Scratchbook

Das Leben ist immer anders als die Realität.

Null, nichts, gar nichts.

Claude, 16. März 2011, 21:06 Uhr

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Die Null (0) ist die einzige reelle Zahl, die weder positiv noch negativ ist. Bezüglich der Addition ist sie das neutrale Element. Die Zahl Null ist die Mächtigkeit der leeren Menge.

Wie verschieden kann man „nichts“ beschreiben?

0
Null
„“ (leerer Text)
nil
undefined
false
void

Ganz amüsant finde ich die Definition von undefinierten Variablen:

var nothing = undefined;

Ist die Variable nothing jetzt definiert oder nicht? Gopferdeckel…

Division durch 0 – redefined

12:4 = 3

Bei 12:0 lautet die Frage: »Wie oft muss man 0 von 12 abziehen um 0 zu erhalten?«

Antwort (Wikipedia):
Keine Anzahl von Operationen bringt das gewünschte Ergebnis.
Bei 0:0 lautet die Frage: »Wie oft muss man 0 von 0 abziehen um 0 zu erhalten?« Antwort: Jede beliebige (also keine eindeutige) Anzahl von Operationen bringt das gewünschte Ergebnis.

Aber…aber… Nein?

Wie oft muss ich 0 von 12 abziehen, um 0 zu erhalten?
Unendlich oft.

Also:

12:0 = ∞

Würd‘ sagen, wir müssen eine Dimension höher, um das Ergebnis herauszubekommen…

Rein theoretisch:

12:∞ = 0

Hat die Unendlichkeit eine Grösse? Ich ziehe unendlich viele „Nichtse“ von 12 ab. Unendlich viele Dinger, die möglicherweise unendlich klein sind. Ich ziehe die so oft ab, bis es 0 gibt. Hmm.

Kauket

Null ist doch nicht definiert als Division um den Körpercharakter der Zahlen zu gewährleisten…

Wenn 12:0 = ∞ stimmen würde, müsste 0*∞ = 12 ergeben, womit wir das Problem hätten, dass 13:0 = ∞ auch dazu führen würde, dass 0*∞ = 13 und somit wäre die Multiplikation nicht mehr eindeutig.

Du könntest dir aber einen endlichen Körper bauen und anhand der Ganzahlringe mit Modulo dennoch eine Nulldivision durchführen. Da wir in einem endlichen Körper nur endlich viele Elemente sowohl als Faktor wie auch als Produkt haben können, müssen wir die Division mit Rest ausführen. Solange der Körper Prim ist, werden wir dennoch eindeutig rechnen können.

Nehme den endlichen Körper mit den Zahlen {0;1;2} Nun rechnest du

Zahl x = 3
Division:

3:1 = 3 mod 1 = 2
3:2 = 3 mod 2 = 1
3:3 = 3 mod 3 = 0
3:0 = 3:3 = 6:3 = 3 mod 0 = 0

Vielleicht war das jetzt ein wenig schnell, aber wenn du willst, schick ich dir mal ne online Vorlesung oder nen Buchtipp zum Thema endliche Körper.

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