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### Re: My Number is Bigger! (Everymen Needed!)

Posted: Fri Jan 01, 2016 4:54 pm UTC
What number do you think we'll reach at the end of this page? 10^^3? A googolplex?

10^256

### Re: My Number is Bigger! (Everymen Needed!)

Posted: Fri Jan 01, 2016 8:55 pm UTC
2{2}7 ~ 4.7335E272

Probably around . 10^{10^{680}}

### Re: My Number is Bigger! (Everymen Needed!)

Posted: Fri Jan 01, 2016 9:47 pm UTC
I've made a blogpost on Googology Wiki for people to edit in their notations. See it here:

http://googology.wikia.com/wiki/User_Bl ... _Notations

I believe you should be able to edit it if you have a registered Wikia account.

Anyway...

1 Centillion = 10^303

### Re: My Number is Bigger! (Everymen Needed!)

Posted: Sat Jan 02, 2016 12:19 pm UTC
That was only three...

### Re: My Number is Bigger! (Everymen Needed!)

Posted: Sat Jan 02, 2016 3:32 pm UTC
2.5F2 = 10^10^2.5 ~ 10^316

### Re: My Number is Bigger! (Everymen Needed!)

Posted: Mon Jan 04, 2016 8:27 am UTC
That was four.

Now we await an everyman to keep the game going.

### Re: My Number is Bigger! (Everymen Needed!)

Posted: Mon Jan 04, 2016 9:46 am UTC
10^(101*pi) ~ 1.999E317

### Re: My Number is Bigger! (Everymen Needed!)

Posted: Mon Jan 04, 2016 1:17 pm UTC
(8/3)F2 ~ 1.44E464

### Re: My Number is Bigger! (Everymen Needed!)

Posted: Mon Jan 04, 2016 2:34 pm UTC
{2}{2}{2}2 = {2}{2}(2x22) = {2}{2}8 = {2}(8x28) = {2}2048 = 2048x22048 ~ 6.62x10619

### Re: My Number is Bigger! (Everymen Needed!)

Posted: Mon Jan 04, 2016 3:09 pm UTC
That's just past username's 2|()|()|() < 10617.

(-1/3)F4 = EEEE(-1/3) ~ EEE0.46416 ~ EE2.91178 ~ E816.1729 ~ 1.489*10816

### Re: My Number is Bigger! (Everymen Needed!)

Posted: Mon Jan 04, 2016 4:11 pm UTC
10^10^3 = 10^1000

### Re: My Number is Bigger! (Everymen Needed!)

Posted: Mon Jan 04, 2016 4:43 pm UTC
Define:
[x,y,z] = x^x^x^...^x^z (with y x's)

So:
[x,y,1] = x^y
[x,y,2] = x^x^y
[x,y,3] = x^x^x^y
[x,y,4] = x^x^x^x^y
<- thanks to Emlightened for spotting this to be an error

[x,1,z] = x^z
[x,2,z] = x^x^z
[x,3,z] = x^x^x^z
[x,4,z] = x^x^x^x^z

and so on.

Send:
[3,2,7] = 3^3^7 = 3^2187 ~ 3x101043

(also, note the following identities always hold:
a^^b = [a,b,1]
aFb = [10,b,a]
)

### Re: My Number is Bigger! (Everymen Needed!)

Posted: Mon Jan 04, 2016 4:50 pm UTC
I think I read that the notation yx#z being the same as that, but I only ever saw it used once.

Also, Psi, your examples are screwed up. They should be:
PsiSquared wrote:[x,1,z] = x^z
[x,2,z] = x^x^z
[x,3,z] = x^x^x^z
[x,4,z] = x^x^x^x^z

[3,2,8] = 3^3^8 = 3^6561 ~ 103130

### Re: My Number is Bigger! (Everymen Needed!)

Posted: Mon Jan 04, 2016 4:58 pm UTC
emlightened wrote:Also, Psi, your examples are screwed up. They should be:
PsiSquared wrote:[x,1,z] = x^z
[x,2,z] = x^x^z
[x,3,z] = x^x^x^z
[x,4,z] = x^x^x^x^z

Ouch. How did that happen?

You're right of-course.

[3,3,2] = 3^3^3^2 = 3^19683 ~ 109391 ~ 10^10^3.973 = 3.973F2

### Re: My Number is Bigger! (Everymen Needed!)

Posted: Mon Jan 04, 2016 5:05 pm UTC
(7!)! = 5040! ~ E16476 ~ 4.217F2

Four.

### Re: My Number is Bigger! (Everymen Needed!)

Posted: Wed Jan 06, 2016 9:33 am UTC
It seems that the everymen lost interest in the game, causing it to stall.
(I'm pretty sure it isn't because of a comprehension issue, given that we haven't even reached a googolplex yet)

So what do we do now?

### Re: My Number is Bigger! (Everymen Needed!)

Posted: Wed Jan 06, 2016 9:56 am UTC
5F2

I'm an everyman (although with a PhD in Cryptography). Hit me with your most crazy notations. ### Re: My Number is Bigger! (Everymen Needed!)

Posted: Wed Jan 06, 2016 9:58 am UTC
6^^3 ~ 2.659E36305

### Re: My Number is Bigger! (Everymen Needed!)

Posted: Wed Jan 06, 2016 12:13 pm UTC
5F2 is larger than 6^^3

5F2 = 10^10^5 = 1E100000 which is larger than 2.7E36305 (because 100000 > 36305)

Or alternatively:

6^^3 ~ 2.7E36305 ~ E36305 = EE(log 36305) ~ EE4.56 = 4.56F2 < 5F2 (because 4.56 < 5)

Anyway:

[8,2,8-2] = [8,2,6] = 8^8^6 ~ 4.2E236739 ~ (log 236739)F2 ~ 5.374F2

### Re: My Number is Bigger! (Everymen Needed!)

Posted: Wed Jan 06, 2016 1:22 pm UTC
PsiSquared wrote:5F2 is larger than 6^^3

I'm aware of that, I was ninja'd.

5.5F2

### Re: My Number is Bigger! (Everymen Needed!)

Posted: Wed Jan 06, 2016 3:13 pm UTC
(10!)! = 3628800! ~ [s]101 859 938 1022 228 109 > 5.5F2 ~ 10316 227[/s]

Edit: Fixed number.

### Re: My Number is Bigger! (Everymen Needed!)

Posted: Wed Jan 06, 2016 3:58 pm UTC
That's actually (9!)!.

And how are you doing the factorial approximations? I'm curious, because your results are almost accurate yet ever-so-slightly off (Wolfram-alpha gives (7!)! as 4x1016473 and (9!)! as 101 859 933)

Anyway, since the actual number you've posted is (10!)! ~ 7.35F2, I'll post:

{3}3 = {2}{2}{2}3 = {2}{2}24 = {2}402653184 = 402653184x2402653184 ~ 10121 210 695 = E(121 210 695) = EE[log(121 210 695)] ~ EE8.08 = 8.08F2

Also notice that {3}3 is not very far off from 1F3 (or 10F2). Make note of this fact, because it will be important later.

### Re: My Number is Bigger! (Everymen Needed!)

Posted: Wed Jan 06, 2016 5:09 pm UTC
Hypercalc. (It gives 3.633825810665 × 1016476 for (7!)!, by the way.)

[e,3,π] ~ 104871463233.4747 ~ 9.68765F2 (accurate in both Hypercalc and Wolfram)

### Re: My Number is Bigger! (Everymen Needed!)

Posted: Wed Jan 06, 2016 5:48 pm UTC
Hypercalc is known for having a bug when it comes to factorials.

You could probably trust it for everything else. But the truth is that for nearly all practical purposes, WolframAlpha can do anything that Hypercalc can do (although W-A has a really annoying bug which causes it to crash when given certain power towers, regardless of the actual size of the number involved: 2^2^2^5 crashes it, yet 2^2^2^6 works just fine).

Anyway:
10^^3 = 10^10^10 = 1F3 = 10F2 = (10 000 000 000)F1 = 1010 000 000 000
(Major Milestone)

And that's four.

### Re: My Number is Bigger! (Everymen Needed!)

Posted: Wed Jan 06, 2016 7:31 pm UTC
10^10987654321

### Re: My Number is Bigger! (Everymen Needed!)

Posted: Wed Jan 06, 2016 9:02 pm UTC
I'd be fine with it, but it's probably best left < 15 or < 10.

[2,3,2*3] = 2^2^2^6 = 2^2^64 = 2^18446744073709551616 ~ EE18.744

### Re: My Number is Bigger! (Everymen Needed!)

Posted: Wed Jan 06, 2016 10:22 pm UTC
I agree.

That's 18.744F2, or in "standard super scientific notation": 1.273F3

So I submit:

{2}{2}{2}4 = {2}{2}64 = {2}(64x264) = {2}(270) = 270 x (2^2^70) =
= 2^(70+(2^70)) = 10^((70+(2^70)) x log 2) ~ 10355 393 490 465 494 856 487 ~ EE20.5507 ~ EEE1.313 = 1.313F3

### Re: My Number is Bigger! (Everymen Needed!)

Posted: Wed Jan 06, 2016 11:23 pm UTC
17^^3 ~ 10^10^21.008

### Re: My Number is Bigger! (Everymen Needed!)

Posted: Thu Jan 07, 2016 12:56 am UTC
I'd be willing to increase it to 7 or even 10. Probably no more than that.

Anyway...

Define a:b as aaa...aaa with b a's (so 6:5 = 66666).

Define a::b as a:(a:(...(a:(a:a)))...))) with b a's (So 2::3 = 2:(2:2) = 2:22 = 2.222E21).

I send:

2::4 = 2:2222222222222222222222 ~ 10^(2.222*10^21)

### Re: My Number is Bigger! (Everymen Needed!)

Posted: Thu Jan 07, 2016 8:10 am UTC
22.2F2 = 10^10^22.2 ~ 1015 848 931 924 611 134 852 021

### Re: My Number is Bigger! (Everymen Needed!)

Posted: Thu Jan 07, 2016 9:50 pm UTC
10^10^25

Also:

I hereby declare that only one out of every ten numbers needs to be made by an everyman. That is, if nine consecutive numbers are submitted by googologists, the next one must be made by an everyman.

If you don't agree, state so now, because this will be official soon.

### Re: My Number is Bigger! (Everymen Needed!)

Posted: Fri Jan 08, 2016 6:16 am UTC
No objection.

[3,3,4] = 3^3^3^4 = 3^3^81 ~ 10^10^38.325 = 38.325F2 ~ 1.583F3

### Re: My Number is Bigger! (Everymen Needed!)

Posted: Fri Jan 08, 2016 5:19 pm UTC
Also no objection.

@user (not related to this game, just posted here because he'll more likely see it):
Spoiler:
I asked people if they minded me taking over the thumbtacks thread, and they didn't. I also sent you a PM, but you haven't read it yet, so I assumed you didn't mind, and I've started Round 2. Could you please change the thread title to remove the Round 1 part?

4↑↑↑2 = 4↑↑4 = 4↑4↑4↑4 = 4↑4↑256 ~ EE153.907 ~ 2.187F3

I don't think anyone's actually explained ↑ arrows fully yet.

a↑b = ab
a↑↑b = a↑a↑...a (for b a's)
a↑↑↑b = a↑↑a↑↑...a (for b a's)
a↑↑↑↑b = a↑↑↑a↑↑↑...a (for b a's)
etc.

We use ↑k as shorthand for ↑↑...↑↑, with k arrows.

Formally, we say that:
a↑b = ab
a↑k1 = a
a↑kb = a↑k-1(a↑k(b-1)).

So the full way to expand 4↑↑↑2 is:

4↑↑↑2 = 4↑↑(4↑↑↑1) = 4↑↑(4) = 4↑4↑↑3 = 4↑4↑4↑↑2 = 4↑4↑4↑4↑↑1 = 4↑4↑4↑4↑ = 4↑4↑(44) = 4↑4↑256
= 4↑(4256) ≈ 4↑(10154.127) = 410^154.127 ≈ 10(10^154.127)*log(4) = 1010^(154.127+log(log(4))) ≈ 1010^153.907 = EE153.907

### Re: My Number is Bigger! (Everymen Needed!)

Posted: Sat Jan 09, 2016 11:36 am UTC
And I wanted to use 3|()() (which is about 40F2)...

10^10^200

### Re: My Number is Bigger! (Everymen Needed!)

Posted: Sat Jan 09, 2016 3:50 pm UTC

I thought you might. That's exactly why I posted [3,3,4], which is a little bit less than that.

Anyway:
2.4F3= 10^10^10^2.4 ~ 10^10^251

P.S.
You should update the OP to reflect that change in the rules.

### Re: My Number is Bigger! (Everymen Needed!)

Posted: Mon Jan 11, 2016 2:14 pm UTC
According to Wolfram Alpha

4.2↑↑4 ~ 10^10^258

### Re: My Number is Bigger! (Everymen Needed!)

Posted: Mon Jan 11, 2016 5:46 pm UTC
2.468F3 = 10^10^10^2.468 ~ 10^10^294

### Re: My Number is Bigger! (Everymen Needed!)

Posted: Tue Jan 12, 2016 10:45 pm UTC
2{2}1000 = {2}(1000*2^1000) ~ 10^10^303

### Re: My Number is Bigger! (Everymen Needed!)

Posted: Wed Jan 13, 2016 12:58 am UTC
10^10^400

### Re: My Number is Bigger! (Everymen Needed!)

Posted: Wed Jan 13, 2016 1:12 am UTC
username5243 wrote:What number do you think we'll reach at the end of this page? 10^^3? A googolplex?

10^256
emlightened wrote:2{2}7 ~ 4.7335E272

Probably around .

10^10^680