Re: abundance of irrationals!)


Virgil wrote:
> In article <1115155424.711718.105580@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
> "Randy Poe" <poespam-trap@xxxxxxxxx> wrote:
> > If we wanted to enumerate the naturals sequentially
> > this would be a way to do it. In principle, every natural
> > will be arrived at after finite time.
>
> Actually, that is a bit ambitious. EACH natural will be arrived as in

> finite time, but not ALL of them collectively in finite time.

You're absolutely correct. That's what I intended to
say. In principle, any natural you choose will be
arrived at in finite time.

I'm unable to discern the nature of Tony Orlow's
mental block. Is it the same dyslexia that plagues
Mueckenheim, the one that can't distinguish between
"for each n in N, there exists m > n" and "there
exists m > all n in N"?

- Randy

.

Relevant Pages

  • Re: abundance of irrationals!)
    ... >>> If we wanted to enumerate the naturals sequentially ... >> finite time, but not ALL of them collectively in finite time. ... I am not the one with a mental block. ... your narrow set of axioms, or the possibility that one or more of the axioms is ...
    (sci.math)
  • Abundance of irrationality was Re: abundance of irrationals!)
    ... >>> If we wanted to enumerate the naturals sequentially ... >> finite time, but not ALL of them collectively in finite time. ... that an infinite set must have elements which are "infinite". ...
    (sci.math)
  • Re: Well Ordering the Reals
    ... It is impossible to enumerate all the elements ... What you are calling "finite naturals" is what everyone else ... The reals are not countable, ... For every well-ordering ...
    (sci.math)
  • Re: abundance of irrationals!)
    ... Cantor does not "enumerate' any diagonal, he constructs it from a given ... in the same way the digits of each of the listed ...
    (sci.math)
  • Re: Two results of set geometry
    ... Where is such a principle ... found in texts in mathematics to make it a "general principle of ... incrementing finite naturals an infinite number of times results ...
    (sci.math)