On May 12, 7:48 pm, WM <mueck...@rz.fh-augsburg.de> wrote: > Matheology § 265 > > Abstract. This paper examines the possibilities of extending Cantor?s > two arguments on the uncountable nature of the set of real numbers to > one of its proper denumerable subsets: the set of rational numbers.
There is Real Mathematical Calculus
and there is LOGIC.
A:[0|1| -> B:[0|1]
Cantor's muffles the 2 arrows together into an infinite sum of logical conditionals and pulls out hyper-contradictions from his bellybutton.
Any REAL MATHEMATICS is based on equivalent FUNCTIONS defined over N!
f(n):N -> R
In CALCULUS you are allowed to use f(r):R -> R but underneath you must have some definable domain
f( g(n):N ) -> R
where g(n) COMPUTES the real domain of the function via integer arithmetic.
LOGIC and f(r):R DO NOT MIX!
f(r):R is just a CALCULUS SHORTHAND!
NEWTON would hit CANTOR with a STICK if he saw the mess that CANTOR made of his CALCULUS!