Search found 2250 matches

by WarDaft
Wed Sep 10, 2014 5:21 am UTC
Forum: Forum Games
Topic: Your number is, in fact, not bigger!
Replies: 1240
Views: 150409

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

Wardraft tends to not overshoot much, so g could work against him. Nope. My syntax is sufficiently dense that it is in fact you who must do more work to beat me, and the very 'g' which you laud is that work . With Wardraft is the same. for a function that grows the same, he'd need to send [[[2|1[1:...
by WarDaft
Wed Sep 10, 2014 5:06 am UTC
Forum: Forum Games
Topic: Your number is, in fact, not bigger!
Replies: 1240
Views: 150409

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

There may be some pathological functions that grow faster than alpha but slower than alpha + 1, but this is most definitely not one of them. Indeed. There are in fact uncountably many such functions. Scratch that edit, the FGH contains a strict subset of total mu-recursive functions which are a str...
by WarDaft
Tue Sep 09, 2014 5:38 pm UTC
Forum: Forum Games
Topic: Your number is, in fact, not bigger!
Replies: 1240
Views: 150409

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

φ(ω,8)? Well, I guess it's time for an extension then. Reusing these guys: f(n+1,k) = f(n,k)||k, f(1,k) = k g(1,X,Y) = X||Y, g(n+1,X,Y) = X||g(n,X,Y)||Y We will split the [] delimiters now, with ":"s, so that they take the form [X:Y] for two arrays X and Y. We will then say that [n|W[X:Y]Z...
by WarDaft
Mon Sep 08, 2014 3:23 pm UTC
Forum: Forum Games
Topic: Your number is, in fact, not bigger!
Replies: 1240
Views: 150409

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

Well, guess I'm lucky my bracket notation affords some easy extension. If an array X reduces like ordinal a, then [n|0[][X]] reduces like epsilon_a. Nesting clearly yields the limit zeta_0, and it's just begging for a third set of brackets, denoting exactly such a. In that manner... [n|0[][][]] has ...
by WarDaft
Sat Sep 06, 2014 8:23 pm UTC
Forum: Forum Games
Topic: Your number is, in fact, not bigger!
Replies: 1240
Views: 150409

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

n[0,0 [0] 0] = n[0 [0] 0 [0]... g [0]s ...0 [0] 0 [0] 0] Okay, pretty big sticking point here. Don't you at some point have something like n[1 [0] 0 [0] 0] become n[0 [0] 1,0,0,0... 0 [0] 0]? Because well... if you do, then you can't use comma separated values to make more [0] separated values. The...
by WarDaft
Wed Sep 03, 2014 2:07 am UTC
Forum: Forum Games
Topic: Your number is, in fact, not bigger!
Replies: 1240
Views: 150409

Re: My number is, in fact, bigger!

So I see you try to fix this, but at a glance it doesn't work as I'd expect it to But it should grow even faster than a function that just has [2] > [1] > [0], because that produces: [0] [0][0] [0][0][0]... [1] [1][0] [1][0][0]... [2] [2][0] [2][0][0]... [2][1] [2][1][1]... [3] ... I have: [0] [0][...
by WarDaft
Wed Sep 03, 2014 12:05 am UTC
Forum: Forum Games
Topic: Your number is, in fact, not bigger!
Replies: 1240
Views: 150409

Re: My number is, in fact, bigger!

Excellent, next of course is [2|2[0[][0[]0[]]][0[]0[]]] at f{ε_2*2+2}(2).

Simplified the colouring a bit, every time you go inside a new pair of brackets we pick a new colour for both brackets and numbers.
by WarDaft
Tue Sep 02, 2014 11:11 pm UTC
Forum: Forum Games
Topic: Your number is, in fact, not bigger!
Replies: 1240
Views: 150409

Re: My number is, in fact, bigger!

Well, isn't it substantially lower than f{ε_0}+2(n) too? The whole concept here is to have it be f{ε_0} < <my function> < f{ε_0}+1 f{ε_0^2}(n) is not the same as f{ε_0}^2(n). The { }s indicate the entirety of the ordinal, f{ε_0}^2(n) is just shorthand for f{ε_0}(f{ε_0}(n)), which is much less than ...
by WarDaft
Tue Sep 02, 2014 2:20 pm UTC
Forum: Forum Games
Topic: Your number is, in fact, not bigger!
Replies: 1240
Views: 150409

Re: My number is, in fact, bigger!

I may have been slightly uncharitable when I said it was effectively a constant value, it would have been f{ε_0}(f{ε_0[6]}(n)) which is f{ε_0}(f{ω^ω^ω^ω^ω}(n)) which is substantially less than f{ε_0}(f{ε_0}(n)) for all n > 6. Also, you've got them inside out, it would be f{ε_0^ω^ω}(f{ε_0^ω^ω[6]}(f{ε...
by WarDaft
Mon Sep 01, 2014 4:19 pm UTC
Forum: Forum Games
Topic: Your number is, in fact, not bigger!
Replies: 1240
Views: 150409

Re: My number is, in fact, bigger!

I'll comment on that when I'm not posting from my phone. In other news... Did ODF actually stop at epsilon_1^2? I thought he went up just past gamma_0. In that case, I don't need to extend anything yet, the rules from last time are enough. [n|0[][0[]]] is f{ε_1}(n) [n|0[][0[]0[]]] is f{ε_2}(n) I sub...
by WarDaft
Mon Sep 01, 2014 1:38 am UTC
Forum: Forum Games
Topic: Your number is, in fact, not bigger!
Replies: 1240
Views: 150409

Re: My number is, in fact, bigger!

There is no largest number, because math is impossible to describe.

It's like birds. What are birds? We just don't know.


Mike-l: Looks good to me.

Hmm, I wonder how well I can compete at both Vytron's and ODF's level with the same notation... I must think on this.
by WarDaft
Mon Sep 01, 2014 12:20 am UTC
Forum: Forum Games
Topic: Your number is, in fact, not bigger!
Replies: 1240
Views: 150409

Re: My number is, in fact, bigger!

I'd use >> in the context of "insurmountably larger" such as describing one ordinal to be vastly larger than another, so much so that it doesn't really matter much what you do with the smaller one, you don't end up with anything close to the size of the larger one. For example, I'd say ome...
by WarDaft
Sun Aug 31, 2014 5:14 pm UTC
Forum: Forum Games
Topic: Your number is, in fact, not bigger!
Replies: 1240
Views: 150409

Re: My number is, in fact, bigger!

It does not terminate, there is a mistake in your assumptions. It's very similar to mistakes you have made before, and I am asking you to find it, because you need the practice.
by WarDaft
Sun Aug 31, 2014 4:42 pm UTC
Forum: Forum Games
Topic: Your number is, in fact, not bigger!
Replies: 1240
Views: 150409

Re: My number is, in fact, bigger!

That is not an explanation of why it does not terminate, try again.

Don't try to prove me wrong this time, because you also didn't do that.
by WarDaft
Sun Aug 31, 2014 2:53 pm UTC
Forum: Forum Games
Topic: Your number is, in fact, not bigger!
Replies: 1240
Views: 150409

Re: My number is, in fact, bigger!

That's unfortunately only f{ε_0}(f{ε_0}(6)) ish which is no faster than f{ε_0}(n) and it... well... it basically flatlines. It grows slower than f{ε_0}(n) in the end. Notice how there's no n in "f{ε_0}(f{ε_0}(6))"? By using a fixed nesting for determining g, you totally kill your recursion...
by WarDaft
Fri Aug 29, 2014 8:26 pm UTC
Forum: Forum Games
Topic: Your number is, in fact, not bigger!
Replies: 1240
Views: 150409

Re: My number is, in fact, bigger!

And I'm editing in a response to your edit, since Vytron isn't online he'll see my edited post first anyway :P Your subsequence function was what I had in mind when I included the word 'almost' infront of 'everything in this thread'. It's conceivable there is an ordinal interpretation of this, but ...
by WarDaft
Fri Aug 29, 2014 8:26 pm UTC
Forum: Forum Games
Topic: Your number is, in fact, not bigger!
Replies: 1240
Views: 150409

Re: My number is, in fact, bigger!

I have no idea why, but that double posted for some reason.

I may edit in something here later to use the space.
by WarDaft
Fri Aug 29, 2014 7:50 pm UTC
Forum: Forum Games
Topic: Your number is, in fact, not bigger!
Replies: 1240
Views: 150409

Re: My number is, in fact, bigger!

Ordinals are literally expressions of recursive fractal complexity, which is exactly how we tend to try and describe large numbers. It's either that, or use a weird problem in math, and those can require PHDs to compare. For example, the subsequence structure I mentioned a while back. That's a simpl...
by WarDaft
Thu Aug 28, 2014 1:20 pm UTC
Forum: Forum Games
Topic: Your number is, in fact, not bigger!
Replies: 1240
Views: 150409

Re: My number is, in fact, bigger!

Oh! Yes! That's the bottom-up-like notation I was looking for! Very cool! I wonder if a "my bottom-up function is, in fact, bigger!" would have worked as a better title. See how's that not arid at all? I guess it'd be like some robot ninja zombie mutant pirate, or thereabouts. Also, love ...
by WarDaft
Thu Aug 28, 2014 11:40 am UTC
Forum: Forum Games
Topic: Your number is, in fact, not bigger!
Replies: 1240
Views: 150409

Re: My number is, in fact, bigger!

Okay then, let's give you a non-ordinal fight like that, since that's clearly what you want. Capitals will represent chunks of the array. [n|] = n [n|0[]X] = [n*2|X] [n|k+1[X]Y] = [n|k[X]k[X]..[X]Y] with n copies of k[X]. Specifically, let's make a useful subdeclaration: f(n+1,k) = f(n,k)||k -- wher...
by WarDaft
Wed Aug 27, 2014 6:21 pm UTC
Forum: Science
Topic: Gravitational waves, potential, and creationism
Replies: 11
Views: 3687

Re: Gravitational waves, potential, and creationism

Do we actually have any model of what gravity would do if new mass suddenly popped into existence? That... doesn't sound like something that would go well with the laws of gravity. Also, they've posited a deceptive god assembling a universe to look like something other than how it was "actually...
by WarDaft
Wed Aug 27, 2014 3:30 pm UTC
Forum: Coding
Topic: Poll! What is the value of this constant?
Replies: 47
Views: 13787

Re: Poll! What is the value of this constant?

What do you mean "every time you use it"? You just test it at the beginning of the function. (This is something you'd do in a dynamically-typed language.) Yes, so the beginning of every function in which you use it you now have to remember to do another test. This is like the exact opposi...
by WarDaft
Wed Aug 27, 2014 1:33 pm UTC
Forum: Coding
Topic: Poll! What is the value of this constant?
Replies: 47
Views: 13787

Re: Poll! What is the value of this constant?

It's terrible for any situation. "Just test for it" means that every time you use it, you must test for it or you have introduced a new opportunity for error. Further, in many strongly typed languages, you probably can't use one in place of another. And this is not support for using a weak...
by WarDaft
Wed Aug 27, 2014 1:12 am UTC
Forum: Forum Games
Topic: Your number is, in fact, not bigger!
Replies: 1240
Views: 150409

Re: My number is, in fact, bigger!

This is a Forum Game. So, it's like, I say "hey, guys! I have this Snakes and Ladders board! Let's play a game!" And I begin explaining "you have this piece, and when you roll the dice, you advance the total you get, and when you hit a snake, you fall down, and when you hit a ladder ...
by WarDaft
Tue Aug 26, 2014 1:05 pm UTC
Forum: Forum Games
Topic: Your number is, in fact, not bigger!
Replies: 1240
Views: 150409

Re: My number is, in fact, bigger!

Actually, that's exactly what it does, but automated. It seems you and mike like generalization and automation very much. Can I ask, why? Why do more work to get to the same point? n[+ {n} 0] calls a function that iterates like x*, and so, n[+ {0} 0] = fω(n), n[+ {1} 0] = fε_0(n), n[+ {2} 0] = fζ_0...
by WarDaft
Tue Aug 26, 2014 11:06 am UTC
Forum: Forum Games
Topic: Your number is, in fact, not bigger!
Replies: 1240
Views: 150409

Re: My number is, in fact, bigger!

Well, F{ε_0+1}(n) works like how you just described f{ε_0[1]}(n). And F{ε_0+2}(n) works just like f{ε_0[1]}(n). F{ε_0+ω}(n) matches to fε_0+1(n) as you have it there. The reason fundamental sequences are needed is because ω-1 doesn't make sense, it's not a shortcoming that successor ordinals don't h...
by WarDaft
Tue Aug 26, 2014 6:13 am UTC
Forum: Forum Games
Topic: Your number is, in fact, not bigger!
Replies: 1240
Views: 150409

Re: My number is, in fact, bigger!

Ok, let's do something a little novel. [a,b,c] is a list of items a, b, and c. '++' is concatenation, so [1,2] ++ [1,2] = [1,2,1,2] [f(x) | x <- k] makes we take each item in list k, then make a new list of those items with f applied to it. [x | k <- g, x <- f(k)] means take an item from list g, the...
by WarDaft
Sun Aug 24, 2014 3:44 am UTC
Forum: Forum Games
Topic: Your number is, in fact, not bigger!
Replies: 1240
Views: 150409

Re: My number is, in fact, bigger!

And you took exactly the wrong message from that. They are actually both fast growing hierarchies. The actual slow growing hierarchy is much much slower. There is still an ordinal at which it catches up to the other two. You've taken the FGH as something that other function caught up to and then it...
by WarDaft
Sat Aug 23, 2014 2:07 pm UTC
Forum: Forum Games
Topic: Your number is, in fact, not bigger!
Replies: 1240
Views: 150409

Re: My number is, in fact, bigger!

And you took exactly the wrong message from that. They are actually both fast growing hierarchies. The actual slow growing hierarchy is much much slower. There is still an ordinal at which it catches up to the other two. You've taken the FGH as something that other function caught up to and then it'...
by WarDaft
Sat Aug 23, 2014 9:50 am UTC
Forum: Forum Games
Topic: Your number is, in fact, not bigger!
Replies: 1240
Views: 150409

Re: My number is, in fact, bigger!

And what is f now, is it the FGH? I don't believe in this. That would mean that no matter how you got to ε_0, suddenly all functions that did are equal, because anything you did before to get there "was forgotten." It's close. Again, look very closely at these two heirarchies: F{0}(n) = 2...
by WarDaft
Fri Aug 22, 2014 5:55 pm UTC
Forum: Forum Games
Topic: Your number is, in fact, not bigger!
Replies: 1240
Views: 150409

Re: My number is, in fact, bigger!

Yeah, imath was disabled quite a while ago, we used it... well, a lot really... in the other thread.
by WarDaft
Fri Aug 22, 2014 1:06 am UTC
Forum: Forum Games
Topic: Your number is, in fact, not bigger!
Replies: 1240
Views: 150409

Re: My number is, in fact, bigger!

So, while g grows like this: g ω ω (n) g ω ω^ω^ω (n) g ω ω^ω^ω^ω^ω (n) f grows like this: f ω ω +ω(n) f ω ω^ω^ω + ω ω +ω(n) f ω ω^ω^ω^ω^ω + ω ω^ω^ω + ω ω +ω(n) This is "insignificant" at these scales. So, what happens at ε_0(n)? Well, g has this: g ε_0 (n) = g ω ω^ω...n-1 times...^ω^ω (n)...
by WarDaft
Thu Aug 21, 2014 7:17 pm UTC
Forum: Computer Science
Topic: Aperiodic RNGs
Replies: 6
Views: 5226

Re: Aperiodic RNGs

It's actually not, at least as LFGs are defined. An LFG uses a fixed offset, there are a 1 through a i such that F n = F n - a_1 ★ F n - a_2 ★ .. ★ F n - a_i for some operator ★. Being fixed offsets, it will necessarily repeat as it has fixed finite state space. And it's not "why not my generat...
by WarDaft
Sun Aug 17, 2014 5:37 pm UTC
Forum: Forum Games
Topic: My number is bigger!
Replies: 1590
Views: 412653

Re: My number is bigger!

Worth a try... # The exponent function, so I can address it by name: exp(x) = 2 where x < 1 exp(x) = 2*x^x where x >= 1 # A template for fast-growing functions. ©(exp, 1), for example, just reduces to exp(1), which, as we know, reduces to 2. ©(f, x) = f(x) where x <= 1 ©(f, x) = f( ©( f, x - 1/©(f,...
by WarDaft
Thu Aug 14, 2014 12:02 am UTC
Forum: Forum Games
Topic: Your number is, in fact, not bigger!
Replies: 1240
Views: 150409

Re: My number is, in fact, bigger!

I'm not changing notation, I'm just changing the way I represent things ... What exactly do you think changing notation means? ^ doesn't traditionally have meaning when it's not in the form a^b, so when you use it outside of that form, we can't really tell what you're meaning to do. So, I see. Than...
by WarDaft
Wed Aug 13, 2014 7:23 pm UTC
Forum: Forum Games
Topic: Your number is, in fact, not bigger!
Replies: 1240
Views: 150409

Re: My number is, in fact, bigger!

I absolutely hate when a stronger function is dominated by just adding 1 to the input of a weaker function... Absolute hate is a pretty strong emotion for that... it just represents the first function taking a little while to uncurl the recursion in it. Generally speaking, any input greater than 2 ...
by WarDaft
Tue Aug 12, 2014 6:26 pm UTC
Forum: Forum Games
Topic: Your number is, in fact, not bigger!
Replies: 1240
Views: 150409

Re: My number is, in fact, bigger!

Looks like it all follows so far, with stacking [+]'s being a modified version of the hyperoperator.
by WarDaft
Mon Aug 11, 2014 4:34 am UTC
Forum: Forum Games
Topic: Woops: Woops: religion wins!
Replies: 205
Views: 25758

Re: Woops

Oh no!
by WarDaft
Sun Aug 10, 2014 10:30 pm UTC
Forum: Forum Games
Topic: Your number is, in fact, not bigger!
Replies: 1240
Views: 150409

Re: My number is, in fact, bigger!

Yep. http://www.wolframalpha.com/input/?i=product+%281-1%2F%284%28n%5E2%29%29%29+for+n+%3D+1+to+infinity You have a ~63.7% chance of never terminating. Having an inkling about infinite series helped spot that it isn't guaranteed to terminate. What would help more, is not assuming it's going to work ...
by WarDaft
Sun Aug 10, 2014 6:47 pm UTC
Forum: Forum Games
Topic: Your number is, in fact, not bigger!
Replies: 1240
Views: 150409

Re: My number is, in fact, bigger!

You have to show that the probability has certain traits in the limit. The fact that it never reaches 0 is.. basically nothing. A random walk in 3 dimensions always has a non-zero chance of reaching each point in the space, but in the limit, no point has a 100% chance of being reached, and it's not ...

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