 > 		-- infinity
 > 		|      1
 > 		|  ---------  d(cabin) = log(cabin) + C
 > 		|    cabin
 > 	       -- 0

Wrong!  This  ( ^ )  integral blows up!  On the RHS the "log(cabin)" term
must be evaluated at both infinity and  0;  log is unbounded in both
places.  Even the integrand is unbounded at 0!  Also the integrand, 1/x,
does not go to zero fast enough in the positive direction for the integral
to be bounded.  Consider the integer sum:

		SUM(1/n) for n = 1,....,infinity

This is unbounded even though the discrete sum contains many fewer
values than the Riemann Sum (i.e. integral).

Hal (I probably spelled Riemann wrong) Chambers