Re: the need for relevance

Jesse F. Hughes wrote:

Yes, I know. You think it's self-evident that N is "potentially
infinite" and that to determine if a property holds on a potentially
infinite set, you check to see how it holds on the finite subsets and
"take a limit". But that doesn't always work, I guess. Here's a
property P: "X is finite (i.e., not potentially infinite)."

P is true of {0}.
P is true of {0,1}.
P is true of {0,1,2}.
...
P is true of {0,1,2,3,...,n}.

so by your reasoning, it follows that P is true of N and hence that N
is not potentially infinite. Geez, where did I go wrong?

A self-referential property P, perhaps? Somehow like the liar paradox?
Anyway, I'm not impressed.

Han de Bruijn

.

Relevant Pages

  • Re: Cantor Confusion
    ... infinite set N there are 250 times more even numbers than odd numbers. ... else but the union of all finite paths. ... And that shows a surjection from N to R how? ... infinite path is the union of all finite subsets of that path. ...
    (sci.math)
  • Re: Cantor Confusion
    ... The union of all finite trees contains the union of all finite paths ... there are uncountably many infinite paths having ... The set of finite subsets of a countably infinite N is countable. ... So counting only the finite subsets doesn't count. ...
    (sci.math)
  • Re: Cantor Confusion
    ... The union (as I defined it for trees) of all finite trees is an ... you can union the nodes and the paths ... uncountable and from finite to infinite, ... the set of finite subsets of R is countable ...
    (sci.math)
  • Re: Cantor Confusion
    ... The union (as I defined it for trees) of all finite trees is an ... you can union the nodes and the paths ... uncountable and from finite to infinite, ... the set of finite subsets of R is countable ...
    (sci.math)
  • Re: the need for relevance
    ... Han de Bruijn wrote: ... infinite" and that to determine if a property holds on a potentially ... infinite set, you check to see how it holds on the finite subsets and ...
    (sci.math)