Date: Jan 29, 2013 3:54 AM
Author: William Hughes
Subject: Re: Matheology § 203
On Jan 29, 9:33 am, WM <mueck...@rz.fh-augsburg.de> wrote:

> "All" and "every" in impredicative statements about infinite sets.

>

> Consider the following statements:

>

> A) For every natural number n, P(n) is true.

> B) There does not exist a natural number n such that P(n) is false.

> C) For all natural numbers P is true.

>

> A implies B but A does not imply C.

Which is the point. Even though A

does not imply C we still have

A implies B.

Let L be a list

d the antidiagonal of L

P(n), d does not equal the nth line of L

We have (A)

For every natural number n, P(n) is true.

This implies (B)

There does not exist a natural number n

such that P(n) is false.

In other words, there is no line of L that

is equal to d.