On 3 Apr., 09:26, Virgil <vir...@ligriv.com> wrote: > In article > <2569eb91-7037-483e-be2c-17fce8394...@j9g2000vbz.googlegroups.com>, > > 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. > > 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?