My Number is Bigger! (Everymen Needed!)

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username5243
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Re: My Number is Bigger! (Everymen Needed!)

Postby username5243 » 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
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emlightened
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Re: My Number is Bigger! (Everymen Needed!)

Postby emlightened » Fri Jan 01, 2016 8:55 pm UTC

2{2}7 ~ 4.7335E272

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

"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! (Everymen Needed!)

Postby username5243 » 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
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Re: My Number is Bigger! (Everymen Needed!)

Postby username5243 » Sat Jan 02, 2016 12:19 pm UTC

That was only three...
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PsiSquared
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Re: My Number is Bigger! (Everymen Needed!)

Postby PsiSquared » Sat Jan 02, 2016 3:32 pm UTC

2.5F2 = 10^10^2.5 ~ 10^316

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

Postby PsiSquared » Mon Jan 04, 2016 8:27 am UTC

That was four.

Now we await an everyman to keep the game going.

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

Postby SirGabriel » Mon Jan 04, 2016 9:46 am UTC

10^(101*pi) ~ 1.999E317

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

Postby emlightened » Mon Jan 04, 2016 1:17 pm UTC

(8/3)F2 ~ 1.44E464

"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! (Everymen Needed!)

Postby PsiSquared » 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

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

Postby emlightened » 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

"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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SirGabriel
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Re: My Number is Bigger! (Everymen Needed!)

Postby SirGabriel » Mon Jan 04, 2016 4:11 pm UTC

10^10^3 = 10^1000

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

Postby PsiSquared » 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]
)
Last edited by PsiSquared on Mon Jan 04, 2016 5:04 pm UTC, edited 4 times in total.

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

Postby emlightened » 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

"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! (Everymen Needed!)

Postby PsiSquared » 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

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

Postby emlightened » Mon Jan 04, 2016 5:05 pm UTC

(7!)! = 5040! ~ E16476 ~ 4.217F2

Four.

"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! (Everymen Needed!)

Postby PsiSquared » 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?

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

Postby Sabrar » 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. :D

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

Postby SirGabriel » Wed Jan 06, 2016 9:58 am UTC

6^^3 ~ 2.659E36305

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

Postby PsiSquared » 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

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

Postby SirGabriel » 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

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

Postby emlightened » 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.
Last edited by emlightened on Wed Jan 06, 2016 4:56 pm UTC, edited 2 times 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! (Everymen Needed!)

Postby PsiSquared » 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.

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

Postby emlightened » 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)

"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! (Everymen Needed!)

Postby PsiSquared » 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.
(that went quickly... maybe Username should consider increasing this limit a bit? What does everybody else think about this suggestion?)

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

Postby SirGabriel » Wed Jan 06, 2016 7:31 pm UTC

10^10987654321

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

Postby emlightened » 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

"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! (Everymen Needed!)

Postby PsiSquared » Wed Jan 06, 2016 10:22 pm UTC

I agree.

As for your number:

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

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

Postby SirGabriel » Wed Jan 06, 2016 11:23 pm UTC

17^^3 ~ 10^10^21.008

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

Postby username5243 » 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)
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Re: My Number is Bigger! (Everymen Needed!)

Postby PsiSquared » Thu Jan 07, 2016 8:10 am UTC

22.2F2 = 10^10^22.2 ~ 1015 848 931 924 611 134 852 021

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

Postby username5243 » 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.
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Re: My Number is Bigger! (Everymen Needed!)

Postby PsiSquared » 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

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

Postby emlightened » 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

"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! (Everymen Needed!)

Postby username5243 » Sat Jan 09, 2016 11:36 am UTC

And I wanted to use 3|()() (which is about 40F2)...

10^10^200
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Re: My Number is Bigger! (Everymen Needed!)

Postby PsiSquared » Sat Jan 09, 2016 3:50 pm UTC

username5243 wrote:And I wanted to use 3|()() (which is about 40F2)...


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.

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

Postby Sabrar » Mon Jan 11, 2016 2:14 pm UTC

According to Wolfram Alpha

4.2↑↑4 ~ 10^10^258

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

Postby PsiSquared » Mon Jan 11, 2016 5:46 pm UTC

2.468F3 = 10^10^10^2.468 ~ 10^10^294

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

Postby emlightened » Tue Jan 12, 2016 10:45 pm UTC

2{2}1000 = {2}(1000*2^1000) ~ 10^10^303

"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! (Everymen Needed!)

Postby username5243 » Wed Jan 13, 2016 12:58 am UTC

10^10^400
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Re: My Number is Bigger! (Everymen Needed!)

Postby emlightened » 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 Image.


10^10^680

"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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