Re: infinity


Tony Orlow (aeo6) wrote:
> Daryl McCullough said:
> > Tony Orlow says:

> Except that, as you just pointed out, for any set of consecutive naturals
> starting from 1, the set size IS an element of the set. Therefore, if the set
> is infinite, then it contains an infinite element. This is a contradiction. So
> how do you resolve this?

Very simply. Extremely simply, though obviously beyond you. We observe
that any element of the set that is equal to the set size must be the
largest element in the set. We deduce that in a set with no largest
element, there is no largest element that could be equal to the set
size.

> This is what I am trying to show you.

No, you can't _show_ us anything, mathematically speaking, because you
have simply no idea at all what a mathematical argument is. Do tell me:
consider a binary tree in which there are only branching nodes - how
many leaf nodes are there? Use Tinduction, or any other favourite tool.

Brian Chandler
http://imaginatorium.org

.

Relevant Pages

  • Re: Well Ordering the Reals
    ... Daryl McCullough said: ... > Tony Orlow says... ... >>If one can, as you did, select an infinite element, can form a set by ... > So you are saying that no uncountable set can be well-ordered. ...
    (sci.math)
  • Re: Well Ordering the Reals
    ... Tony Orlow says... ... >If one can, as you did, select an infinite element, can form a set by ... So you are saying that no uncountable set can be well-ordered. ... So you *don't* claim to have a well-ordering for the reals? ...
    (sci.math)
  • Re: An uncountable countable set
    ... Tony Orlow wrote: ... defines an infinite element of *N as being "larger than any finite ... But none of Robinson's non-standard numbers are cardinalities. ... No kidding. ...
    (sci.math)
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