Re: Cantor was Right!


Tony Orlow (aeo6) wrote:

> Of course there are more reals than naturals, but reals are countable
too.

What do you mean by "countable"? Does your definition involve listing
all real numbers in a sequence?

If so - great. Give us this sequence.

I know how to produce a sequence of all rational numbers and can tell
you what rational number is in what position.

But I will be willing to suggest to you a bet. If you can produce a
sequence of all real numbers and tell me in which postion each real
number is, I will pay you $1 million. If you can't - you will stop
posting to sci.math until you pay me $1 million.

Make sure that your definition of real numbers is such that any Cauchy
sequence of real numbers has a real limit.

A deal?

.

Relevant Pages

  • Re: Multiple infinities - one more look
    ... continued for lager length of digit sequences without limit. ... infinite digit sequences... ... so the resulting reals have an order. ... (i.e. having a finite program to output their digits in sequence). ...
    (sci.math)
  • Re: Galileos Paradox and the Project of the Reals
    ... The way you get reals by a neverending process of generating digits ... and which thereby constructs a sequence of nested intervals whose ... It isn't *already* in the rationals you started with. ...
    (sci.math)
  • Re: Cantor Confusion
    ... least appears to totally disconnect the set of those remaining. ... sequence of reals with each term less than all terms of a strictly ... This is not the case for rationals. ...
    (sci.math)
  • Re: Review of Mueckenheims book.
    ... If infinite, the limits of the ... that the reals are not countable. ... He starts with the sequence of rationals: ... in the building of the diagonal *each* digit has to be changed. ...
    (sci.math)
  • Re: Why is Cantor a target for cranks?
    ... Zeno's paradoxes are a good example of this situation. ... The sequence CONVERGES to 1. ... But in NAFL direct quantification over real numbers is banned, ... sequence without quantifying over reals. ...
    (sci.logic)