Re: abundance of irrationals!)

Virgil wrote:

> In article <1114703327.169375.6520@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
> mueckenh@xxxxxxxxxxxxxxxxx wrote:
>
>> Virgil wrote:
>>
>> > Does WM declare that there cannot be a bijection between the odd
>> > naturals and even naturals?
>>
>> Yes, because none of these sets does exist.
>
> The rule 'add 1 to odds (or subtract 1 from evens)' does it nicely, even
> though WM claims it is impossible.
>
> If this rule fails, then ther must be a smallest odd, or asmallest even,
> for which it fails, and someone of WM's great intellect should have no
> trouble in producing that smallest odd (or smallest even) as proof of
> his claim of impossibility.
>
> Of course, if WM should fail, we might be inclined to take his failure
> as evidence that there are no naturals for which this bijection fails.
>> >
>> > Unless he is wiling to do so, we have established that bijections can
>>
>> > sometimes be carried out between infinite sets.
>> >
>> > No one has claimed that it can always be done, and, as Cantor has
>> > proved, despite WM's allegations to the contrary, it sometimes cannot
>> be
>> > done.
>>
>> It can never be done, because of lacking infinity. But that's not the
>> point.
>
> When WM has found the least odd, or least even, for which the above
> described mapping between odds and even naturals fails, only then need
> we take him seriously. Until then WM is merely a clownish troll.

It seems to me (from his statement "because none of these sets
does exist") that he may be disagreeing with the statement that "the set
of all even (odd, respectively) numbers exists."

Matt
.

Relevant Pages

  • Re: abundance of irrationals!)
    ... >> naturals and even naturals? ... If this rule fails, then ther must be a smallest odd, or asmallest even, ... as evidence that there are no naturals for which this bijection fails. ...
    (sci.math)
  • Re: abundance of irrationals!)
    ... > Does WM declare that there cannot be a bijection between the odd ... > naturals and even naturals? ... > sometimes be carried out between infinite sets. ...
    (sci.math)
  • Re: infinitely many nns = infinite nns?
    ... NO, dumbass, you canNOT express THAT bijection THIS way: ... between the odd naturals and the positive naturals. ... INFINITE number, and yet be finite? ...
    (sci.logic)
  • Re: 50%+1 and 55%
    ... shortage of accurate ways of describing the concept, ... happen to be one of them; it fails when the total is odd. ... now you have 649 seats ...
    (uk.politics.misc)
  • Re: 50%+1 and 55%
    ... shortage of accurate ways of describing the concept, ... happen to be one of them; it fails when the total is odd. ... web site at www.abelard.org - news comment service, logic, economics ...
    (uk.politics.misc)