My number is bigger! (New Everyman version)

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username5243
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My number is bigger! (New Everyman version)

Postby username5243 » Sat Sep 24, 2016 8:51 pm UTC

The old one seems to have died down. Let's do a new one.

The rules (shamelessly stolen from last time):

username5243 wrote:The rules:
1. Post a number which is bigger than the previous number.
2. Each entry must define a single computable positive number.
3. You're not allowed to reference previously posted numbers directly (you can't post stuff like "the sum of all previous numbers plus one" or "double the previous number").
4. You can use any notation you want, but it must be understandable by the average math-oriented joe who has no specific background in "Big Number-ology". I know that many large-numbers enthusiasts love to create (or copy) incredibly obscure notations without explaining them properly, but this is not the place for it. Here, you should strive to be as clear as possible (Note to the experts: This does not - in any way - limit the size of the numbers you can reach. It simply means that as the game progresses, we need to be clearer with our explanations).
5. If you're "a math-oriented average joe" and an entry seems completely unintelligible to you, you may challenge it. You may not continue to submit numbers until all challenges have been resolved.
6. People are encouraged to ask questions about the numbers and notations posted.
7. Borrowing notations from other players is allowed. In this case, the "borrower" does not need to explain the notation again.
8. Don't make too big a jump. The idea is to progress gradually, so even the uninitiated could feel at home.
9. If you need a general (and rough) guideline: A good number to reach at the end of page 1 would be a million. And a good number for the end of page 2 would be a googol. Note that this is only a guideline, and not a hard limit. The only reason I've posted it is so you'll have a better idea of what I mean by "too big a jump", which is - obviously - a subjective term.
10. Since there is no hard-set "Cap" for the numbers one may post, I reserve the right to disqualify blatant overkills. I will, however, do this only in the most extreme of situations (and sincerely hope such drastic measures will never be needed).
11. All posters are either "googologists" or "everymen". A player specifies which one they are once they make their first post, and may never switch. It is the responsibility of the googologists to explain things to the everymen.
12. At least one in every ten submitted numbers must be made by an everyman. That is, if the last nine numbers were posted by googologists, a fifth number may not be posted by a googologist.

And now, I'll start nice and easy:

I am a googologist.

...And send:

1


(Please, as soon as you are confused, CHALLENGE THE NUMBER! Don't be afraid to speak up!)
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ygh
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Re: My number is bigger! (New Everyman version)

Postby ygh » Sat Sep 24, 2016 9:58 pm UTC

2.

I'll see if I can trick Flicky into joining.
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Re: My number is bigger! (New Everyman version)

Postby emlightened » Sat Sep 24, 2016 10:09 pm UTC

Let ()a = a+1,
(')0 = ()1, and (')a+1 = ()(')a,
and ('')0 = (')1, and ('')a+1 = (')('')a.

Note that ()a = a+1, (')a = a+2, and ('')a = 2a+3

('')0 = (')1 = ()(')0 = ()()1 = ()2 = 3

Don't expect me to cone on here often; I seem only to come on here once or twice a week at the moment. It might increase. Oh, and I guess I'm a googologist.

"Therefore it is in the interests not only of public safety but also public sanity if the buttered toast on cats idea is scrapped, to be replaced by a monorail powered by cats smeared with chicken tikka masala floating above a rail made from white shag pile carpet."

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Re: My number is bigger! (New Everyman version)

Postby username5243 » Sat Sep 24, 2016 11:16 pm UTC

let n|() = n^n

Send:

2|() = 2^2 = 4
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Re: My number is bigger! (New Everyman version)

Postby emlightened » Sun Sep 25, 2016 6:27 pm UTC

And let (''')0 = ('')1, and (''')n+1 = ('')(''')n. (''')n = 2n+3-3

(''')0 = ('')1 = (')('')0 = (')(')1 = (')()(')0 = (')()()1 = (')()2 = (')3 = ()(')2 = ()()(')1 = ()()()(')0 = ()()()()1 = ()()()2 = ()()3 = ()4 = 5

"Therefore it is in the interests not only of public safety but also public sanity if the buttered toast on cats idea is scrapped, to be replaced by a monorail powered by cats smeared with chicken tikka masala floating above a rail made from white shag pile carpet."

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Re: My number is bigger! (New Everyman version)

Postby ygh » Sun Sep 25, 2016 8:47 pm UTC

Let's define the fast-growing hierarchy up to fω.
f0(x)=x+1
fy(x)=fy-1fy-1...fy-1(x) with x fy-1's
fω(x)=fx(x)

I send fω(2)=f2(2)=f1f1(2)=f1f0f0(2)=f1(4)=f0f0f0f0(4)=8

It's a bit of a jump, but hopefully not too bad?
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Re: My number is bigger! (New Everyman version)

Postby username5243 » Mon Sep 26, 2016 12:26 am UTC

It's fine.

Let En = 10^n and aEb = a*10^b.

I send E1 = 10.
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Re: My number is bigger! (New Everyman version)

Postby ygh » Mon Sep 26, 2016 2:16 am UTC

16

Let's go a bit faster than the other thread did.
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Re: My number is bigger! (New Everyman version)

Postby emlightened » Mon Sep 26, 2016 6:37 pm UTC

(''')(')0 = (''')2 = ('')('')('')1 = ('')('')5 = ('')13 = 29

"Therefore it is in the interests not only of public safety but also public sanity if the buttered toast on cats idea is scrapped, to be replaced by a monorail powered by cats smeared with chicken tikka masala floating above a rail made from white shag pile carpet."

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Re: My number is bigger! (New Everyman version)

Postby ygh » Tue Sep 27, 2016 12:32 am UTC

50
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Re: My number is bigger! (New Everyman version)

Postby emlightened » Wed Sep 28, 2016 10:21 pm UTC

(''')()('')0 = (''')4 = 125

"Therefore it is in the interests not only of public safety but also public sanity if the buttered toast on cats idea is scrapped, to be replaced by a monorail powered by cats smeared with chicken tikka masala floating above a rail made from white shag pile carpet."

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Re: My number is bigger! (New Everyman version)

Postby ygh » Sun Oct 02, 2016 5:15 pm UTC

500
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Re: My number is bigger! (New Everyman version)

Postby emlightened » Mon Oct 03, 2016 8:14 pm UTC

(''')('')(')()0 = 4093

"Therefore it is in the interests not only of public safety but also public sanity if the buttered toast on cats idea is scrapped, to be replaced by a monorail powered by cats smeared with chicken tikka masala floating above a rail made from white shag pile carpet."

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Re: My number is bigger! (New Everyman version)

Postby ygh » Mon Oct 03, 2016 9:11 pm UTC

10^5
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Re: My number is bigger! (New Everyman version)

Postby emlightened » Mon Oct 03, 2016 9:21 pm UTC

(''')(''')(')0 = 4294967293

"Therefore it is in the interests not only of public safety but also public sanity if the buttered toast on cats idea is scrapped, to be replaced by a monorail powered by cats smeared with chicken tikka masala floating above a rail made from white shag pile carpet."

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Re: My number is bigger! (New Everyman version)

Postby ygh » Mon Oct 03, 2016 9:29 pm UTC

f2(f1(f2(3)))

or about 13.5 quadrillion*.

*A quadrillion is a thousand trillion.
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Re: My number is bigger! (New Everyman version)

Postby emlightened » Wed Oct 05, 2016 7:22 pm UTC

(''')(''')(')(')0 = 340282366920938463463374607431768211453 ~ 1038.532

"Therefore it is in the interests not only of public safety but also public sanity if the buttered toast on cats idea is scrapped, to be replaced by a monorail powered by cats smeared with chicken tikka masala floating above a rail made from white shag pile carpet."

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Re: My number is bigger! (New Everyman version)

Postby ygh » Fri Oct 07, 2016 1:06 am UTC

10100, also known as a googol.
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Re: My number is bigger! (New Everyman version)

Postby emlightened » Fri Oct 07, 2016 3:13 pm UTC

Let ('''')0 = (''')1 and ('''')n+1 = (''')('''')n. ('''')n = 2↑↑(n+3)-3

('''')(')0 ~ 2x1019728

Hope you don't mind.

"Therefore it is in the interests not only of public safety but also public sanity if the buttered toast on cats idea is scrapped, to be replaced by a monorail powered by cats smeared with chicken tikka masala floating above a rail made from white shag pile carpet."

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Re: My number is bigger! (New Everyman version)

Postby Daggoth » Fri Oct 07, 2016 11:11 pm UTC

0.21x1019729

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Re: My number is bigger! (New Everyman version)

Postby ygh » Fri Oct 07, 2016 11:32 pm UTC

fω(3)
or about 6.9*10121210694.

Also, Daggoth, do you want to slow down? Because that was a tiny increase.
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Re: My number is bigger! (New Everyman version)

Postby username5243 » Fri Oct 07, 2016 11:45 pm UTC

I do. I see the point of speeding past the small range, but by now we should slow down.

10^^3 = 10^10^10

(a^^b = a^a^a^...^a^a with b a's)
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Re: My number is bigger! (New Everyman version)

Postby emlightened » Sat Oct 08, 2016 9:11 am UTC

I don't really think that we're out of the 'small range' yet.

We're still working with elementary recursive functions (boundedly iterated exponentiation), and are far below most of the primitive recursive functions (which include all hyperoperators). I'd say we'd stop being small when we get past 3↑69 or somesuch.

ω

(''')(''')(''')(')(')0 = 2↑2↑128-3 ~ 10↑10↑38

"Therefore it is in the interests not only of public safety but also public sanity if the buttered toast on cats idea is scrapped, to be replaced by a monorail powered by cats smeared with chicken tikka masala floating above a rail made from white shag pile carpet."

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Re: My number is bigger! (New Everyman version)

Postby username5243 » Sat Oct 08, 2016 3:28 pm UTC

If it were up to me, I would've DQ'd the jump from 10^5 to 1.39E16.

But since everyone else was fine, I'll roll with it. This is a fair game, not a dictatorship, after all, and if I did that you'd all stop playing.

@emlightened: I think your (') type punction are just a re-written version of the Ackermann function...

I think 10^^10 may be a good time to slow down, that way we've gone beyond everyday without going too far ahead.

I send:

3|()()

What does THAT mean? Well n|()() = n|()|()|...|() with n (('s. So this is 3|()|()|() = 27|()|() = (27^27)^(27^27) = 27^(27^27+27). It is about 10^10^40.
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Re: My number is bigger! (New Everyman version)

Postby ygh » Sat Oct 08, 2016 5:29 pm UTC

1010^50
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Re: My number is bigger! (New Everyman version)

Postby username5243 » Sat Oct 08, 2016 5:59 pm UTC

1 Googolplex = 10^10^100
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Re: My number is bigger! (New Everyman version)

Postby emlightened » Sat Oct 08, 2016 6:03 pm UTC

username5243 wrote:@emlightened: I think your (') type punction are just a re-written version of the Ackermann function...

That's funny, so do I!

:P

username5243 wrote:If it were up to me, I would've DQ'd the jump from 10^5 to 1.39E16.

Oh, you mean the one with 4.2*10^9 in the middle of it?

Oh, and feel free to disqualify me if I'm going to fast. Going slow just seems, and always has seemed, pointless, assuming that everybody has a decent level of understanding of the 'level' we're at.

Anyhow,

(''')(''')(''')('')(')0 = 2↑2↑1024-3 ~ 10↑10↑308

"Therefore it is in the interests not only of public safety but also public sanity if the buttered toast on cats idea is scrapped, to be replaced by a monorail powered by cats smeared with chicken tikka masala floating above a rail made from white shag pile carpet."

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Re: My number is bigger! (New Everyman version)

Postby username5243 » Sat Oct 08, 2016 10:40 pm UTC

10^10^1000
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Re: My number is bigger! (New Everyman version)

Postby Daggoth » Sat Oct 08, 2016 11:28 pm UTC

Alright lets go faster then
10^^7

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Re: My number is bigger! (New Everyman version)

Postby emlightened » Sun Oct 09, 2016 7:10 am UTC

('''')('''')0 = 2↑↑16-3

"Therefore it is in the interests not only of public safety but also public sanity if the buttered toast on cats idea is scrapped, to be replaced by a monorail powered by cats smeared with chicken tikka masala floating above a rail made from white shag pile carpet."

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Re: My number is bigger! (New Everyman version)

Postby username5243 » Sun Oct 09, 2016 9:52 pm UTC

Daggoth wrote:Alright lets go faster then
10^^7


Whoa! Slow down!

Sorry, but that's too much IMO. If all the others want to I will allow it, but that's too fast if someone wants to join.
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Re: My number is bigger! (New Everyman version)

Postby ygh » Mon Oct 10, 2016 1:54 am UTC

Wait, no one defined tetration. x^^y=x^(x^^(y-1)), x^^0=1.
I send 10^^20.
Also, Daggoth, that's not what we meant.
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Re: My number is bigger! (New Everyman version)

Postby Daggoth » Mon Oct 10, 2016 6:28 pm UTC

Set some guidelines

10^^(10^2)

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Re: My number is bigger! (New Everyman version)

Postby emlightened » Mon Oct 10, 2016 7:47 pm UTC

Oh, the guidelines! I remember them!

250 000

Sorry, I seem to be in a bit of a sarcastic mood in this thread. Not helpful.

Anyhow, I'm fine with Daggoth's speed. It's either user's descision, or a vote, but I'm fine with it.

If we do come up with some new guidelines, then could we please all contribute and then take the "average"?

('''')(''')('')(')()0 = 2↑↑4096-3
Last edited by emlightened on Mon Oct 10, 2016 8:14 pm UTC, edited 1 time in total.

"Therefore it is in the interests not only of public safety but also public sanity if the buttered toast on cats idea is scrapped, to be replaced by a monorail powered by cats smeared with chicken tikka masala floating above a rail made from white shag pile carpet."

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Re: My number is bigger! (New Everyman version)

Postby Daggoth » Mon Oct 10, 2016 7:57 pm UTC

that number doesnt seem bigger than mine

// Offtopic
Emlightened, do you know where i can find guidelines on fundamental sequences for ordinals in the extended veblen function up to svo?, i've found some resources online but they only cover up to φ(1,0,0). I've also found conflicting help on relating φ(x) to Γ_x ie. some pages implying Γ_1 = φ(2,0,0) and others Γ_1 = φ(1,1,0). If you feel like this is inappropiate for the thread, i beg for your help over pm. Thanks in advance! :mrgreen:

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Re: My number is bigger! (New Everyman version)

Postby username5243 » Mon Oct 10, 2016 8:57 pm UTC

@daggoth: I propose we set up a PM. You can always ask on the wiki too. But Γ1 is φ(1,0,1); φ(1,1,0) is the first fixed-point of x > Γx. (At least in the φ-function used on the wiki, which was always the one I used.)

Anyway, how about sometime between now and 10^^^10 level we slow down?

10^^10^5
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Re: My number is bigger! (New Everyman version)

Postby Daggoth » Mon Oct 10, 2016 9:03 pm UTC

i accept your proposal, i understand the wikipedia article, however it seems i was misled by this blog
http://quibb.blogspot.mx/2012/03/infinity-impredicative-ordinals.html
which indicates the wrong value, thanks in advance for your help :D

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Re: My number is bigger! (New Everyman version)

Postby username5243 » Mon Oct 10, 2016 9:08 pm UTC

no number?

You can start if you want. I think it would be good to stop because any "average" readees we may have don't understand it. (Even if we were to keep going at this pace, we'd probably need at least 20-30 pages to reach Γ0.)
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Re: My number is bigger! (New Everyman version)

Postby Daggoth » Mon Oct 10, 2016 9:12 pm UTC

10^^(100^5) = 10^^(10^10)

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Re: My number is bigger! (New Everyman version)

Postby ygh » Thu Oct 13, 2016 1:20 pm UTC

x^^^y=x^^(x^^^(y-1))
x^^^0=1

x^^^^y=x^^^(x^^^^(y-1))
x^^^^0=1

In general, x(z arrows)y=x(z-1 arrows)x(z arrows)y-1

I send 3^^^^2.

Spoiler:
Expansion:
3^^^^2
3^^^3
3^^3^^3
3^^3^3^3
3^^3^27
3^^7625597484987
(power tower 7625597484987 numbers tall)
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