Drexel dragonThe Math ForumDonate to the Math Forum


Math Forum
 Ask Dr. Math
 Discussions
 Internet Newsletter
 MathTools
 Problems of the Week
 Teacher2Teacher
 Teacher Exchange
 Workshops

Search All of the Math Forum:
Browse our Internet Mathematics Library

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


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

Topic: Matheology § 210
Replies: 24   Last Post: Feb 12, 2013 1:12 PM

Advanced Search
Reply to this Topic Reply to this Topic

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

Posts: 1,033
Registered: 12/4/12
Re: Matheology § 210
Posted: Feb 10, 2013 4:10 PM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

On 2/10/2013 3:37 AM, WM wrote:
> On 9 Feb., 22:09, Virgil <vir...@ligriv.com> wrote:
>
>> Does the finiteness of the members of that set establish the finiteness
>> of the set itself?
>
> The finiteness of the natural numbers in combination with the constant
> difference of 1 establishes that the natural numbers are in bijection
> with the initial segments. This together with principle of induction
> implies that the sequence 1, 2, 3, ... has no upper threshold. It is
> potentially infinite, but it is not actually infinite.

Neither yes or no.

But, one has

1) the natural numbers

2) something different from the natural numbers

This *combination* establishes a choice function for
the natural numbers

Hence, infinity is assumed

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

[Privacy Policy] [Terms of Use]

© Drexel University 1994-2013. All Rights Reserved.
The Math Forum is a research and educational enterprise of the Drexel University School of Education.