My number is bigger and smaller!

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Daggoth
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My number is bigger and smaller!

Postby Daggoth » Sat May 19, 2018 3:59 pm UTC

Silver rule : Given the previous two entries A and B, post a number thats bigger than A and smaller than B, or viceversa

Bronze rule : No bulls***** entries , e.g.(the biggest number that will be posted on page x etc..., you aren't creative or funny, go away) to be determined and disqualified at my discretion

Copper rule: No double posting! (except for this post)

Golden rule: You must to define and explain any notation that does not appear in the Scientific mode of Calc.exe and are liable to service up to 1 questions / clarification requests per user per entry, reference posts in the thread are allowed, external links are supplements and don't fulfill this rule.

Bonus rule: The first two posts in a page don't have to follow the silver rule


1
Last edited by Daggoth on Mon May 21, 2018 5:20 pm UTC, edited 2 times in total.

Daggoth
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Re: My number is bigger and smaller!

Postby Daggoth » Sat May 19, 2018 4:01 pm UTC

203045

Deedlit
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Re: My number is bigger and smaller!

Postby Deedlit » Sat May 19, 2018 4:59 pm UTC

203045

Daggoth
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Re: My number is bigger and smaller!

Postby Daggoth » Sat May 19, 2018 5:02 pm UTC

203044

Deedlit
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Re: My number is bigger and smaller!

Postby Deedlit » Sat May 19, 2018 5:41 pm UTC

2^2^2^2^2

PsiSquared
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Re: My number is bigger and smaller!

Postby PsiSquared » Sun May 20, 2018 5:40 pm UTC

I don't recall tetration and pentation appearing on any standard calculator...

But since they are obviously considered legal here:
10↑↑↑19

Spoiler:
Just in case someone claims that triple-arrows are somehow any less standard than the notation Daggoth used, I'll define:

a↑↑↑b = ba.

That way I'm covering all the bases :)

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emlightened
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Re: My number is bigger and smaller!

Postby emlightened » Sun May 20, 2018 9:09 pm UTC

2↑↑2↑3

I was going to ask about the operator precedence for exponentiation vs pentation, but realise that it's effectively immaterial given the magnitude.

a↑b = ab
a↑↑b = (a↑)b1

"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 and smaller!

Postby PsiSquared » Mon May 21, 2018 3:46 am UTC

2↑↑↑2↑3

Daggoth
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Re: My number is bigger and smaller!

Postby Daggoth » Mon May 21, 2018 5:19 pm UTC

i used the wrong formatting.. i meant to enter repeated exponentiation.. but i'm rolling with it.. precedence, lets go with that expression meaning (20↑↑↑30)↑45, by extrapolation on pemdas
the remaining details have already been explained by your entries

4↑↑7

Deedlit
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Re: My number is bigger and smaller!

Postby Deedlit » Mon May 21, 2018 5:25 pm UTC

5 in a pentagon using Steinhaus-Moser notation

PsiSquared
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Re: My number is bigger and smaller!

Postby PsiSquared » Mon May 21, 2018 5:50 pm UTC

Daggoth wrote:i used the wrong formatting.. i meant to enter repeated exponentiation


So apparently, the current lower limit is already larger than the original upper limit you've envisioned.

Let me try to partially correct that:

F(20^30^45)

(Fn is defined as 10↑↑n)

Now, basically, we're almost back to the original intended situation, just with an additional "F" prefixing all entries.


Scratch that. I just realized this post is going to set a new lower bound, so that was quite stupid of me.

Let me try again:

8↑↑8
(the next poster can shamelessly steal the number I've crossed off, if they want to set things right)

Daggoth
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Re: My number is bigger and smaller!

Postby Daggoth » Mon May 21, 2018 6:35 pm UTC

yeah nah thats ok lets just keep on trucking as is

5↑↑↑5

PsiSquared
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Re: My number is bigger and smaller!

Postby PsiSquared » Mon May 21, 2018 6:38 pm UTC

F10 = Decalogue
(Fn is defined as 10↑↑n)

Daggoth
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Re: My number is bigger and smaller!

Postby Daggoth » Tue May 22, 2018 6:04 pm UTC

5↑↑5↑↑5↑↑5↑5↑5↑400

PsiSquared
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Re: My number is bigger and smaller!

Postby PsiSquared » Tue May 22, 2018 8:32 pm UTC

3 in a triangle in a square, using Steinhaus-Moser notation.

Definitions:
Spoiler:
N in triangle = NN
N in a square = N in N triangles

So 3 in a triangle is 27, and my number is "27 in 27 triangles" which is somewhere between F28 and F29

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emlightened
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Re: My number is bigger and smaller!

Postby emlightened » Tue May 22, 2018 10:25 pm UTC

6↑↑5↑↑4↑↑3↑↑2↑↑1 = 6↑↑5↑↑4↑↑27 ~ FFF27

"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 and smaller!

Postby PsiSquared » Wed May 23, 2018 12:12 am UTC

2↑↑↑4 ~ F65533

Daggoth
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Re: My number is bigger and smaller!

Postby Daggoth » Fri May 25, 2018 8:31 pm UTC

6↑↑5↑↑4↑↑100

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emlightened
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Re: My number is bigger and smaller!

Postby emlightened » Fri May 25, 2018 9:26 pm UTC

Your number is too big.

2↑↑↑4 = 2↑↑65536
2↑↑65536 < 6↑↑5↑↑4↑↑27 < 6↑↑5↑↑4↑↑100


FF2 = 10↑↑10 000 000 000

"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 and smaller!

Postby PsiSquared » Sun May 27, 2018 1:34 pm UTC

FE5 = 10↑↑10↑5

(can also be called "giggolgong")

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emlightened
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Re: My number is bigger and smaller!

Postby emlightened » Mon May 28, 2018 11:11 am UTC

9↑↑10↑↑2 = 9↑↑10 000 000 000

Only slightly* smaller than the previous large one.

*depending on your definition of slightly.

"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 and smaller!

Postby PsiSquared » Tue May 29, 2018 7:30 pm UTC

Define:
Ex = 10^x
Fx = EEEE...EEEE(frac(x)) with int(x) E's
Gx = FFFF...FFFF(frac(x)) with int(x) F's

Submit G(√5)
Spoiler:
G(√5) ~
G2.2360679774997896964091736687313 ~
FF1.72213810979817716203568567853 ~
FE5.273975522226054773355128465 ~
F187921 = 10↑↑187921

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patzer
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Re: My number is bigger and smaller!

Postby patzer » Thu May 31, 2018 1:07 am UTC

(π^20)9
= 9↑↑π↑20
= approx. 87699567969
If it looks like a duck, and quacks like a duck, we have at least to consider the possibility that we have a small aquatic bird of the family Anatidae on our hands. –Douglas Adams

PsiSquared
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Re: My number is bigger and smaller!

Postby PsiSquared » Thu May 31, 2018 1:17 am UTC

That's not well-defined, because tetration is only defined for integer heights.

Let us just pertend that you've written int(π^20)9, which would be exactly 87699567969.

And mine:

7 in a triangle in a square, using Steinhaus-Moser notation ~ 10↑↑823543

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emlightened
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Re: My number is bigger and smaller!

Postby emlightened » Fri Jun 01, 2018 4:23 pm UTC

8 in a triangle in a square, using Steinhaus-Moser notation ~ 10↑↑16777216

"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 and smaller!

Postby PsiSquared » Sat Jun 02, 2018 6:48 pm UTC

FE6 = 10↑↑1000000

Fejfo
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Re: My number is bigger and smaller!

Postby Fejfo » Sun Jun 24, 2018 5:16 pm UTC

This wasn't between the previous two, ignore this
Last edited by Fejfo on Tue Jun 26, 2018 8:25 pm UTC, edited 1 time in total.

PsiSquared
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Re: My number is bigger and smaller!

Postby PsiSquared » Sun Jun 24, 2018 10:11 pm UTC

Huh?

Every new number has to be between the previous two. Currently, a valid entry must be between 10↑↑1000000 and 10↑↑16777216.

fω(4) ~ 10↑↑10↑↑10↑↑10↑10↑10↑21 is way too large to qualify.
And 2↑↑↑4 ~ 10↑↑65536 is abit too small.

Fejfo
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Re: My number is bigger and smaller!

Postby Fejfo » Tue Jun 26, 2018 8:26 pm UTC

It seems like I used too low of a lower bound and didn't think about how 2↑↑x and 10↑↑x relate properly. I've removed my post.

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thunk
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Re: My number is bigger and smaller!

Postby thunk » Tue Feb 19, 2019 4:20 am UTC

10^^16777215
Free markets, free movement, free plops
Blitz on, my friends Quantized, GnomeAnne, and iskinner!
troo dat

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Meowers
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Re: My number is bigger and smaller!

Postby Meowers » Wed Mar 20, 2019 9:36 pm UTC

(10^^9876543)^21

Daggoth
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Re: My number is bigger and smaller!

Postby Daggoth » Mon Mar 25, 2019 1:58 am UTC

10^^16,000,000

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Meowers
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Re: My number is bigger and smaller!

Postby Meowers » Tue Apr 02, 2019 6:53 pm UTC

10^^10000000 (or FE7 using pretty much any variant of PsiCubed2-or-whatever-his-name-is-now's letter notation)

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threetwoone
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Re: My number is bigger and smaller!

Postby threetwoone » Wed Apr 03, 2019 12:38 am UTC

10^^10^6.1
---Three Two One!---

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SuperJedi224
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Re: My number is bigger and smaller!

Postby SuperJedi224 » Wed Apr 03, 2019 1:19 am UTC

Using Hyper-E Notation:

E6#1#2=E6#1000000=E1000000#999999

PsiCubed2
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Re: My number is bigger and smaller!

Postby PsiCubed2 » Wed Apr 03, 2019 3:03 pm UTC

Meowers wrote:or FE7 using pretty much any variant of PsiCubed2-or-whatever-his-name-is-now's letter notation


I don't have any other name. I can take a hint, and do not impose myself on others. Nice to know my notation is still used, at least.

11^^11111111
(the last two entries weren't valid - the first ill-defined, the other out of range)

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Meowers
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Re: My number is bigger and smaller!

Postby Meowers » Sun Apr 07, 2019 4:07 am UTC

I thought you had recovered the password to your PsiSquared account and were using that (but now that I think about it that was quite a while ago), what hint, and I'm not sure why you thought I thought you were imposing yourself on others.

10.5^^10510510

PsiCubed2
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Re: My number is bigger and smaller!

Postby PsiCubed2 » Sun Apr 07, 2019 8:47 am UTC

Oh. I didn't realize you meant here on the XKCD forums. Sorry for the confusion.

10.5^^10510510


I was beginning to protest that this isn't well-defined, but then I realized x^^n (unlike n^^x) is well-defined for non-integer x>0 and integer n.

G(34/15) ~ 10^^11078830


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