On Monday, November 6, 2017 at 12:17:08 PM UTC+3, WM wrote: > Am Montag, 6. November 2017 08:21:29 UTC+1 schrieb bassam king karzeddin: > > Why do we really need those real non-constructible numbers, if it is impossible to express them exactly except only by constructible numbers or as meaningless notation in mind only? > > Neither does anyone need them nor can anyone use them. At least not in mathematics. The only occupation for such non-existing creatures is matheology. > > "how can one assert that something like the continuum exists when there is no way one could even in principle search it, or even worse, search the set of all subsets, to see if there was a set of intermediate cardinality? Faced with these two choices, I choose the first. The only reality we truly comprehend is that of our own experience. But we have a wonderful ability to extrapolate. The laws of the infinite are extrapolations of our experience with the finite." [Paul J. Cohen: "The discovery of forcing", Rocky Mountain Journal of Mathematics 32,4 (2002) 1099f] > > Most of these extrapolations, starting with the use of the bijection as a measure for infinite sets, are absolutely unscientific because > (1) really scientific results will never depend on "clever choice" of indices, and > (2) universal quantification over infinite sets shows that every element is followed by infinitely many elements, proving that universal quantification is impossile per se. > > Regards, WM
So great that you recognize those real irrational algebraic and transcendental numbers (which are not constructible numbers) as being non-existing creatures
But so, unfortunately, those fictional creatures constitute the main backbone of what is called nowadays the modern mathematics, where almost 90% of mathematics stand on which represent a great tragedy for all other sciences too, especially physics
And the coming even greater future tragedies that the mathematics is expanding indefinitely in that so fictional direction and building very easily many more baseless towers of so unnecessary mathematics without a stop, thinking that they are trying to understand the universe and much alleged fictional universes too, which makes the whole world swim randomly in many fictional stories than any previous stage of human accumulative ignorance ever happened in history
And the professional mathematicians are so much delusional about their naive thinking that the fictional expansion of a real number would ultimately solve the real world problem especially in physics, whereas physics is the ultimate truth of existence principle even in real numbers throw exactly geometry
So, mathematics is definitely violating every principle of little logic and the so elementary physical proof of existence, in reality, had managed and escaped completely from obeying any rules or any scientific evidence of real existence to be truly pure fictions in mind only, which is meaningless
So, how can we subject mathematics not to go astray and to obey some basic fundamental rules of existence in order to be at least legal? wonder!