Books on Amazon
|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.
Philosophie und Mathematik Darmstadt 1995