Am Mittwoch, 8. November 2017 10:06:49 UTC+1 schrieb bassam king karzeddin: > 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.
> So great that you recognize those real irrational algebraic and transcendental numbers (which are not constructible numbers) as being non-existing creatures
I meant chiefly such numbers that have not any chance to be expressed or pointed to. Irrational algebraic or transcendental numbers have at least a finite definition. When I wrote the first edition of my book "Mathematik für die ersten Semester", 4th ed., De Gruyter, Berlin 2015 I seriously considered whether I should call these objects numbers because you never can describe their exact value in what we call our numeral system, i.e., decimal system. But that would have raised too much confusion because most other teachers of mathematics would call these objects numbers. Therefore I decided to join them. After all these limits have one and only one value. Although it is not describable by decimals, we can describe them in systems based on irrational bases. But I understand fully that you are not happy with calling them numbers.