|Infinity, infinite, philosophy: infinity is a result of a not stopping procedure, e.g. counting or dividing, or e.g. the continued description of a circular motion. In life-related contexts, infinitely continuous processes, e.g. infinite repetition, or never ending waiting are at least logically not contradictory. A construction rule does not have to exist to give an infinite continuation, such as e.g. in the development of the decimal places of real numbers. See also boundaries, infinity axiom, repetition, finitism, numbers, complex/complexity._____________Annotation: The above characterizations of concepts are neither definitions nor exhausting presentations of problems related to them. Instead, they are intended to give a short introduction to the contributions below. – Lexicon of Arguments. |
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|Thiel I 169
Infinity/Zeno/Thiel: Problem of infinitely small quantities. Could a series of infinitely many points linked to each other be produced?
Zeno of Elea (5th century BC). It is precisely because of the possibility of an infinite number of divisions that we cannot build the entire route "from the bottom". There are no first building blocks.
Zeno's paradox: the arrow never arrives, it appears to never be able to leave the bow.
In today's usual computational "resolution" it is preceeded as following:
Achilles 5m/s, turtle 5cm/s. Lead over 15 m. The lead of the turtle is increased by 5 cm per sec but simultaneously reduced by 20 m. From 1500 + 5t 500t = 0 is obtained as the time t of the overtaking: t = 1500/495 s, slightly more than 3 seconds.
Modern representations use decimal fraction notation: 3.030303 ....
Vs: the essential is hidden, namely
The sequence 3 + (3 divided by 102, 104, 106, etc.).
This sequence can only represent a finite value. But the riddle is only repeated once again for the layman by the decimal fraction._____________Explanation of symbols: Roman numerals indicate the source, arabic numerals indicate the page number. The corresponding books are indicated on the right hand side. ((s)…): Comment by the sender of the contribution.
Philosophie und Mathematik Darmstadt 1995