On 1 Mai, 11:15, Dan <dan.ms.ch...@gmail.com> wrote: > > It is necessary for Cantor's proof. Unless every digit exists on the > > diagonal, the diagonal number is undefined in an undefined list. But > > that is Cantor's claim: forall n : a_nn =/= d_n. > > It exists "as formula" , whether or not you know the formula .
There are only countably many formulas. If all diagonals exist as formulas, then all belong to a countable set.
> > Yes, but there are only countably many formulas. > > Formulas as "strings of characters"/syntax are defined relative to a > language . > There is no 'completed language' that proves that formulas are > countable . A language cannot count over its own formulas:
That does not matter. The formulas are a subset of all finite strings. All finite strings are countable. All possible languages interpreting these strings are finite, because every language has to be made. > > Every language L_2 that counts the formulas in L_1 has its own new > uncountable formulas.
No. That is absolute nonsense, contradicting the fact that a subset of a countable set is countable. Of course such nonsense is required to maintain matheology, but it is not set theory (ZFC) let alone mathematics. > > > It is true, since light velocity cannot be exceeded without time > > reversal. If time reversal was possible, we would have noticed it. > > Quantum mechanics . Non-locality (faster than light influences)
impossible to send signals in thsi way.
> > I (and many others ) demand a contradiction in mathematics by a > mathematical argument .
I told you the argument. Read it. Every rational has a number does not mean all rationals have numbers.