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Jörg Wallraf
Lives in Kerpen
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Jörg Wallraf

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Empty space isn't really...empty. To create a truly empty vacuum would cost a large amount of energy to create, so much energy so that the vacuum would be full of fluctuations.
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Jörg Wallraf

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Jörg Wallraf

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An alle Kaffejunkies:
Kennt jemand diese Firma oder kann jemand einen Kaffe Dauerfilter empfehlen, der wirklich langlebig ist? Preislich bewegen sich ja alle so zwischen 10€ und 35€. Gold mit Titan scheint so das teuerste zu sein. Gewebtes Sieb soll angeblich das beste sein, steht aber leider nirgends dabei... für Tips bin ich sehr dankbar!
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funktioniert super, man muss jedoch grob gemahlenen kaffee nehmen!
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[NEU+OVP] Kingston KFJ-FPC50/512 MB PC2100 SO-DIMM Ram Speicher
35€ inkl. Versand
266 MHz / 200 Pin / DDR / PC2100 / CL2.5 / SO-DIMM / SMALL OUTLINE DIMM
Speicher in OVP ungeöffnet und noch versiegelt! Festpreis, kein Handeln! Preis inklusive Versand als Brief/Päckchen! Abholung möglich. Privatverkauf, keine Garantie, keine Rücknahme! Garantie evtl. über Kingston da Speicher m.M. nach in Deutschland 10 Jahre Garantie hat.
Zufriedenheitsgarantie siehe traumphase/Ebay 70+ 100% Bewertungen!
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Jörg Wallraf

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World. 3D chalk street art by Julian Beever.
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Jörg Wallraf

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Hier einfach deine Anzeige reinsetzen und privat verkaufen!

KLEINES REGELBUCH FÜR ALLE UNERZIEHBAREN:

Bitte hier keine Anfragen einstellen, dafür den Poster anschreiben!

Bitte Texte lesen.

Wer Produktfragen stellt die einfach im INet nachzusehen wären, wird sofort gebannt! Wer fragt "Lezzta Preiss" wird sofort zum Mond geschossen!

Geht vernünftig miteinander um!
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PRIVATE KLEINANZEIGEN
Sun, November 25, 2012, 11:00 AM

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WAS: SAMSUNG 160GB SATA 2,5 ZOLL FESTPLATTE  HM160HI
WIE: gebraucht, keine garantie
WO: Kerpen
WIEVIEL: 50€

Ideal für Samsung N130 Benutzer, da die Recovery Partition intakt ist!!!
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Have him in circles
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Jörg Wallraf

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1541 i like...
 
Schönes Wochenende!
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Jörg Wallraf

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Mehr von Klaus Stuttmann unter www.tagesspiegel.de/karikatur
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[NEU+OVP] LEXMARK X340A11G LASERKARTUSCHE
50€ inkl. Versand
Neupreis ab 70€ siehe http://goo.gl/HkoAS
Siegel intakt!
Für Drucker X 340/340 N/342 N
Toner schwarz return program, 2.500 Seiten ISO/IEC 19752
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Jörg Wallraf

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When you repeat addition you get multiplication.  When you repeat multiplication you get exponentiation.  And when you repeat that, you get tetration!

Let's follow Donald Knuth and write exponentiation as ↑.  Then 4 cubed is

4↑3 = 4 × (4 × 4) = 64

We are multiplying 4 by itself 3 times.   Next comes tetration, which we write as ↑↑.   Here's how it works:

4↑↑3 = 4 ↑ (4 ↑ 4) = 4 ↑ 256 ≈ 1.3 × 10¹⁵⁴

We are raising 4 to itself 3 times.  Before the parentheses didn't matter, but now they do: we put the parentheses all the way to the right, since (a ↑ b) ↑ c equals a ↑ (b × c) while a ↑ (b ↑ c) is something really new. 

As you can see, tetration lets us describe quite large numbers.   10↑↑10 is much bigger than the number of atoms in the observable universe.   

In fact, 10↑↑10 is so big that you couldn't write it down if you wrote one decimal digit on each atom in the observable universe!

In fact, 10↑↑10 is so big you couldn't write the number of its digits if you wrote one digit of that number on each atom in the observable universe!!

In fact, 10↑↑10 is so big you couldn't write down the number of digits in its number of digits if you wrote one digit of that number on each atom in the observable universe!!!

Puzzle: About how many times could I keep going on here?   Let's say there are 10 ↑ 80 atoms in the observable universe; this seems roughly right. 

We could march forwards and create notations for numbers so huge that 10↑↑10 looks pathetically small.   And we will!   We can even look at infinite tetration.  And we will - that's our main goal here!   But it's also fun to ask questions like:

Puzzle: What is 10↑↑10.2 ? 

This makes no sense at first: you can't write down a tower of powers with 10.2 tens in it.   But you couldn't add 10.2 tens together at first, either, so 10 × 10.2 didn't make sense until someone explained what it meant.  Same for exponentiation.  So, maybe tetration can also be defined for fractions in some nice way.   And maybe real numbers too.  And maybe even complex numbers.

Believe it or not, this seems to be an open question!  It's phrased as a precise conjecture here:

http://en.wikipedia.org/wiki/Tetration#Extension_to_complex_heights

and there's a good candidate for the answer.  The picture here shows a graph of the candidate for e↑↑z as a function on the complex plane.
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Jörg Wallraf

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Semiconductor band gap is temperature dependent LED changes color in liquid nitrogen.

Orange LED in liquid nitrogen
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Have him in circles
25 people
Gi dith's profile photo
Joerg Wallraf's profile photo
Martina Schwarzer's profile photo
Christoph Wichterich's profile photo
Micha Schlieper's profile photo
KupkeWebDesign's profile photo
Ernst Frielingsdorf's profile photo
Ingrid Poehlchen's profile photo
Wir 3 - Interessengemeinschaft Brüggen Balkhausen Türnich's profile photo
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