Re: infinity

Tony Orlow wrote:
>
>Daryl McCullough said:

>> >> [1] For all s a string, exists L a length s.t. L > len(s)
>> >>
>> >> [2] Exists L a length s.t. for all s a string, L > len(s)

>> So are you saying that [2] means the same thing as [1], even though
>> the quantifiers are reversed?

>No, I am saying that [1] implies [2].

But [1] is true even if we restrict L and s to be *finite*:

[1'] For all s a finite string, exists L a finite length
s.t. L > len(s)

In contrast, [2] is certainly *false* if we restrict s and L to be
finite:

[2'] Exists L a finite length s.t. for all s a finite
string, L > len(s)

--
Daryl McCullough
Ithaca, NY

.

Relevant Pages

  • Re: infinity
    ... > Tony Orlow wrote: ... >>Daryl McCullough said: ... > For all s a finite string, ... all lengths are finite, then none are infinite, and the language cannot be ...
    (sci.math)
  • Re: infinity
    ... Daryl McCullough said: ... > Tony Orlow says... ... >>Indeed, in my theory, an infinite set is one with an infinite number of ... Has it taught me I'm wrong? ...
    (sci.math)
  • Re: infinity
    ... Daryl McCullough said: ... > Tony Orlow says... ... > there exists a finite time t such that forall finite numbers n, ... For all finite naturals the time when it will be generated is a finite amount ...
    (sci.math)
  • Re: Well Ordering the Reals
    ... Daryl McCullough said: ... > Tony Orlow says... ... > I've already given you my objection. ... > has infinite descending chains. ...
    (sci.math)
  • Re: Well Ordering the Reals
    ... >> Tony Orlow wrote: ... >> Daryl McCullough wrote: ... >> David R Tribble said: ...
    (sci.math)
Loading