> You did not write down any digits. Therefore your example fails
> > > A real number can be listed by a terminating decimal, by a periodic > > > decimal, or by a formula supplying each of its decimals.
I gave you a formula for each of the decimals of the anti-diagonal , provided you would have given the formula for the list.By your own definition (the third case you mentioned, that is) , I succeed .The antidiagonal is list-dependent . Cantor himself never claimed otherwise .
> No. I know that any language that can be used cannot have more than > countably many words.
Yes , but no language can express all the reals. If you manage to count all the reals R_1 expressed in a language L_1 , then , since you can't do such a thing in the language L_1 , you're already using a stronger language L_2 .
L_2 can count the reals of L_1 , but L_2 itself has even more reals , that it cannot itself count . To count the reals of L_2 , you need an even stronger language L_3 ,and so on .
There's actually an uncountable amount of "languages that have countably many words". And every consistent language can express a countable subset of the reals .
>I know that everything that can be stored in the universe belongs to a >finite set.
Do you really want to go in the physics? The most accepted cosmological model predicts the universe is spatially infinite and roughly homogenous in large scales.
>If all places are occupied and you want to store something >else you have to forget something former - without any traces.
Erasing information without leaving traces in the environment would decrease entropy , thus violating the second law of thermodynamics . Information is never truly 'erased' . All places are never occupied . We have a lot of space around , and it's expanding .
>In science one knows this, one knows it everywhere >apart from matheology.
>Religions and matheology have no real limits and no real contents.
Differential equations.They work with infinite digits , and real numbers, and get results, used by real scientists .
Every mathematician with a bizarre new idea has,eventually, managed to make his concepts understood to the mathematical community, or at least someone else ,for that matter . The fact that you haven't , and , sadly ,most likely can not, should give you an idea of the situation . There's only one true practitioner of matheology . The rest of us , well ... we're just doing mathematics .