Date: Apr 3, 2013 6:40 AM
Subject: Re: Matheology § 224
On 3 Apr., 09:26, Virgil <vir...@ligriv.com> wrote:
> In article
> WM <mueck...@rz.fh-augsburg.de> wrote:
> > On 3 Apr., 00:29, Virgil <vir...@ligriv.com> 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.
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