My Number is Bigger! (Everymen Needed!)

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

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!)

2{2}7 ~ 4.7335E272

Probably around $10^{10^{680}}$. 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!)

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!)

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

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

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

That was four.

Now we await an everyman to keep the game going.

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

10^(101*pi) ~ 1.999E317

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

(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."

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

{2}{2}{2}2 = {2}{2}(2x22) = {2}{2}8 = {2}(8x28) = {2}2048 = 2048x22048 ~ 6.62x10619

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

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."

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

10^10^3 = 10^1000

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

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.

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

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."

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

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

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

(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."

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

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?

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

5F2

I'm an everyman (although with a PhD in Cryptography). Hit me with your most crazy notations.

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

6^^3 ~ 2.659E36305

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

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

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

PsiSquared wrote:5F2 is larger than 6^^3

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

5.5F2

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

(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."

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

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.

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

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."

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

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.

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

10^10987654321

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

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."

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

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

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

17^^3 ~ 10^10^21.008

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

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

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!)

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

No objection.

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

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

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!)

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

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

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.

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

According to Wolfram Alpha

4.2↑↑4 ~ 10^10^258

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

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

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

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!)

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

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 $10^{10^{680}}$.

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."