Search All of the Math Forum:

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

Topic: Why does Cantor's diagonal argument fail?
Replies: 44   Last Post: Jan 26, 2014 10:54 AM

 Messages: [ Previous | Next ]
 ross.finlayson@gmail.com Posts: 915 Registered: 2/15/09
Re: Why does Cantor's diagonal argument fail?
Posted: Jan 18, 2014 5:01 PM

On 1/18/2014 11:48 AM, John Gibson wrote:
>> Here I have one for you, consider the function as you draw
>> a line from zero to one, and: only a direct line segment
>> [0,1].

>
>> Among all the functions about which the antidiagonal
>> doesn't exist, the function you noted, in those proofs,
>> sees a different result, than any other function.

>
>> Then, it is widely so that for a given function, it would
>> be accepted. And, there's a structural conterexample to
>> reflect the incompleteness of that, for which it
>> represents a structural counterexample to reflect the
>> incompleteness of that. The functions of here Russell's
>> extraordinary and ordinary infinities, simply enough, has
>> that drawing a line is as mathematically consistent as
>> enumerating the rational points.

>
> Wow, another Google-poster who seems to be trying to communicate
> something using text, and failing horribly.
>

Gibson, there's a modern retro argument that the natural numbers
are onto the real numbers of the unit interval: exactly, specifically,
precisely, and uniquely.

Followups set to sci.math, sci.logic.

And if there's not, I have one.