19 = 4!-4-(4/4)
The Weak Force, dare I ask what “chained arrows” are?
Paraphrased from The Book of Numbers, by Conway and Guy:
a -> 1 -> b is a^b.
a -> n -> b is a -> (n - 1) -> (a -> (n - 1) -> … (a -> (n - 1) -> a )…), where there are b a -> (n - 1)'s.
a -> … -> x -> y -> (z + 1) is…
a -> … -> x if y = 1;
a -> … -> x -> (a -> … -> x -> (y - 1) -> (z + 1)) -> z if y > 1.
Also, a -> … -> b -> 1 is a -> … -> b.
I hope I got that right…
IIRC, there’s one in Unix.
What does the strange looking operator do? I don’t think you are allowed to concatenate the digits, either.
[symbol]Ö[/symbol] is the radical sign, i.e., square root.
Whoa. I’m confused, The Weak Force. There seem to be several different ways of expanding these expressions.
a -> 1 -> b = a[sup]b[/sup] = a * a * a … * a * a (for b multiplications of a).
What would a -> 2 -> b be?
My TI-89 will do it. 
Takes less than a second, but that’s no surprise. What is suprising is that I don’t feel like copying down all 155 digits.
This time.
Urban Ranger, does your machine have the Symbol font? Mine doesn’t, and I’m seeing the alleged square-root sign as a capital O with umlaut.
4^256 = 13407807929942597099574024998205846127479365820592393377723561443721764030073546976801874298166903427690031858186486050853753882811946569946433649006084096
Oh, okay, it just doesn’t show up that way on my browser. Thanks.
Yes, that’s exactly what I am seeing, even though I have the Symbols typeface. I reckon only IE would render it correctly, while I am using Mozilla.
About This Message Board thread: Symbol font does not work in Netscape
Well put, RM, but now you’re wallowing in the quicksand of formality…
Gyan9 grabbed me and dragged me in. Sorry we got mud on y’all.
Interesting. I just opened this thread under IE5.0, and none of the multiple exponents are displayed correctly.4[sup]4[sup]4[/sup][/sup] looks like 4[sup]44[/sup]. However, it does show the square-root sign.
…and a Google search yielded this page: http://www.wschnei.de/number-theory/large-numbers.html
Looks like tetration is just a minor bump in the foothills of Large Numbers…
20 = 4 x (4 + 4/4)
21 = 4! - (4 - 4/4)
22 = 4! - (4 + 4)/4
23 … already done
24 = (4 x 4) + 4 + 4
My software won’t let me do 4[sup]4[sup]4[sup]4[/sup][/sup][/sup]. Just as well, it’s probably a scary-big number. :eek:
Whatever it is, it’s bigger than 268435448 digits!