Date: Apr 3, 2013 6:40 AM
Subject: Re: Matheology § 224

On 3 Apr., 09:26, Virgil <> wrote:
> In article
> <>,
>  WM <> wrote:

> > On 3 Apr., 00:29, Virgil <> wrote:
> > > The point being that removing one object from an infinite set does not
> > > diminish the infinite number left in the set

> > That is a good point. Alas induction holds for every natural number.
> No!

Your no is wrong. Induction holds for every natural number.

> It only holds for inductive sets:

But you don't know what the natural numbers are.
> One valid form of induction is:
> There exists a set of objects, N,

In mathematics that kind of nonsense is not required.

> and a special object such that:
>    1. The special object is a member of N.
>    2. For every object in N there is a successor object also in N.

That is not induction, but the property of natural numbers that is
required as the foundation of induction.

>    3. The special object is not a successor object of any object in N.

The special object it 2^22 and the elements of your N are 1^33, 0^44,
(-1)^55 and so on.

>    4. If successors of two objects in N are the same,
>       then the two original objects are the same.
>    5. If any set contains The special object and the successor
>       object of every object in N, then that set contains N as a subset.

The elements of N are the humans starting from Adam in the sequence of
their birth?

Regards, WM