Article View: aus.mathematics
Article #73Re: zero exponent
From: Virgil
Date: Sun, 20 Apr 2008 19:35
Date: Sun, 20 Apr 2008 19:35
29 lines
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2495 bytes
In article <QIMOj.3408$ko5.2468@news-server.bigpond.net.au>, "Don H" <donlhumphries@bigpond.com> wrote: > <Pfsszxt@aol.com> wrote in message > news:jlah04drbo3nucjn5n7n438gqbng4auf0r@4ax.com... > > On Thu, 17 Apr 2008 19:40:24 GMT, "Don H" <donlhumphries@bigpond.com> > > wrote: > > > > >1^0 = 1 ; 2^0 = 1; 3^0 = 1 ; etc. > > >Is this axiomatic, or is there a proof? > > >============================== > > > > > It isn't a math fact --- it's a definition --- made so as to be > > consistant and for convenience when writing infinite series etc. > > # And so is an arbitrary definition? > What is a number n to the power x? > The x indicates how many n must be multiplied together. > Thus, > n^x = n by n (x times) > 2^2 = (2, twice) = 4 > 2^1 = (2, once) = 2 > 2^0 = (2, no times) = 1 ? > - but if you multiply 2 by itself, no times, you've still 2 ? > Whereas, if you multiple 0 by 0, two times, you've still 0 ? The standard inductive (or, if you prefer, recursive) definition of powers with positive integer exponents is: For any real/complex number x, x^1 = x and x^(n+1) = x^n * x.
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X-Google-Thread: 10d67e,bafdb25448f2a9e6 X-Google-Attributes: gid10d67e,domainid0,public,usenet X-Google-Language: ENGLISH,ASCII-7-bit Path: arc1-ca.pugleaf.net!g2news1.google.com!news1.google.com!news.glorb.com!border1.nntp.dca.giganews.com!nntp.giganews.com!local02.nntp.dca.giganews.com!nntp.comcast.com!news.comcast.com.POSTED!not-for-mail NNTP-Posting-Date: Sun, 20 Apr 2008 14:35:54 -0500 From: Virgil <Virgil@gmale.com> Newsgroups: aus.mathematics Subject: Re: zero exponent References: <IINNj.2620$ko5.41@news-server.bigpond.net.au> <jlah04drbo3nucjn5n7n438gqbng4auf0r@4ax.com> <QIMOj.3408$ko5.2468@news-server.bigpond.net.au> User-Agent: MT-NewsWatcher/3.5.1 (Intel Mac OS X) Date: Sun, 20 Apr 2008 13:35:53 -0600 Message-ID: <Virgil-6FD0F3.13355320042008@comcast.dca.giganews.com> Lines: 29 X-Usenet-Provider: http://www.giganews.com NNTP-Posting-Host: 24.9.123.80 X-Trace: sv3-uoXmJyKaOhrPQruAVk2ahd8lCFnq9UnCGWfRNb7TFE7Z+4L6CKI944YMZPoVa52jKZwsrEf5HyZL+AU!9hdpddhr6Tng/aBusufian7yikyQSV+G0mH7aM1AjRvjg74I2DIwgcql5cqcDxuDLXxOjaQ1zbR5!f9snT1g8mtJ1DCS2Fws3aZ8bMo5Ab92ENM3EicA= X-Complaints-To: abuse@comcast.net X-DMCA-Complaints-To: dmca@comcast.net 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: 1.3.39