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Topic: pi + e
Replies: 46   Last Post: Nov 9, 2005 8:52 PM

 Messages: [ Previous | Next ]
 Dave Seaman Posts: 3,624 Registered: 12/8/04
Re: pi + e
Posted: Nov 16, 2004 12:23 PM

On 16 Nov 2004 09:08:02 -0800, David Bandel wrote:
&gt; "G.A." &lt;smNOecklSPAMers@hotmTHANKSail.com&gt; wrote in message news:&lt;cncm73\$3lg\$1\$8302bc10@news.demon.co.uk&gt;...
&gt;&gt; "Robert Israel" &lt;israel@math.ubc.ca&gt; wrote in message
&gt;&gt; <a href="news://cncjt1\$gb9\$1@nntp.itservices.ubc.ca...">news://cncjt1\$gb9\$1@nntp.itservices.ubc.ca...</a>
&gt;&gt; &gt; In article &lt;LsqdncyEcPWZTQTcRVnyhA@casema.nl&gt;,
&gt;&gt; &gt; Thinus Pollard &lt;thinusp@gmail.com&gt; wrote:
&gt;&gt; &gt;
&gt;&gt; &gt; &gt;Given the above, what's the difference between irrational and
&gt;&gt; &gt; &gt;transcendal numbers? I read, only a few days ago, e is transcendal, pi
&gt;&gt; &gt; &gt;is transcendal, but it's unknown if pi + e is. Are these two concepts
&gt;&gt; &gt; &gt;related?
&gt;&gt; &gt;
&gt;&gt; &gt; The word is "transcendental", not "transcendal". A number x is
&gt;&gt; &gt; transcendental if there is no polynomial of degree at least 1
&gt;&gt; &gt; with rational coefficients that has x as a root. All transcendental
&gt;&gt; &gt; numbers are irrational, but not all irrational numbers are
&gt;&gt; &gt; transcendental.
&gt;&gt; &gt;
&gt;&gt;
&gt;&gt; Also, 100% of real numbers are transcendental.

&gt; that's incorrect. 2 is a real number and it's not transcendental.

That does not contradict what he said. Think measure theory.

&gt; it was mentioned earlier in this post that the cardinality of
&gt; irationals is 1 lower than the cardinality of reals... i wouldn't be
&gt; surprised if the same were true for transcendentals vs. irationals

The cardinality of the transcendentals is the same as the cardinality of the
irrationals, which is the same as the cardinality of the reals.

--
Dave Seaman
Judge Yohn's mistakes revealed in Mumia Abu-Jamal ruling.
&lt;<a href="http://www.commoncouragepress.com/index.cfm?action=book&amp;bookid=228">http://www.commoncouragepress.com/index.cfm?action=book&amp;bookid=228</a>&gt;

Date Subject Author
11/16/04 kalikinkar
11/16/04 Daniel McLaury
11/16/04 kalikinkar
11/16/04 Daniel McLaury
11/16/04 tp
11/16/04 Robert Israel
11/16/04 G.A.
11/16/04 Dave Seaman
11/16/04 Phil Carmody
11/16/04 The Ghost In The Machine
11/17/04 G.A.
11/17/04 robert j. kolker
11/8/05 0101010101
11/8/05 Dirk Van de moortel
11/8/05 David R Tribble
11/8/05 Proginoskes
11/8/05 Gib Bogle
11/9/05 Proginoskes
11/9/05 Gib Bogle
11/9/05 schoenfeld1@gmail.com
11/8/05 0101010101
11/16/04 David Bandel
11/16/04 Dave Seaman
11/16/04 robert j. kolker
11/16/04 robert j. kolker
11/16/04 Robert Israel
11/16/04 Daniel McLaury
11/16/04 kalikinkar
11/16/04 Norm Dresner
11/16/04 Robert Israel
11/16/04 Oscar Lanzi III
11/17/04 Norm Dresner
11/17/04 Robin Chapman
11/17/04 Norm Dresner
11/17/04 Robin Chapman
11/17/04 r3769@aol.com
11/18/04 Robin Chapman
11/17/04 Dave Rusin
11/17/04 Keith A. Lewis
11/16/04 Nat Silver
11/16/04 kalikinkar
11/17/04 Stephen Herschkorn
11/17/04 Robert Israel
11/17/04 Stephen Herschkorn
11/17/04 Robert Israel
11/17/04 Nat Silver
11/17/04 G. A. Edgar