[ExI] There are Infinitely Many Numbers, But Each of them is Finite (reply to Bryan Bishop)

[Lee Corbin]

Hi Bryan,

Welcome to the list!  By the way, one really should change the subject
line whenever they're a significant change of subject. If you've perused
our archives at all, you'll see the pattern, and see how (just to help an
archive reviewer) sometimes the construction

        [Exi] <newSubjectLine> (was <old subject line prefix>)

is used, except the [Exi] part is automatically generated and need
not be added by you.

When there is *no* connection, then make *no* "(was..." construction).

I perused the cryonics section's titles. It all looked pretty familiar (I've
been signed up for nearly 20 years, and many people here are signed
up with either Alcor or CI.)  Is there something in particular about it
that you wanted to discuss?

Also, your list of essays and references looks like a non-trivial subset of
the entire web!  A list, evidently (so far as I have had time to peruse it)
reflecting good taste!

Ahem, on to the meat.  One entry you list is

http://www.marknielsen.net/Math/Counting/Diagonalization/Diagonalization_Disproof2.html

which is a fun construction that produces a list of Very Rational numbers,
where I am defining Very Rational (Decimal Fractions) to be those that
terminate after a finite number of digits.  The list you create begins

0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 0.01, 0.11, 0.21, 0.31, 0.41, 0.51, 0.61, 0.71, 0.81, 0.91, 0.02, 0.12, 0.22, 0.32, 
0.42, 0.52, 0.62, 0.72, 0.82, 0.92, 0.03, 0.13, 0.23, 0.33, 0.43, 0.53, 0.63, 0.73, 0.83, 0.93,

The problem is that all these *are* indeed rational, but that the *infinite* string
produced by the diagonalization is *not* rational.  So of course it does not
appear on the list.

The Step 5 of the ISSUES SECTION illustrates the error. It reads

Step 5:  "Also, the sequence 0.33333... and so on is in my set D. There is no single entry which matches 1/3, but if can accept that 
a sequence 0.33333... is equal to 1/3, then after my list has been generated, 1/3 is in the list. --- I think."  is mistaken.  All 
the numbers

      0.3
      0.33
      0.333
      0.3333
      0.33333
      0.333333
      ...

is in the list, but the writer apparently does not understand that the *infinite* string .333333333...
does not anywhere appear on the list!

Lee

----- Original Message ----- 
From: "Bryan Bishop" <kanzure at gmail.com>
To: "ExI chat list" <extropy-chat at lists.extropy.org>
Sent: Sunday, July 15, 2007 6:59 AM
Subject: Re: [ExI] Next moment, everything around you will probably change


> Hi all. I am new to the list, and have something to contribute.

> But this is more fiction than anything practical. And so to make up
> for this mostly fiction making, let me link over to my notes on
> cryonics. Warning, the file is ~1.6 megabytes in size:
> http://heybryan.org/bookmarks/kanzure_bookmarks_July15th02007.html#2.7
>
> I look forward to discussions on the list :)
>
> - Bryan
> _______________________________________________
> extropy-chat mailing list
> extropy-chat at lists.extropy.org
> http://lists.extropy.org/mailman/listinfo.cgi/extropy-chat
>