@misc{Lexicon of Arguments, title = {Quotation from: Lexicon of Arguments – Concepts - Ed. Martin Schulz, 29 Mar 2024}, author = {Thiel,Christian}, subject = {Real Numbers}, note = {Thiel I 238 Def Real transcendental numbers: such real numbers which are not solutions of any algebraic equations anxn+....= 0 are with integer coefficients ai. They could indicate a simple procedure, from which they concluded, because of the non-countability of the totality of the real numbers proved by Cantor, that after deduction of the real numbers a non-empty totality must remain, I 239 the transcendental real numbers. However, due to this typical "classical" conclusion, one is not in a position to actually produce such a number. Nevertheless, Liouville had long before constructed real transcendental numbers in 1844: 1/10 + 1/10² faculty + 1/10 3 faculty... If one wanted both cases (conservative and classical) logically simply by "(Ex)Tr(x)" (with "Tr" for transcendental), one would simply blur the difference. For the fundamentals of mathematics it is important to mark effective proofs of existence as such. In some cases the existence is not questioned at all, but a concrete answer to a mathematical question is sought. I 240 Example: largest common divisor of two basic numbers. An "effective method" does not solve the problem by trial and error, but in a finite number of steps. >Calculability, >Infinity, >Continuum.}, note = { T I Chr. Thiel Philosophie und Mathematik Darmstadt 1995 }, file = {http://philosophy-science-humanities-controversies.com/listview-details.php?id=804184} url = {http://philosophy-science-humanities-controversies.com/listview-details.php?id=804184} }