From: Sir Robin of Locksley <tozser@stolaf.edu>
Date: Sun, 19 Jan 1997 10:21:07 -0800 (PST)
To: Secret Squirrel <nobody@squirrel.owl.de>
Subject: Re: I beg you, PLEASE prove that 0.123456789101112131415 is IRRATIONAL
Message-ID: <199701191820.MAA24006@nic.stolaf.edu>
MIME-Version: 1.0
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>Dear Cypher Punks,
 >
 >I BEG YOU TO HELP ME!!!
 >
 >Is it possible to prove that number 0.1234567891011121314151617181920...
 >iz irrational? 
 
Most definately. All you need to do is prove that the set of this number is
uncountable, ergo is irrational. If you have friend who have done math in real
analysis they can explain more.

>
 >Or may be it is rational?
 >
 >Also, another question for math geniuses here: 
 >
 >Is it REALLY true that there are real numbers that cannot be generated
 >by any algorithm? Some guy said that since the set of algorithms is
 >countable, but the set of real numbers is more than countable, there 
 >must be some numbers for which there is no algorithms that generate them.
 
If you show me an algorythm that calculates the real number TT (=3.14.....)
I'll give you a Nobel Prize personally!

>
 >But I still do not believe him.
 >
 >Also, is it true that the sequence of digits in e is random because the ONLY
way to get to the
 >p'th digit is to calculate the p-1'st digits?
 >
Exactly! This is called recursive definition. To get the p-th set in the
sequence you need to find p-1 first...

>Also, is it the correct definition of a real number: 
 >
 >``A real number is the class of numbers which can represent the length of
 >an arbitrary line.''
 
Well, that is not entirely true... The length of any arbitrary line can be any
number, rational, natural, etc. Real numbers are the numbers that defy all
other categorization (they are not rational, irrational, natural, etc.) They
are complex and despite any instinctual perception, there are a lot of them!
 
I don't know if these maed a lot of sense but all of these questions are
answered in a good Elementary Real Analysis book.

>
 >
 >I AM REAL DESPERATE FOR YOUR ASS ISTANCE.

Sincerely,

Gabe
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|    Gabor K. Tozser     |  1500 St. Olaf Ave.      |
|     St. Olaf College   |  Northfield, MN 55057    |
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