Das Kalenderblatt 091230

29/12/2009 - 12:07 von WM | Report spam
The third point is that under these conditions it is straightforward
to show that the procedure “Give me any numeral n you can imagine, I
will give you the next one” has to break down at a certain point. Ask
any person to imagine a very large numeral, say, in decimal
presentation. Usually what we do is to form a picture, say, we see a
blackboard and it is covered with ciphers all over. But that won’t do.
For once we have such a picture, it is obvious that is communicable,
hence that it is finitely expressible and hence that there is room to
imagine the next numeral and to communicate it. Thus, the alternative
must be that the numeral is so large that it cannot be imagined,
thereby making it senseless to talk about the next one. I will return
to the implicit paradoxical nature of what I just wrote. What is being
asked is to imagine a numeral so huge that it cannot be imagined.

[Jean Paul Van Bendegem: "Why the largest number imaginable is still a
finite number"; p. 11]
http://www.vub.ac.be/CLWF/members/j...inable.pdf

Gruß, WM
 

Lesen sie die antworten

#1 Thomas Plehn
29/12/2009 - 13:45 | Warnen spam
Hallo,
das scheint mir ein àhnlicher Einwand zu sein, wie die Feststellung, dass
ein Computer diesen konstruktiven Prozess irgendwann nicht mehr fortführen
könnte. In der Mathematik geht man doch aber, wie ich es verstehe, nicht von
der Berschrànktheit der Resourcen aus, sondern hat beliebig viel Speicher
und beliebig viel Zeit zur Verfügung. Unter diesen Bedingungen ist aber ein
Increment immer möglich. Oder sehe ich da etwas falsch?

"WM" schrieb im Newsbeitrag
news:

The third point is that under these conditions it is straightforward
to show that the procedure “Give me any numeral n you can imagine, I
will give you the next one” has to break down at a certain point. Ask
any person to imagine a very large numeral, say, in decimal
presentation. Usually what we do is to form a picture, say, we see a
blackboard and it is covered with ciphers all over. But that won’t do.
For once we have such a picture, it is obvious that is communicable,
hence that it is finitely expressible and hence that there is room to
imagine the next numeral and to communicate it. Thus, the alternative
must be that the numeral is so large that it cannot be imagined,
thereby making it senseless to talk about the next one. I will return
to the implicit paradoxical nature of what I just wrote. What is being
asked is to imagine a numeral so huge that it cannot be imagined.

[Jean Paul Van Bendegem: "Why the largest number imaginable is still a
finite number"; p. 11]
http://www.vub.ac.be/CLWF/members/j...inable.pdf

Gruß, WM

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