On 13 Dez., 21:02, Zuhair <zaljo...@gmail.com> wrote:
> Note: definable is short for "definable by parameter free finite > formula"
What do you believe to gain by parameters in definitions? Do you want to define the real numbers by using real numbers as parameters?
Otherwise you will not arrive at uncountably many definitions, you may use all natural numbers and all rational numbers. Or has some great leading matheologian who bolsters his ego by calling himself a logican told you that by parametric definitions the real numbers all can be defined?
Be informed, that is not the case. If there are uncountable many real numbers, then they are not real in that nearly all are completely undefined. Therefore they cannot be used in Cantor lists and cannot spring off as diagonals. They would be completely unrelated to Cantor's "proof" and to mathematics.