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.
