My Number is Bigger! (Everymen Needed!)

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

Postby SirGabriel » Wed Dec 23, 2015 3:01 pm UTC

123456789

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

Postby emlightened » Wed Dec 23, 2015 3:03 pm UTC

2{2}3 = {2}24 = 402,653,184

"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 Dec 23, 2015 3:15 pm UTC

9>0 = 10^9 = 1,000,000,000 = 1 billion
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Re: My Number is Bigger! (Everymen Needed!)

Postby emlightened » Wed Dec 23, 2015 3:53 pm UTC

{2}26 = 26*2^26 = 1,744,830,464

"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 Dec 23, 2015 4:13 pm UTC

3*10^9
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SirGabriel
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Re: My Number is Bigger! (Everymen Needed!)

Postby SirGabriel » Wed Dec 23, 2015 4:23 pm UTC

pi^e^pi ≈ 319,442,280,000

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

Postby emlightened » Wed Dec 23, 2015 4:30 pm UTC

Eeeϕ ≈ 903,116,782,624

"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 Dec 23, 2015 4:47 pm UTC

3↑↑3

Remember this means 3^3^3 = 3^27 = 7,625,597,484,987.
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Re: My Number is Bigger! (Everymen Needed!)

Postby Yrgos » Wed Dec 23, 2015 10:44 pm UTC

10!^2! = 10!^2 > 1.3E13

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

Postby PsiSquared » Wed Dec 23, 2015 11:57 pm UTC

Wow, we're in the trillions already?

Guess it's time to extend scientific notation. So what comes after "E"? Why F, of-course:

Define:

aFn c EEEE...EEEEa (with n E's)

Note that since 10 = E1, this "super-scientific-notation" can represent any number as:

(a number between 1 and 10)F(some integer)

For example, Yrgos number is:

10!^2 = 13168189440000 ~ 10^13.12 ~ 10^10^1.11792 = EE1.11792 = 1.11792F2

And I send:
1.15F2 = EE1.15 = 10^10^1.15 ~ 133 467 475 574 035
(or about 1.3E14)

(if anything here is unclear, please say so)

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

Postby username5243 » Thu Dec 24, 2015 2:26 am UTC

15>0 = 10^15
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Re: My Number is Bigger! (Everymen Needed!)

Postby SirGabriel » Thu Dec 24, 2015 9:52 am UTC

pi^^3 ≈ 1.34016418*10^18

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

Postby username5243 » Thu Dec 24, 2015 11:25 am UTC

10^20
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Re: My Number is Bigger! (Everymen Needed!)

Postby emlightened » Thu Dec 24, 2015 2:42 pm UTC

1.444678^^997 ~ 1.48E20

"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 SirGabriel » Thu Dec 24, 2015 4:08 pm UTC

emlightened wrote:1.444678^^997 ~ 1.48E20

How did you calculate that? None of the online calculators I've found will accept that notation.

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

Postby Yrgos » Thu Dec 24, 2015 6:50 pm UTC

I think theres a typo, because 1.44^^997 > 1.44^997 since 1.44 > 1 and 1.44^997 ~ 7E157

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

Postby Yrgos » Thu Dec 24, 2015 7:05 pm UTC

Nvm, will post again after x-mas ;)

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

Postby emlightened » Thu Dec 24, 2015 8:13 pm UTC

SirGabriel wrote:
emlightened wrote:1.444678^^997 ~ 1.48E20

How did you calculate that? None of the online calculators I've found will accept that notation.

I coded it into python (but the result was wrong anyway).
Spoiler:

Code: Select all

def tet(a,b):
   n=1
   try:
      for i in range(b): n = a**n
   except OverflowError: pass
   return a,i+1,n

for j in range(1000):
   k = tet(1.4446+j*10**-7, 10000)
   if 10**20 < k[2] < 10**22: # change the numbers here to control how large the output is
      print(k)

# This code outputs numbers in the form (a, b, c), where a^^b = c, a < 1.44475, and 10^20 < c < 10^22.


Yrgos wrote:I think theres a typo, because 1.44^^997 > 1.44^997 since 1.44 > 1 and 1.44^997 ~ 7E157

Not always true. For instance, consider (√2)^^4. (√2)^4 = 2^2 = 4, but (√2)^^4 = (√2)^(√2)^(√2)^(√2) ~ (√2)^(√2)^1.6325 ~ (√2)^1.7608 ~ 1.8409 < (√2)^4 = 4. In fact, for 0.066 < k < 1.4446, k↑↑∞ is well-defined, and is less than 2.72.

(Using the code above,) 1.4446915^^666 ~ 2.362E20

"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 Yrgos » Fri Dec 25, 2015 3:00 am UTC

Yes, I realized after I posted that that x^a > x^b if a>b>1 and x > 1 doesn't mean in any way that I can claim that x^^a > x^a for x > 1 and a>1. But I would presume that it is true if a > 2 though. The ^^ is fairly new to me, powertowers aren't part of my university math study or the corriculum I teach :) I did go and read up on it, but slightly intoxicated still, so my mileage may vary :)

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

Postby username5243 » Sat Dec 26, 2015 11:08 am UTC

{2}70

= 70*2^70 ~ 8.2641E22
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Re: My Number is Bigger! (Everymen Needed!)

Postby emlightened » Sun Dec 27, 2015 7:29 pm UTC

-0.87F4 = EEEE-0.87 ~ EEE0.1349 ~ EE1.3643 ~ E23.1343 ~ 1.073×1023

"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 » Mon Dec 28, 2015 6:05 pm UTC

I'll be using my brackets from the other thread, too.

We have:

n|() = n^n

Okay?

Anyway, send:

19|() = 19^19 ~ 1.97482E24
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Re: My Number is Bigger! (Everymen Needed!)

Postby SirGabriel » Tue Dec 29, 2015 5:16 pm UTC

5^4^3 ~ 5.42101086E44

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

Postby emlightened » Tue Dec 29, 2015 5:19 pm UTC

2{2}5 = 160×2160 ~ 2.3384E50

"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 SirGabriel » Tue Dec 29, 2015 5:22 pm UTC

42! ~ 1.40500612E51

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

Postby emlightened » Tue Dec 29, 2015 5:35 pm UTC

-0.6F4 ~ 4.955E60

"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 Dec 30, 2015 12:41 pm UTC

10^65
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Re: My Number is Bigger! (Everymen Needed!)

Postby PsiSquared » Thu Dec 31, 2015 10:55 am UTC

10^70

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

Postby username5243 » Thu Dec 31, 2015 7:44 pm UTC

45|() ~ 2.48E74
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Re: My Number is Bigger! (Everymen Needed!)

Postby username5243 » Thu Dec 31, 2015 7:45 pm UTC

That's four, by the way.

Also, if anyone wants a game more like the other one to start again, I'd be happy to do it. I think I'll start it tomorrow for the new year and see how far it gets.
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Re: My Number is Bigger! (Everymen Needed!)

Postby SirGabriel » Thu Dec 31, 2015 8:20 pm UTC

60! ~ 8.32E81

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

Postby emlightened » Thu Dec 31, 2015 9:31 pm UTC

googol-42 =
99999 99999 99999 99999 99999 99999 99999 99999 99999 99999
99999 99999 99999 99999 99999 99999 99999 99999 99999 99958
~ 10^100

I'd be fine with it, but you'd definitely want something to prevent tensions rising again.

Edit: P.S: We both joined the googology wiki on the same day (today). Huh.

"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 » Fri Jan 01, 2016 7:24 am UTC

A googol and one =
1 00000 00000 00000 00000 00000 00000 00000 00000 00000 00000
00000 00000 00000 00000 00000 00000 00000 00000 00000 00001


"Rising tensions" isn't the main problem. Or rather, it is a very simple problem to fix: In extreme cases the host can tell both parties to stop. In very extreme cases, a PM to the forum moderators will solve the problem. That's exactly what the moderators are here for.

The really sticky problem, is to ensure that people who break the rules can't disrupt the game for everybody else. This requires the cooperation of both the host and the other players.

For example, one thing that did work well on the other thread, is the way everybody treated overkills. Whenever someone posted a number which was obviously too large, everybody simply ignored it. People didn't endlessly debate the matter, and they certainly didn't cooperate with the violation.

And the same should be done with any other form of blatant rule-breaking. If an entry is obviously illegal, it should be treated as such and the game should move on.

Oh, and another thing:
It should be understood by everyone that when everything else fails, the host of the game (which will certainly not be me) is the final judge of everything game-related. The concept of "game referee" exists for a good reason, and it is critical if you want to make sure that things won't spiral out of control.

(that was a pretty long post. Please tell me if you think this discussion is getting too distracting)

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

Postby username5243 » Fri Jan 01, 2016 1:18 pm UTC

Okay.

However, if Psi isn't an "everyman", then I'm certainly not, either. I suggest that one of the everymen on this thread co-hosts, if he/she is willing.

If not, I want to require participation, but more like twice a page.

Now that me and emlightened have registered accounts, we can make blogposts to describe our notations. If you want to do so, Psi, you need to make a wikia account. It only takes a minute. (unless you already have one, but there's no user named PsiSquared on Wikia.)
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Re: My Number is Bigger! (Everymen Needed!)

Postby username5243 » Fri Jan 01, 2016 1:19 pm UTC

Oh, by the way, 10^112
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Re: My Number is Bigger! (Everymen Needed!)

Postby SirGabriel » Fri Jan 01, 2016 1:25 pm UTC

2^500 ~ 3.27E150

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

Postby PsiSquared » Fri Jan 01, 2016 2:06 pm UTC

200E200 (=2x10202)

username5243 wrote:Okay.

However, if Psi isn't an "everyman", then I'm certainly not, either. I suggest that one of the everymen on this thread co-hosts, if he/she is willing.

If not, I want to require participation, but more like twice a page.


This really raises the question: Why do you feel the need for a new thread, when we already have this one?

I think you've done an excellent job with this thread, and it is proceeding nicely. I also think that requiring everyman participation is a good rule. Why try to fix something that is already working perfectly?

EDITED TO ADD:

I whole-heartedly support the notion of officially adding an everyman co-host to this thread. This is actually a position I would have gladly volunteered for (if not for me being obviously overqualified for it).

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

Postby username5243 » Fri Jan 01, 2016 2:16 pm UTC

Thanks.

111|()() = 111^111 ~ 1.0736E227
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Re: My Number is Bigger! (Everymen Needed!)

Postby emlightened » Fri Jan 01, 2016 2:49 pm UTC

123 456 789 101112 131415 161718 192021 222324 252627 282930 313233 343536 373839 404142
434445 464748 495051 525354 555657 585960 616263 646566 676869 707172 737475 767778 798081
828384 858687 888990 919293 949596 979899 100101102 103104105 106107108 109110111 112 ~ 1.23456789E227

I agree with Psi. While it would be nice to have another thread so that we can play with larger numbers faster, there's no need for it; we'll be there on this thread in a month or two.

"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 SirGabriel » Fri Jan 01, 2016 4:30 pm UTC

3^500 ~ 3.636E238


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