Die 50.000 Coins Frage für wirklich Kluge Köpfe!

Zitat:

---

Zitat von Paul

Steht das Googolplexplexplexplexen jetzt noch mit im Exponenten oder "hinter" der zahl 10^166?

Wenns dahintersteht, könnte ich mich noch damit anfreunden... Wenns zum Exponent gehört, ist das wohl n bisschen viel...

---

ne so wie ich das Verstehe meint er es sind 10 hoch 66 Googolplexplexplexplexen ales ander währe glaube ich wirklich zuviel.
Obwohl seine Umrechnung der Zahl in die Anzahl der darin entahltenen Googolplexplexplexplexen falsch ist...(auf den ersten Blick)

hab alle noch einmal genau nachgerechnet.
müsste aber richtig seinrechne doch mal nach...

[quote=Mario]...wenn es alleine nach 1000 Teilungen schon 5,3575E+300 Universen gibt..../quote]

Ich mußte das jetzt mal aufgreifen. Damit hab ich per Verhältnisgleichung die Universen :

Zeit: 365,25x24x60x60x18E+9 = 5,680368E+17 sec.

Teilungen: 5,680368E+17 sec x 10E+43 = 5,680368E+61

1000 Teilungen -> 5,3575E+300 Universen

5,680368E+61 Teilungen -> 3,043257156E+18300 Universen

Teilchen: 3,043257156E+18300 x 6E79 = 1,8259E+19100 Teilchen insgesamt

Hm, irgendwie brauch ich nen anderen Taschenrechner!
Gibts da was, welcher solch riesige Zahlen bewältigt?

Mal ein Versüchchen:

t=18*10^9*365*24*3600s (Zeit)
a=6.1^79 (Anzahl Teilchen am Anfang, dimensionslos)
tp=10^-43s (Planck-Zeit)
gesucht A (Anzahl Teilchen am Ende, dimensionslos)

Anzahl Verdoppelungen: t/(tp)

daraus die geometrische Folge: A=a*2^(t/(tp))

numerisch A=6.1^79*2^(18*365*24*3600*10^52)

ohoh, grosse Zahl

6.1^79 in Zehnerpotenz
6.1^79=10^x -> x=log(6.1^79,10) (sollte den Zehnerlogarithmus darstellen)
x=79*log(6.1,10) (log-Gesetz)
6.1^79=10^(79*log(6.1,10))

analog mit 2^t/(tp)
2^t/(tp)=10^x -> x=log(2^t/(tp),10) (sollte den Zehnerlogarithmus darstellen)
x=t/(tp)*log(2,10) (log-Gesetz)
2^t/(tp)=10^(t/(tp)*log(2,10))

wir nähern uns dem Ende:
A=10^(79*log(6.1,10))*10^(t/(tp)*log(2,10))
=10^(79*log(6.1,10)+t/(tp)*log(2,10))
=10^(23.781...+1.708*10^60)
der erste Summand ist wohl vernachlässigbar klein, auch den Faktor lasse ich mal weg, somit hätten wir noch

ca.10^10^60

das auf Googolplex gerundet wäre dann wohl 0 Googolplex?

So eine schöne Rechnung, aber ich habe ein paar Zweifel an deren Richtigkeit... Glaube aber der Ansatz ist nicht schlecht, vielleicht hat jemand Lust was draus zu machen.

Zitat:

---

Zitat von mir

18*365,25*24*3600*10^(52) Teilungen
=> 2^(18*365,25*24*3600*10^(52)) Universen
=> 2^(18*365,25*24*3600*10^(52)) * 6 * 10^79 Teilchen

---

=> (2^(18*365,25*24*3600*10^(52)) * 6 * 10^79) / 10^(10^(100)) Googoplex Teilchen
und das ist meines Erachtens weniger als eins

Stimmt, falsch gerundet... wäre eher 0. Ich lege mich auf 0 Googolplex fest.

stimmt den diese teilungsliste schon mnal oder hab ich da was falsch verstanden

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Natenjo
hat recht...
gib ich 50.000 coins :P


ich verstehe wirklich sehr wenige wörter ins diesem thread o_O

Ja müsste stimmen, aber warum fängst du nicht bei 1 an? :-)

Ich bin auch der Meinung das es auf Googolplexe gerundet 0 (Null) sind.
Denn

1 Googol = 1E+100
1 Googolplex = 1E+ 10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000

Und die Zahl die wir ausrechnen wollen ist "2^5,680368E+60 * 6,1E+79". wenn wir diese Zahl ausrechnen könnten (Sorry aber ich selber bin da scheinbar zu blöd zu) wäre sie immer noch kleiner als 1 Googolplex. Weil 1 Googolplex hat 100 Stellen in der Zehnerpotenz und die gesuchte Zahl hat so ca. 60 + 79 = 139, das sind 3 Stellen in der Zehnerpotenz. Die Zahl ist zwar ein paar mal so groß wie ein Googol, aber viel viel kleiner als ein Googolplex.

So ich hoffe da nicht ganz falsch zu liegen.

MfG
Supermario!

oh die von 0 sind nicht mehr da vlt war der post uzu lang und wurd automatisch gekürzt

18 Milliarden Jahre = 18 * 10^9 * 365 * 24 * 3600 / 10^(-43) = 5,67648 * 10^60 Plancksche Zeitquanten

Wenn ich eine Startzahl S genau n mal verdopple, erhalte ich S*2^n Objekte.

Also würde es nach 18 Milliarden Jahren aus Anfangs 6*10^79 Teilchen

2^(5,67648 * 10^60) * 6 * 10^79 Teilchen geben

= 10^[log10(2) * 5,67648 * 10^60] * 6 * 10^79
= 10^[1,7088*10^60] * 6 * 10^79
= 10^[1,7088*10^60 + log10(6) + 79 ]
= 10^[1,7088*10^60] (da log10(6) + 79 vernachlässigbar klein)

= 0 Googolplex (gerundet), da ein Googolplex = 10^(10^100)

Genauer gesagt ergeben sich 10^(1,7088*10^60 - 10^100) Googolplex also rund 0 Googolplex.

wo Ihr alle falsch rechnet ist die Verdoppelung der Universen.

Auch ich wusste nicht wie man das berechnet und hab in einen Mathematik Forum tolle hilfe bekommen.

Die Verdoppelungen werden mittels Geometrischer reihe berechnet:

http://de.wikipedia.org/wiki/Geometrische_Reihe


ist mir aber irgendwie noch zu hoch...

@ hh221:

Das ist leider falsch. Unsere Formel ist korrekt, wir wissen nur nicht wie wir sie ausrechnen sollen.

Die Universen verdoppeln sich bei jeder Teilung, deswegen "2 hoch n". Das was du vorschlägst ist alle Ergebnisse von "2 hoch n" noch zu addieren. Was wie in dem Wikipedia-Beispiel für Zinseszinsrechnung gut ist. Bei unserer Rechnung ist das fehl am Platz.

MfG
Supermario!

@Mario
War denn jetzt wenigstens schon irgendjemand wenigsten knapp an der Lösung oder ist das alles ganz falsch was hier geschrieben wird??

P.S.: Versehe zu meinen bedauern diesen Thread auch nicht.....

nun was heißt nahe... aber gute versuche wahren dabei