I'm a math hobbyist, so forgive me if what I ask is silly.
I just learned that the cardinality of Reals is greater than the Naturals.
So, because of that, there can be no turing machines which generate all real numbers (ignore the fact that the turing machine would never halt).
In particular, there can be no algorithm which sequentially generates all real numbers, because, since turing machines operates sequentially, we could put them into correspondence with the Naturals, which would be a contradiction of the Cantor Theorem.
Is my thinking correct? Could you imagine what other implications would this have?
Thanks for the time.