Article View: alt.linux
Article #1040Re: 0^0=Indeterminate quantity right ?
From: Erik Max Francis
Date: Thu, 02 Jan 2003 04:58
Date: Thu, 02 Jan 2003 04:58
34 lines
3213 bytes
3213 bytes
Kasper Dupont wrote:
> Erik Max Francis wrote:
>
> > x^0 = 1 holds for all x
>
> OTOH 0^x = 0, and you can probably argue for anything
> between 0 and 1 by similar arguments.
This is a very weak argument, because for one thing, 0^x = 0 is simply
not true; consider x = -1. (And y^x isn't defined at _all_ for negative
irrational x, regardless of y!) The properties of exponentiation are
defined in terms of the exponent, not the base; nowhere is there a rule
that 0^x = 0 for all x. You are taking a very small pattern (certainly
it's true for positive numbers) and extending it into domains where it
does not belong. That 0^x = 0 for some x doesn't tell us anything about
the situation.
There are very strong algebraic reasons for considering 0^0 = 1 (for
instance, making the binomial theorem pretty), just as there are strong
reasons for, say, not considering 1 to be prime (namely, unique prime
factorization). We're making the definitions, we get to choose how they
work in the edge cases.
As I've already pointed out, the FAQ is the place to go for the complete
rundown on this information for mathematicians and by mathematicians.
--
Erik Max Francis / max@alcyone.com / http://www.alcyone.com/max/
__ San Jose, CA, USA / 37 20 N 121 53 W / &tSftDotIotE
/ \ Women are equal because they are not different any more.
\__/ Erich Fromm
WebVal / http://www.alcyone.com/pyos/webval/
URL scanner, maintainer, and validator in Python.
Technical Details
Message-ID:
<3E13C6FE.FF4E67A6@alcyone.com>Path:
arc1-ca.pugleaf.net!archiver1.google.com!news1.google.com!newsfeed.stanford.edu!news-spur1.maxwell.syr.edu!news.maxwell.syr.edu!newsfeed-east.nntpserver.com!nntpserver.com!border1.nntp.aus1.giganews.com!nntp.giganews.com!nntp3.aus1.giganews.com!news.giganews.com.POSTED!not-for-mailReferences:
<auvg0g$8jf$1@news.vsnl.net.in> <3E135361.2C13B99F@alcyone.com> <3E1359C8.F423ABC8@daimi.au.dk>Show Full Headers
Complete Article Headers
X-Google-Language: ENGLISH,ASCII-7-bit X-Google-Thread: 10c696,49fa7379441f7903 X-Google-Attributes: gid10c696,public X-Google-Thread: f45a7,49fa7379441f7903 X-Google-Attributes: gidf45a7,public X-Google-Thread: 100c5f,49fa7379441f7903 X-Google-Attributes: gid100c5f,public X-Google-ArrivalTime: 2003-01-01 20:58:43 PST Path: arc1-ca.pugleaf.net!archiver1.google.com!news1.google.com!newsfeed.stanford.edu!news-spur1.maxwell.syr.edu!news.maxwell.syr.edu!newsfeed-east.nntpserver.com!nntpserver.com!border1.nntp.aus1.giganews.com!nntp.giganews.com!nntp3.aus1.giganews.com!news.giganews.com.POSTED!not-for-mail NNTP-Posting-Date: Wed, 01 Jan 2003 22:58:40 -0600 Message-ID: <3E13C6FE.FF4E67A6@alcyone.com> Date: Wed, 01 Jan 2003 20:58:38 -0800 From: Erik Max Francis <max@alcyone.com> Organization: Alcyone Systems X-Mailer: Mozilla 4.79 [en] (X11; U; Linux 2.4.5 i686) X-Accept-Language: en, eo MIME-Version: 1.0 Newsgroups: alt.linux,comp.os.linux.development.apps,fr.education.entraide.maths Subject: Re: 0^0=Indeterminate quantity right ? References: <auvg0g$8jf$1@news.vsnl.net.in> <3E135361.2C13B99F@alcyone.com> <3E1359C8.F423ABC8@daimi.au.dk> Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit Lines: 34 NNTP-Posting-Host: 64.81.79.102 X-Trace: sv3-sqM4aO/vPBaeUiEq9/MUKXwYKgxy0FVQefQefNjcfe1/TLjgj3IifhPdsouF5yotCHhO2ecfhts4cZq!G/QjfdfbiAaK+DYKggSx8gk+DpQ6rYw99NNkqI9XdlwLkLVB4cx8PDzHRxb5Az4/r60Qi2Hsnxwi!MGM= X-Complaints-To: abuse@giganews.com X-DMCA-Notifications: http://www.giganews.com/info/dmca.html X-Abuse-and-DMCA-Info: Please be sure to forward a copy of ALL headers X-Abuse-and-DMCA-Info: Otherwise we will be unable to process your complaint properly X-Postfilter: 1.1