The Math Forum

Search All of the Math Forum:

Views expressed in these public forums are not endorsed by NCTM or The Math Forum.

Math Forum » Discussions » sci.math.* » sci.math

Notice: We are no longer accepting new posts, but the forums will continue to be readable.

Topic: § 473 Thomas Jech on Potential and Actual

Replies: 4   Last Post: Apr 19, 2014 2:59 PM

Advanced Search

Back to Topic List Back to Topic List Jump to Tree View Jump to Tree View   Messages: [ Previous | Next ]
Tommy Jensen

Posts: 249
From: Daegu, Korea
Registered: 12/6/09
Re: § 473 Thomas Jech on Potential and Actual

Posted: Apr 19, 2014 3:46 AM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

On Sun, 13 Apr 2014 05:54:19 -0700, mueckenh wrote:

> On Sunday, 13 April 2014 14:07:54 UTC+2, Tommy Jensen wrote:

>> Let a(i) be the real number defined by the interpretation of the
>> i'th
>> sentence (in lexicographic ordering) of a language in which it defines
>> a real number of D. For each i and j let b(i,j) be the binary bit of
>> a(i) which is read j positions after the binarypoint. The let u be the
>> real number between 0 and 1, excluding 1, for which its binary bit in
>> the position j after the binarypoint is equal to 1-b(j,j).

> First, do you believe that this very short sequence of letters is not in
> the infinite list of finite expressions that I defined? You remember?
> 0
> 1
> ...
> Second, the list of finite definitions does not contain b(j,j). The
> second bit of the second line is undefined.
> Regards, WM

And with that, you not only have admitted to believing in a "set
of definable real numbers" (and we note that "definable real number" is
itself an undefined term), but you also now say that you believe in such
real numbers that have undefined bits in their binary expansion.
Or likely you misunderstood when I referred to the j'th bit of a
real number. I meant the j'th bit of its binary expansion, counting j
binary digits to the right of the binarypoint. Not the j'th bit of its
finite definition, whatever that means.
But you seem to believe in many things that neither you nor anyone
else has ever encountered, so who knows.

Point your RSS reader here for a feed of the latest messages in this topic.

[Privacy Policy] [Terms of Use]

© The Math Forum at NCTM 1994-2018. All Rights Reserved.