Individual Arrangement (Voller Text als pdf-Dokument)
Stichworte: Erstes Hilbert Problem, Cantor'sches Diagonalverfahren, Abzählbare Anordnung der reellen Zahlen, Kontinuumhypothese, Überabzählbarkeit, First Hilbert Problem, Cantor's diagonal process (Critic), continuum hypothesis, countable arrangement, uncountability
Abstracts:
Language is used to transmit messages. The "meaning" of a message should be given from the informant to the recipient of the message. A written, oral or otherwise formulated message is taken on its own not yet "meaningful". It is a "physical reality" such as a handwritten piece of paper, a monitor covered with signs, an acoustic phenomenon such as language etc. It can get a "meaning" only through the informant himself or through a receiving person. Such a " meaning" is therefore dependent on individuals.
Starting from these considerations, one comes to conclusions for the set theory. It turns out that all proofs of the existence of uncountable sets contains a contradiction. As an example the set of real numbers between 0 and 1 is checked. Finally, it follows that every proof of the existence of sets with a cardinality größer als |N| contains a contradiction.