Re: infinity

Jonathan Hoyle said:
> >> This is related to your error of assuming that the natural numbers
> >> must include its size as a last element. You assume in your "proof"
> >> that if its true for any fixed limit L, it must be true for where there is
> >> no fixed limit. Neither are true (although I strongly suspect you'll
> >> answer back with another circular argument).
> >
> >I do not assume it. I proved that all finites up to and including any
> >given finite is a set with that finite as a size.
>
> Exactly. What you have not proven is that it is true when there is no
> finite size limitation. You assume it without proof (because frankly,
> it's improvable). Once again, your hidden assumption circles back into
> your "proof".
It is NOT true that the set is finite without the finite size limitation. That
is the point. It IS true for all n, finite or infinite, that the number of
whole numbers from 1 to that number is a set with size equal to that number.
>
> >> If NO element is preceded by an infinite number of elements,
> >> how do you claim the set is infinite?
>
> Because those two concepts are not equivalent.
Indeed, in my theory, an infinite set is one with an infinite number of
elements after the start and before the end of the set.
>
> >> Only because it has no last element. It is certainly
> >> unbounded. It also certainly does not contain a truly
> >> infinite number of elements.
>
> If it's unbounded, how can you claim that it's finite?
Because it has a finite value range, given that all differences between
elements are finite, and each element occupies a finite unit of that range, and
you can only squeeze a finite number of finite segments out of any finite
distance. Assume the value range is x units: you can only have x+1 naturals in
that range.
>
>

--
Smiles,

Tony
.

Relevant Pages

  • Re: Cool visual illusion
    ... > Regards the last, of course, theoretically infinite processing power ... So the limitation we do of focusing our attention is at a minimum likely to ... >> Oh, and if you know so much, tell me if emotions are required for an ... it IS a yes/no answer: does an intelligent agent ...
    (comp.ai.philosophy)
  • Re: infinity
    ... > finite naturals with a finite unit of time. ... I claim that it takes an unbounded but finite amount of time, ... There is no element which will take infinite time to count to. ...
    (sci.math)
  • Re: Calculus XOR Probability
    ... with an infinite number of elements between them. ... But Tony is using some ... finite unit. ... Symbolic sets are very well handled, thank you, and other inductively defined ...
    (sci.math)
  • Re: Calculus XOR Probability
    ... with an infinite number of elements between them. ... Of course no one has ever claimed that omega ... It's not a matter of that, but choosing a point infinitely far away as ... finite unit. ...
    (sci.math)
  • Re: Calculus XOR Probability
    ... with an infinite number of elements between them. ... This is why he thinks omega is a contradiction. ... It's not a matter of that, but choosing a point infinitely far away as a unit, ... finite unit. ...
    (sci.math)