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by WarDaft
Fri Jul 28, 2017 1:58 pm UTC
Forum: Forum Games
Topic: My number is bigger!
Replies: 1582
Views: 330328

Re: My number is bigger!

The largest uncontested number is currently Deedlit's. There are two potentially larger numbers, but they are floating around at sizes where you can't hand-wave things that are being hand-waved, and I'll let someone with a sufficient math degree suss that out. Instead, let's add more chaos. I'm goin...
by WarDaft
Thu Jul 27, 2017 12:51 pm UTC
Forum: Forum Games
Topic: Take a penny leave a penny.
Replies: 2203
Views: 277532

Re: Take a penny leave a penny.

I try to read the contents of the pile out loud, accidentally completing the ritual.

Arrrrr matey, thar be a C'Thulu in the pile!
by WarDaft
Sun Dec 20, 2015 7:33 pm UTC
Forum: Forum Games
Topic: My Number is Bigger (Crazy Edition)
Replies: 25
Views: 1641

Re: My Number is Bigger (Crazy Edition)

Well, in the interest of keeping things rolling...

Since {ZF}0(n) grows faster than BBa(n) for any recursively defined, naturally the next stop on the crazy train is {ZF}[ZF|{ZF}0(1010)](10)
by WarDaft
Thu Dec 17, 2015 12:44 pm UTC
Forum: Forum Games
Topic: My Number is Bigger (Crazy Edition)
Replies: 25
Views: 1641

Re: My Number is Bigger (Crazy Edition)

Oh, yes, that's defnitely bigger. The thing was you used one on an older number that had a 10 in it rather than an 11, and you applied it to the final value, which wasn't enough to overcome the bump to 11.
by WarDaft
Thu Dec 17, 2015 12:22 pm UTC
Forum: Forum Games
Topic: My Number is Bigger (Crazy Edition)
Replies: 25
Views: 1641

Re: My Number is Bigger (Crazy Edition)

Aha, the oracle machines show up. Oracle is the word your looking for, when you give a Turing Machine the ability to solve the halting problem. I'm very sorry Vytron, but that's actually smaller than {ZF+Con(ZF)} 11 (10). {ZF} 10 (10) already includes statements which describe oracle Turing machines...
by WarDaft
Thu Dec 17, 2015 12:21 am UTC
Forum: Forum Games
Topic: My Number is Bigger (Crazy Edition)
Replies: 25
Views: 1641

Re: My Number is Bigger (Crazy Edition)

{ZF} ω^77 (77↑ 77 77) (I personally feel that applying these simple recursions to the ZF thing is actually far more naïve than saying "Graham's plus one" - relatively speaking. I wonder if there's an objective way to compare such things on such vastly different scales) In a sense, I agree...
by WarDaft
Wed Dec 16, 2015 10:08 pm UTC
Forum: Forum Games
Topic: My Number is Bigger (Crazy Edition)
Replies: 25
Views: 1641

Re: My Number is Bigger (Crazy Edition)

Well escalated quickly. Or, you know, not. As posted, username5243's number is undefined, because there is no largest number not definable in a finite number of characters in ZF. As far as emlightened, I don't actually know how many characters it takes to express the operation of a Turing Machine in...
by WarDaft
Wed Dec 16, 2015 9:50 pm UTC
Forum: Forum Games
Topic: My Number is Bigger (Crazy Edition)
Replies: 25
Views: 1641

My Number is Bigger (Crazy Edition)

'Ello. This version is not for the faint of heart. There are three rules. 1. Unless it is blatantly obvious, you must show that your number is finite when you post it. 2. Unless it is blatantly obvious, you must show that your number is winning, otherwise it is not. 3. You must define a specific num...
by WarDaft
Sat Aug 01, 2015 4:50 pm UTC
Forum: Mathematics
Topic: I don't seem to understand my own brain teaser, please help!
Replies: 22
Views: 4257

Re: I don't seem to understand my own brain teaser, please h

Okay, that all makes sense for the multi play case.

But what about the single play case? Does it make sense to play the game once, or no times at all?
by WarDaft
Sat Aug 01, 2015 6:22 am UTC
Forum: Mathematics
Topic: I don't seem to understand my own brain teaser, please help!
Replies: 22
Views: 4257

I don't seem to understand my own brain teaser, please help!

So, you're dying, and the reaper shows up early to play a game with you. The game is, the reaper will flip a biased coin. There is a 55% chance of heads, which will double your remaining earthly time, and a 45% chance of tails, which will reduce your remaining earthly time by 70%. The reaper will pl...
by WarDaft
Sun Jun 28, 2015 11:50 pm UTC
Forum: Forum Games
Topic: Take a penny leave a penny.
Replies: 2203
Views: 277532

Re: Take a penny leave a penny.

I marvel at the density of the pennies, amazed at how a pile with an average thickness of 1.15 pennies managed to crush two adult humans. In my awestruck state, I accidentally take the ability to get the reference and put it in the pile. I take a penny. In a large penny on the penny, there is a diso...
by WarDaft
Sun Jun 28, 2015 10:47 pm UTC
Forum: Forum Games
Topic: 4 letter mastermind
Replies: 296
Views: 12855

Re: 4 letter mastermind

Fats
Parry?
by WarDaft
Sun Jun 28, 2015 12:05 am UTC
Forum: Forum Games
Topic: What is the worst movie ever made?
Replies: 17
Views: 1556

Re: What is the worst movie ever made?

Suggesting any of these as the worst movie ever when there are movies in IMDB with a rating of less than 2 is... really rather quite mean.
by WarDaft
Sun Jun 28, 2015 12:03 am UTC
Forum: Forum Games
Topic: Count up using the Busy Beaver function
Replies: 3
Views: 834

Count up using the Busy Beaver function

Specifically, you may use the operations /,-,+,*,^,BB(), grouping via parentheses, and the value 1; where BB(n) is the maximum number of shifts of a 2-symbol n-state Turing Machine.

Here, let me get things started:

BB(1)/(1+1+1+1+1+1)
by WarDaft
Sat Jun 27, 2015 11:57 pm UTC
Forum: Forum Games
Topic: My Number is Bigger! (again)
Replies: 402
Views: 15201

Re: My Number is Bigger! (again)

Where BB(n) is the maximum number of shifts of a 2-symbol n-state Turing Machine:

BB(3)^2 = 11449
by WarDaft
Sun Mar 08, 2015 5:48 pm UTC
Forum: Forum Games
Topic: Your number is, in fact, not bigger!
Replies: 1240
Views: 123817

Re: Your number is, in fact, not bigger!

Very well then, n|0 = n n|X = n+1|X-- (b)-- = b (X,0,0)-- where X contains no non-zero terms = <(X,>0<)> (X,0,b,Y)-- where X contains no non-zero terms = <(X,>0<,b--,Y)> (a,X,0,b,Y)-- where X contains no non-zero terms, and b does not contain square brackets = <(a--,X,>((a--,X,0,b,Y))<,b--,Y)> (a,b,...
by WarDaft
Sun Mar 08, 2015 3:26 am UTC
Forum: Forum Games
Topic: Your number is, in fact, not bigger!
Replies: 1240
Views: 123817

Re: Your number is, in fact, not bigger!

Vytron wrote:People watching know that the notation can reach:

n,{0-0} = φ(1,0)
n,{0,0-0} = φ(2,0)
n,{{0}-0} = φ(ω,0)
n,{{{0}-0}-0} = φ(φ(ω,0))
n,{0-0-0} = φ(1,0,0)


The way you do that is by basically re-inventing the Veblen notation in your own words. There's not really any way around that.
by WarDaft
Sat Mar 07, 2015 2:45 am UTC
Forum: Forum Games
Topic: Your number is, in fact, not bigger!
Replies: 1240
Views: 123817

Re: Your number is, in fact, not bigger!

Vytron, what, exactly is the reduction for 3{0-{0,0-0}}, step by step? Just because {0-X} is a more powerful function in general does not mean it is always larger than X,0, for the same X in both cases. If 3{0-{0,0-0}} does not become 3{0-{0-{0-{0-{0}}}}, what does it become? And I've already said t...
by WarDaft
Fri Mar 06, 2015 4:33 am UTC
Forum: Forum Games
Topic: Describe the biggest number (10^10^10^10^1000)
Replies: 57
Views: 3146

Re: Describe the biggest number (10^10^101)

10^10^10^10

A discrete 10-hyper-hyper-hyper-cube.
by WarDaft
Thu Mar 05, 2015 10:25 pm UTC
Forum: Forum Games
Topic: Your number is, in fact, not bigger!
Replies: 1240
Views: 123817

Re: Your number is, in fact, not bigger!

Don't take my accepting of that as meaning it was true, merely that I accepted it without further fuss. In my own notation, (((0,1))) is larger than ((0,1),0), even though the latter is applying a more powerful function [ ( ,0) instead of (( ))] to the same base value. The difference is in what is r...
by WarDaft
Thu Mar 05, 2015 5:49 am UTC
Forum: Forum Games
Topic: Your number is, in fact, not bigger!
Replies: 1240
Views: 123817

Re: Your number is, in fact, not bigger!

Deedlit wrote:I know WarDaft could really dial things up as well if he wanted to. :wink:

That is indeed what the colon is for.
by WarDaft
Tue Mar 03, 2015 11:43 pm UTC
Forum: Forum Games
Topic: Your number is, in fact, not bigger!
Replies: 1240
Views: 123817

Re: Your number is, in fact, not bigger!

Wow, I honestly don't know how I managed to fail at copy and pasting . n|0 = n n|X = n+1|X-- (b)-- = b (X,0,0)-- where X contains no non-zero terms = <(X,>0<)> (X,0,b,Y)-- where X contains no non-zero terms = <(X,>0<,b--,Y)> (a,X,0,b,Y)-- where X contains no non-zero terms, and b does not contain sq...
by WarDaft
Tue Mar 03, 2015 10:32 pm UTC
Forum: Forum Games
Topic: Your number is, in fact, not bigger!
Replies: 1240
Views: 123817

Re: Your number is, in fact, not bigger!

Hmm, that actually does look like the appropriate rule. It would seem I am missing a base case, because that was not the rule I was applying in my head. Let me think... this might not actually be a problem in the long run though it would change the nature of the example proof. (0,1) would be the fir...
by WarDaft
Tue Mar 03, 2015 5:41 pm UTC
Forum: Forum Games
Topic: Your number is, in fact, not bigger!
Replies: 1240
Views: 123817

Re: Your number is, in fact, not bigger!

Ah, yes, that one should read (0[b:]0,X)-- = <(>0<[b--:]0,X)>, I moved the positional term from after the square braces to the first place in them, and that line of definition got messed up in the update. I'll double check the rest. The updated rules. n|0 = n n|X = n+1|X-- (b)-- = b (X,0,0)-- where ...
by WarDaft
Tue Mar 03, 2015 4:27 pm UTC
Forum: Forum Games
Topic: Your number is, in fact, not bigger!
Replies: 1240
Views: 123817

Re: Your number is, in fact, not bigger!

< > is a repetition operator, so I don't have to specify with a function or keep typing "(0,0,..0) for n 0's" 5|(0,0) uses the rule (X,0,0)-- = <(X,>0<)> , X is an empty array, so <(X,> is really just <(>, so it simplifies to 5|(0,0) = 5+1|<(>0<)> = 6|(((((0)))))
by WarDaft
Tue Mar 03, 2015 12:59 am UTC
Forum: Forum Games
Topic: Your number is, in fact, not bigger!
Replies: 1240
Views: 123817

Re: Your number is, in fact, not bigger!

I generally agree with you up to n,{0,0} = ω^ω, with caveats about being careful about making sure your notation terminates properly because I'm not going to prove that... But then: n,0,{0,0} = ω^ω*ω = ω^(ω+1) n,0,0,{0,0} = ω^(ω+1)*ω = ω^(ω+2) n,{0},{0,0} = ω^ω*ω^ω = ω^(ω*2) n,0,{0},{0,0} = ω^(ω*2)*...
by WarDaft
Mon Mar 02, 2015 10:57 pm UTC
Forum: Forum Games
Topic: Your number is, in fact, not bigger!
Replies: 1240
Views: 123817

Re: Your number is, in fact, not bigger!

Okay Vytron, here goes, I'll try not to skip anything. So, only two parts of my notation were used so far. First off, every array enclosed in parenthesis acts more or less exactly like an ordinal. Second, this will be based on the Hardy Hierarchy. Third, a[n] will refer to the n-th item from the fun...
by WarDaft
Mon Mar 02, 2015 9:54 pm UTC
Forum: Forum Games
Topic: Your number is, in fact, not bigger!
Replies: 1240
Views: 123817

Re: Your number is, in fact, not bigger!

We do not know that BB(10) is less than g2.

We do not have concrete values for anything larger than BB(4). BB(10) could be larger than every number in the serious bigger number thread.

There is no possible way to approximate the BB function, at all. It is literally not something you can do.
by WarDaft
Sun Mar 01, 2015 4:45 pm UTC
Forum: Forum Games
Topic: Your number is, in fact, not bigger!
Replies: 1240
Views: 123817

Re: Your number is, in fact, not bigger!

I'm cleaning it up, and building a longer, more detailed explanation in another browser tab. 'n' is indeed shorthand for <(>0<)>, because it's far more readable, they are functionally equivalent.

If it's causing errors, I guess I'll switch back to colons rather than semi-colons.
by WarDaft
Sat Feb 28, 2015 10:07 pm UTC
Forum: Books
Topic: Harry Potter and the Methods of Rationality
Replies: 1035
Views: 342983

Re: Harry Potter and the Methods of Rationality

Well
Spoiler:
That's a crappy kind of trick to pull Mr. Yudlowsky.
by WarDaft
Wed Feb 25, 2015 11:53 pm UTC
Forum: Forum Games
Topic: Your number is, in fact, not bigger!
Replies: 1240
Views: 123817

Re: Your number is, in fact, not bigger!

Technically, every recursive notation is really just a mapping to ordinals. That doesn't make them all easily readable, and there may be new errors introduced with a new format that we don't notice at first. I'll type up something later about how my notation works, and what is required when dealing ...
by WarDaft
Wed Feb 25, 2015 1:29 pm UTC
Forum: Forum Games
Topic: Your number is, in fact, not bigger!
Replies: 1240
Views: 123817

Re: Your number is, in fact, not bigger!

It started to feel like a Sisyphean task to watchdog Vytron's notation, find something wrong with it and he starts over, negating any work you've done to understand everything so far.

As for no one challenging my claims... there's not a lot I can do about that.
by WarDaft
Tue Feb 24, 2015 6:30 pm UTC
Forum: Forum Games
Topic: Your number is, in fact, not bigger!
Replies: 1240
Views: 123817

Re: Your number is, in fact, not bigger!

Here's an idea vytron. Why dont you fix, JUST the mistakes that people point out, instead of discarding everything you just did everytime someone quotes a portion of your text? Do you really expect me to make the effort to learn how your stuff works every other day? Because that is sort of the reas...
by WarDaft
Tue Feb 24, 2015 3:39 pm UTC
Forum: Forum Games
Topic: Your number is, in fact, not bigger!
Replies: 1240
Views: 123817

Re: Your number is, in fact, not bigger!

The way it can jump like that is because Ω (just Ω, no Ω^Ω or anything) is bigger than every ordinal it is used to define. ψ(a) = φ(1,a) for a up to φ(2,0) where ψ(φ(2,0)) = φ(1,φ(2,0)) = φ(2,0), but it stops here because the ψ function can't make zetas on it's own, so it can't 'use' ψ(2,0) when it'...
by WarDaft
Tue Feb 24, 2015 12:09 am UTC
Forum: Forum Games
Topic: Your number is, in fact, not bigger!
Replies: 1240
Views: 123817

Re: Your number is, in fact, not bigger!

Maybe I'm missing something, but I don't see any rules that would make two adjacent {..}+ terms multiply their ordinal value together. That's just a weird operation to have. Considering that you yourself are getting two different results... I call shenanigans . Also, ψ(Ω) = φ(2,0), if you're meaning...
by WarDaft
Sun Feb 22, 2015 8:23 pm UTC
Forum: Forum Games
Topic: Your number is, in fact, not bigger!
Replies: 1240
Views: 123817

Re: Your number is, in fact, not bigger!

Hmm, I think I also just noticed that I got part of my notation switched around from what I originally intended to go with. I'll fix it when it becomes relevant.
by WarDaft
Sun Feb 22, 2015 8:07 pm UTC
Forum: Forum Games
Topic: Your number is, in fact, not bigger!
Replies: 1240
Views: 123817

Re: Your number is, in fact, not bigger!

No, there aren't any gaps in the countable ordinals constructed (unless you choose omega to be countable, but that's just nitpicking) P(W^W+W) is indeed phi_2(G_0+1) P(W^W+W*2) is phi_2(G_0+2) P(W^W+W*a) is phi_2(G_0+a) The fixed points of phi_2(G_0+a) is phi_3(G_0+1) P(W^W+W^2) is phi_3(G_0+1) and ...
by WarDaft
Sun Feb 22, 2015 1:48 pm UTC
Forum: Forum Games
Topic: Your number is, in fact, not bigger!
Replies: 1240
Views: 123817

Re: Your number is, in fact, not bigger!

Okay, time to drag things into the 21st century! < > are the repeater operator, such that <X> means the string X repeated n times ( ) denote an array, which is to be evaluated lazily, rather than immediately. [;] is an advanced delimiter. : and ; will not work the same, so I'm not re-using :. Capita...
by WarDaft
Sat Feb 21, 2015 6:14 pm UTC
Forum: Forum Games
Topic: Your number is, in fact, not bigger!
Replies: 1240
Views: 123817

Re: Your number is, in fact, not bigger!

That's one of the reasons I didn't nitpick the notation too much. Using the hyphen notation correctly, it would be the only thing that mattered and the end target would still be reached. I suppose I should have checked that the hyphen notation was working optimally.
by WarDaft
Sat Feb 21, 2015 11:26 am UTC
Forum: Forum Games
Topic: Your number is, in fact, not bigger!
Replies: 1240
Views: 123817

Re: Your number is, in fact, not bigger!

I'm going to take this time to introduce another notation I've been pondering for ages but never really explored. This one doesn't even use numbers, just parenthesis. (a,X,[Y],Z)-- = <(a--,X,(a--,X,[Y],Z)> (a,X)-- = <(a--,X)> [ ]-- = () [a,X]-- = <[a--,X]> ()-- = null, or nothing. I have called it t...

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