/sci/ - Science & Math

File: 122 KB, 600x603, science.jpg [View same] [iqdb] [saucenao] [google]

Anonymous Fri May 16 13:52:48 2014 No.6537780 [DELETED]

What is the largest number that can be written in a 4chan post given the 2000 character limit? Digits are allowed, as are an unlimited number of exponentials (^), factorials (!), and multiplication/division/subtraction/addition, parenthesis, etc. However, non-integer symbols denoting numbers (for example, pi and e, any symbol for Graham's number, etc) are not allowed.

At first I thought it would be a repetition of 9^9^9... for all 2000 characters. Then I realized that 9^9999... would be larger. But what if the exponentiation was doubled up? 9^(9^99999999999999999)). Surely that would be larger yet. So then should it be a repetition of 9^(9^(9^(9^...)))? But then factorials could perhaps make it even larger. 9!^(9!^(9^!...)).

So what is it /sci/?

Anonymous Fri May 16 13:56:42 2014 No.6537784

9!^9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))

Anonymous Fri May 16 13:58:40 2014 No.6537788

>>6537784
Is this correct? And if so, when I had 3 leftover characters (for each added ^(9!) there is 5 characters, but the first one has no parenthesis or exponent so I had 3 leftover characters) was I write to throw on a 9!^ at the beginning? Or should it have been after the very last 9!, i.e. 9!^(9!^...9!^(9!^9!)))))))...))))))?

>>	Anonymous Fri May 16 14:01:16 2014 No.6537792 >>6537788 Okay I figured that out, I should have put the extra three characters after the last 9!.

Anonymous Fri May 16 14:03:01 2014 No.6537796

9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^(9!^9!)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))

>>	Anonymous Fri May 16 14:05:12 2014 No.6537800 you could just keep inventing single symbols to denote ever larger numbers arbitrarily forever, so your question is meaningless. its like asking what is the largest number.

>>	Anonymous Fri May 16 14:06:27 2014 No.6537803 >>6537800 I specified in the OP that regular digits are allowed but pi, e, a symbol denoting Graham's number, etc are not allowed. Consider only the following are allowed: 0 1 2 3 4 5 6 7 8 9 ( ) + - * / ! ^

>>	Anonymous Fri May 16 14:09:22 2014 No.6537812 ∞

Anonymous Fri May 16 14:09:25 2014 No.6537813

9!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

>>	Anonymous Fri May 16 14:09:40 2014 No.6537815 >>6537780 1/0

>>	Anonymous Fri May 16 14:11:42 2014 No.6537818 1 + 2 + 3 + ...

>>	Anonymous Fri May 16 14:12:03 2014 No.6537819 >>6537815 =0

>>	Anonymous Fri May 16 14:15:41 2014 No.6537826 up arrow allowed?

>>	Anonymous Fri May 16 14:16:04 2014 No.6537828 >>6537812 No ∞. Only symbols in >>6537803 >>6537813 You might be right. Would it be bigger than >>6537796? I am leaning to yes. >>6537815 You win. Second biggest? Biggest that doesn't equal infinity? >>6537818 No '...'

>>	Anonymous Fri May 16 14:17:06 2014 No.6537830 >>6537826 You mean ^? If so yeah, if not idk what you mean.

>>	Anonymous Fri May 16 14:18:37 2014 No.6537834 >>6537818 -1/12 isnt that large of a number

>>	Anonymous Fri May 16 14:20:48 2014 No.6537835 >>6537834 >being this retarded

>>	Anonymous Fri May 16 14:22:09 2014 No.6537837 ackermann "function tower" A^A^...A^(A^A(9)(9))(9)...(9)(9) 286 terms in a post

>>	Anonymous Fri May 16 14:39:16 2014 No.6537848 Back in school our teacher asked us what the largest number is that we could do with only 3 figures and someone answered 13^8. I can still laugh about that.

Anonymous Fri May 16 14:51:36 2014 No.6537864

>>6537830
hes speaking about up arrow notation. If you are allowing it then '9' followed by 1998 'up arrows' followed by a second '9' is the biggest number possible.

But you ruled out Grahams number so I guess you wont allow this as well.

Heres a wiki link for you:
http://en.wikipedia.org/wiki/Knuth%27s_up-arrow_notation

>>	Anonymous Fri May 16 14:55:28 2014 No.6537869 >>6537848 top kek

>>	Anonymous Fri May 16 14:58:40 2014 No.6537873 >>6537834 http://blogs.scientificamerican.com/roots-of-unity/2014/01/20/is-the-sum-of-positive-integers-negative/?WT.mc_id=SA_facebook

>>	Anonymous Fri May 16 15:09:39 2014 No.6537891 >>6537815 >>6537828 Sorry, 1/0 is not a number

>>	Anonymous Fri May 16 15:32:08 2014 No.6537923 >>6537848 G99

>>	Anonymous Fri May 16 15:33:43 2014 No.6537927 >>6537864 except Knuth is a raving faggot for defining <span class="math">\rm{ ↑_{Knuth}=⌃ ~ ⇈_{Knuth}=↑ }[/spoiler]

Anonymous Fri May 16 15:38:15 2014 No.6537936

G9999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999

>>	Anonymous Fri May 16 16:00:12 2014 No.6537966 >>6537819 =)

>>	Anonymous Fri May 16 16:06:51 2014 No.6537976 >>6537780 1/0

>>	Anonymous Fri May 16 16:11:32 2014 No.6537984 [latex]\lim_{x\rightarrow 0+} \frac{1}{x}[/latex] or how about just [latex]M > x \ \| \ x \in \mathbb{R}[/latex]

>>	Anonymous Fri May 16 16:13:09 2014 No.6537988 9!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!....

>>	Anonymous Fri May 16 16:19:54 2014 No.6537999 >>6537976 But 1/0 might be negative infinity, so let's write -1/0 too and one of these will be the answer.

>>	Anonymous Fri May 16 16:21:13 2014 No.6538000 OP, why can't you let us make new notation or denote numbers with symbols? It would be more interesting to see how good /sci/ is at making notation that creates huge numbers. The only rule should be that you can't reference other posts in this thread.

>>	Anonymous Fri May 16 16:22:43 2014 No.6538002 >>6537780 ⒛ is the biggest single character number ⒛⇈(1998 times)⒛ is the biggest number

>>	Anonymous Fri May 16 16:24:04 2014 No.6538008 >>6538002 If you read the thread, OP is a faggot who limited the notation you can use.

>>	Anonymous Fri May 16 16:26:16 2014 No.6538012 >>6538000 My notation is N = the largest number definable in a post And my number is N + 1

Anonymous Fri May 16 16:26:55 2014 No.6538014

>>6538002
⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈⒛⇈9⇈

>>	Anonymous Fri May 16 16:27:17 2014 No.6538015 im pretty sure that 9!!!!!!!!!.... is the solution. 7!! has already 16747 digits and i did not find a tool yet, which could even calculate 9!!

>>	Anonymous Fri May 16 16:27:57 2014 No.6538018 >>6538012 N*2.

>>	Anonymous Fri May 16 16:28:46 2014 No.6538020 >>6538018 N+1 is all that is necessary to show what anon suggested won't work.

>>	Anonymous Fri May 16 16:30:06 2014 No.6538022 >>6538012 Okay, why don't we make things like that an exception? I want to see creative notation, that's all.

Anonymous Fri May 16 16:36:30 2014 No.6538033

Considering the stirling approximation of factorials, I'm pretty sure >>6537784 and >>6537796 are suboptimal.

For n large enough, n! > 9!^n. And we'd be fine with having just n!!!!! > 9!^(n) to conserve the number of symbols, so the fact that just n! is already greater than 9!^n shows much stronger factorials are.

Indeed, the Stirling approx is n! ~ sqrt(2pi n) (n/e)^n. As soon as n/e > 9!, factorials grow faster.

Even something like (9!^9!) is much lower than 9!!!!!!!:
(9!^9!) is about 10^(10^6), while 9!!!!!!! is about 10^(10^(10^1000))

The guys who suggested 9!!!!!!!!!!!!!!... is most likely right.

>>	Anonymous Fri May 16 16:42:36 2014 No.6538042 >>6538033 unfortunately, without parentheses, 9!!!... means a multifactorial, not an iterated factorial

>>	Anonymous Fri May 16 16:45:39 2014 No.6538045 >>6538042 what is a multifactorial? anyway, i guess (9!)! still wind the 5 character competition

>>	Anonymous Fri May 16 17:01:07 2014 No.6538059 File: 781 B, 264x49, sage.png [View same] [iqdb] [saucenao] [google] >>6538015 Are you even trying?

>>	Anonymous Fri May 16 17:10:27 2014 No.6538074 >>6538042 Not according to OP's post, which doesn't allow multifactorials. But even then, you'd just start with a few exponentials and then you'd add the necessary parenthesis for the factorial chain, and you'd still be far above >>6537784 / >>6537796.

>>	Anonymous Fri May 16 17:16:55 2014 No.6538086 >>6538074 He later clarified we may use these symbols 0 1 2 3 4 5 6 7 8 9 ( ) + - * / ! ^ I assume that means in their conventional meaning.

>>	Anonymous Fri May 16 17:18:39 2014 No.6538091 >>6538086 He wrote "! (factorial)", not "! (factorials and multifactorials".

>>	Anonymous Fri May 16 17:19:41 2014 No.6538096 >>6538091 Yes. Look up the words later and clarified maybe.

>>	Anonymous Fri May 16 17:24:18 2014 No.6538104 >>6537780 <span class="math">\infty^\infty[/spoiler]

>>	Anonymous Fri May 16 17:25:28 2014 No.6538107 >>6537834 <span class="math"> \sum_{a=1}^{\infty} a \neq - \frac{1}{12} [/spoiler]

Anonymous Fri May 16 19:46:42 2014 No.6538311

>>6537864
Interesting, I'll take a look at the article. Thanks.

>>6538008
I wasn't even aware of up arrows, I just didn't want someone to say something like "x=the square of Graham's number, then take x^x, etc".

>>6538033
Thanks for the explanation. Because of what other anon said about multifactorials it would then have to be something like ((((9!)!)!)!)!

>>6538042
((((9!)!)!)!)! would still work

>>6538045
http://mathworld.wolfram.com/Multifactorial.html

>>6538074
>>6538086
>>6538091
>>6538096
OP here and multifactorial is fine, I just didn't know it existed. Anything that is commonly accepted as standard notation.

>>	Anonymous Fri May 16 19:50:03 2014 No.6538314 >>6538311 >I just didn't want someone to say something like "x=the square of Graham's number, then take x^x, etc". But wouldn't that be a greater challenge if we could do things like that?

>>	Anonymous Fri May 16 19:56:36 2014 No.6538319 >>6538314 That is a different challenge entirely. If you want to try, go for it... But I can almost guarantee you won't get the largest you possibly could. With just standard notation it is reasonable.

>>	Anonymous Fri May 16 19:59:10 2014 No.6538322 >>6537834 good thing -1/12 isn't the sum of all positive integers.

>>	Anonymous Fri May 16 20:12:31 2014 No.6538332 >>6538322 Can you explain why you believe so?

>>	Anonymous Fri May 16 20:23:43 2014 No.6538340 I think no one's non-recursively beaten mine yet: >>6537936

Anonymous Fri May 16 20:32:27 2014 No.6538346

the largest number I can imagine is:

1. define a hyperoperation of the degree hyper-γ, where γ is a transfinite number
2. the hyperoperation is repeated ε times, where ε is also a transfinite number
3. the hyperoperation is applied to any number "k" provided that k exceeds 1

consider this:

hyper-2: 2*3 = 6
hyper-3: 2^3 = 8
hyper-4: 2^^3 = 16
hyper-5: 2^^^3 =2^^2^^2 = 65536
hyper-6: 2^^^^3 = 2^^^4 = 2^^2^^2^^2 = 2^^65536
it grows ridiculously fast.
so basically apply a hyper-γ operation to k, and repeat it ε times.

if Latex works:
<span class="math">k\Uparrow^{\gamma}\epsilon[/spoiler]

>>	Anonymous Fri May 16 20:53:08 2014 No.6538367 This can be even larger than Graham's number, because Graham's number is a special case of this where k = 3, ε = 3, and γ = <span class="math">g_63[/spoiler]

>>	Anonymous Fri May 16 20:54:16 2014 No.6538369 oops, γ = <span class="math">g_(63)[/spoiler]

>>	Anonymous Fri May 16 22:29:47 2014 No.6538510 >>6538340 No graham's number, you dumbshit.

>>	Anonymous Sat May 17 17:54:53 2014 No.6539782 >>6538346 >2^^^^3 = 2^^^4 u wot m8? 2^^^^3=2^^^2^^^2 2^^^(2^^2) 2^^^(2^2) 2^^^4 2^^2^^2^^2 2^^(2^^(4)) 2^^(2^2^2^2) 2^^(2^2^4) 2^^(2^16) 2^^(65536) 2^2^2^2^2... Okay you're right.

>>	Anonymous Sat May 17 17:57:30 2014 No.6539789 File: 35 KB, 300x226, mahnigga.jpg [View same] [iqdb] [saucenao] [google] >mfw 2^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^2=4

>>	Anonymous Sat May 17 18:13:36 2014 No.6539815 >>6539789 2 is just a little bitch that won't grow the fuck up even when you up-arrow his ass like you mean it.

>>	Anonymous Sat May 17 19:17:27 2014 No.6539911 Any proof that 1998 Knuthian up-arrows is better than a shitload of factorials and parentheses?

>>	Anonymous Sat May 17 19:44:21 2014 No.6539935 >>6537813 This seems most likely.

Anonymous Sun May 18 02:31:52 2014 No.6540543

>>6539911
It's an intuitive result that can be derived from studying graph behavior.

Compare:
Gamma(x) vs. x^x
Gamma(Gamma(x)) vs. x^^x
Gamma(Gamma(Gamma(x))) vs. x^^^x

For x = 4:
Gamma(4) = 6 < 4^4 = 256
Gamma(Gamma(4)) = 120 < 4^^4 = a number with 8.07*10^153 digits
Gamma(Gamma(Gamma(4)) = 5.57*10^196 < 4^^^4 = 4^^4^^4^^(the number with 8.07*10^153 digits)

Without a doubt, up-arrows defeat a shitload of factorials.

>>	Anonymous Sun May 18 02:43:18 2014 No.6540548 Should've been Gamma(x+1), but yeah, the point is hyperoperations grow much much much fucking faster than composite factorials. <span class="math">\Gamma^n (x+1)< x\uparrow^n x[/spoiler] for x>1 basically

>>	Anonymous Sun May 18 07:46:52 2014 No.6540765 >>6537780 Obviously 1 followed by 1999 zeros.

>>	Anonymous Sun May 18 07:50:12 2014 No.6540769 >>6537780 You people. Suppose a largest number that can be typed with the 2k character limit. Define that number to be x. Then x + 1 > x. Contradiction. Therefore, no such number exists.

>>	Anonymous Sun May 18 09:11:40 2014 No.6540815 >>6540769 It's like you didn't even read the whole post.

Anonymous Sun May 18 09:20:22 2014 No.6540820

Let BB(n) be the maximum number of 1s finally on the tape, among all halting 2-symbol n-state Turing machines, when started on a blank tape.

BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(99))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))

should dwarfs anything in this thread.

Anonymous Sun May 18 09:38:59 2014 No.6540832

>>6540820
BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(99)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))

> trollface.jpeg

>>	Anonymous Sun May 18 09:43:09 2014 No.6540839 >>6540820 Why is noone iterating functions (same notation as exponentiation) instead of just nesting them

>>	Anonymous Sun May 18 10:11:24 2014 No.6540869 >>6539789 Okay, I hadn't thought about this at all, but that's honestly pretty sweet. Nice job, 2.

>>	Anonymous Sun May 18 10:12:34 2014 No.6540870 >>6540832 >your post >take out 99 >put in 9! >trollface.jpg

>>	Anonymous Sun May 18 12:23:56 2014 No.6540991 >>6537813 never seen anyone so excited about the number 9 before

>>	Anonymous Sun May 18 14:35:30 2014 No.6541136 >>6540991 Lol'd.

>>	Anonymous Sun May 18 15:55:17 2014 No.6541266 More interesting is the question, what is the biggest number (if there is one) to have Kolmogorov complexity under 2000 symbols if we fix some turing-complete language.

Anonymous Sun May 18 22:34:08 2014 No.6542022 [DELETED]

>>6539911
Think about it this way. 9!=9*8*7*6*5*4*3*2*1. 9^9=9*9*9*9*9*9*9*9*9.

9!=362880.
9^9=387420489.
362880! ((9!)!) is well below 362880^362880 (9!^9!).
9^9^9=9^387420489 which is of course going to be many orders of magnitude bigger than the previous. And it continues...

Or it's easier to see with 3s...

3!=6
3^3=9

(3!)!=36
3^^3=3^3^3=3^27=~7,625,597,485,000. Way bigger than 36.

>>	Anonymous Sun May 18 22:35:10 2014 No.6542025 >>6540765 10^199+1

>>	Anonymous Sun May 18 22:39:32 2014 No.6542029 >>6542022 *3^3=27. Point stands.

Anonymous Sun May 18 22:40:33 2014 No.6542031

>>6539911
Think about it this way. 9!=9*8*7*6*5*4*3*2*1. 9^9=9*9*9*9*9*9*9*9*9.

9!=362880.
9^9=387420489.
362880! ((9!)!) is well below 362880^362880 (9!^9!).
9^9^9=9^387420489 which is of course going to be many orders of magnitude bigger than the previous. And it continues...

Or it's easier to see with 3s...

3!=6
3^3=27

(3!)!=6!=720
3^^3=3^3^3=3^27=~7,625,597,485,000. Way bigger than 720.

>>	Anonymous Sun May 18 22:41:35 2014 No.6542032 File: 22 KB, 235x235, trollface.png [View same] [iqdb] [saucenao] [google] >>6540765 10^1999+1

>>	Anonymous Sun May 18 23:11:14 2014 No.6542077 almost certainly 9 with as many ! as can fit after it

Anonymous Tue May 20 00:44:54 2014 No.6543852

let f(0) be (1/0),f(1) =(1/0)^(1/0),f(2) =(1/0)^(1/0)^(1/0)
let g(0) be f(1/0),g(1)=f(1/0)^f(1/0),g(2) =f(1/0)^f(1/0)^f(1/0)
let h(0) be g(1/0),h(1)=g(1/0)^g(1/0),h(2)=g(1/0)^g(1/0)^g(1/0)
repeat the process until you fill 2000 chars, take the last function and replace x(n) to x(1/0)

>>	Anonymous Tue May 20 19:49:34 2014 No.6545257 the largest number in x characters isn't well defined lel

>>	Anonymous Wed May 21 00:42:44 2014 No.6545730 (9!)!^{(9!)!^[(9!)!^(9!)!^........

>>	Anonymous Wed May 21 23:55:41 2014 No.6547449 >>6537780 ∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞ /thread.

>>	Anonymous Thu May 22 06:32:13 2014 No.6547829 >>6547449 >posts disallowed answer >doesn't even make shit sense >then /threads own post You are the scum that we should boil slowly over your familie's heads, forcing you to watch as they are seared by your dripping flesh. You piece of crap.

Anonymous Thu May 22 06:46:41 2014 No.6547844

>>6537864
Well looking at the numbers here, none of them close to up arrow notation, 9<span class="math"> \uparrow \uparrow [/spoiler]9 is larger than every thing else not including similar notions.

>>6545730
>(9!)!^{(9!)!^[(9!)!^(9!)!^........
is smaller than 9<span class="math"> \uparrow \uparrow [/spoiler]9

Advanced search
Text to find
Subject [?]Search by post subject. Leave empty for any.
Username [?]Search for user name. Leave empty for any user name.
Tripcode [?]Search for tripcode. Leave empty for any.
Email [?]Search by email. Leave empty for any.
Filename [?]Search by image filename. Leave empty for any.
From Date [?]Enter what date to start searching from. Format is YYYY-MM-DD
To Date [?]Enter what date to start searching until. Format is YYYY-MM-DD
Image hash
Search in	All Posts OPs Only
Deleted posts	Show all posts Show only deleted posts Only show non-deleted posts
Internal posts	Show all posts Show only internal posts Show only archived posts
Order	New posts first Old posts first
Capcode	All Posts Only by Users Only by Mods Only by Admins Only by Developers
Results	Posts Threads
Action	[ Simple ]