My number is bigger and smaller!

For all your silly time-killing forum games.

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Daggoth
Posts: 52
Joined: Wed Aug 05, 2009 2:37 am UTC

My number is bigger and smaller!

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
Posts: 52
Joined: Wed Aug 05, 2009 2:37 am UTC

Re: My number is bigger and smaller!

203045

Deedlit
Posts: 91
Joined: Sun Mar 08, 2009 2:55 am UTC

Re: My number is bigger and smaller!

203045

Daggoth
Posts: 52
Joined: Wed Aug 05, 2009 2:37 am UTC

Re: My number is bigger and smaller!

203044

Deedlit
Posts: 91
Joined: Sun Mar 08, 2009 2:55 am UTC

Re: My number is bigger and smaller!

2^2^2^2^2

PsiSquared
Posts: 126
Joined: Wed May 09, 2012 6:02 pm UTC

Re: My number is bigger and smaller!

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

emlightened
Posts: 42
Joined: Sat Sep 26, 2015 9:35 pm UTC
Location: Somewhere cosy.

Re: My number is bigger and smaller!

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
Posts: 126
Joined: Wed May 09, 2012 6:02 pm UTC

Re: My number is bigger and smaller!

2↑↑↑2↑3

Daggoth
Posts: 52
Joined: Wed Aug 05, 2009 2:37 am UTC

Re: My number is bigger and smaller!

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

4↑↑7

Deedlit
Posts: 91
Joined: Sun Mar 08, 2009 2:55 am UTC

Re: My number is bigger and smaller!

5 in a pentagon using Steinhaus-Moser notation

PsiSquared
Posts: 126
Joined: Wed May 09, 2012 6:02 pm UTC

Re: My number is bigger and smaller!

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
Posts: 52
Joined: Wed Aug 05, 2009 2:37 am UTC

Re: My number is bigger and smaller!

yeah nah thats ok lets just keep on trucking as is

5↑↑↑5

PsiSquared
Posts: 126
Joined: Wed May 09, 2012 6:02 pm UTC

Re: My number is bigger and smaller!

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

Daggoth
Posts: 52
Joined: Wed Aug 05, 2009 2:37 am UTC

Re: My number is bigger and smaller!

5↑↑5↑↑5↑↑5↑5↑5↑400

PsiSquared
Posts: 126
Joined: Wed May 09, 2012 6:02 pm UTC

Re: My number is bigger and smaller!

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

emlightened
Posts: 42
Joined: Sat Sep 26, 2015 9:35 pm UTC
Location: Somewhere cosy.

Re: My number is bigger and smaller!

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
Posts: 126
Joined: Wed May 09, 2012 6:02 pm UTC

Re: My number is bigger and smaller!

2↑↑↑4 ~ F65533

Daggoth
Posts: 52
Joined: Wed Aug 05, 2009 2:37 am UTC

Re: My number is bigger and smaller!

6↑↑5↑↑4↑↑100

emlightened
Posts: 42
Joined: Sat Sep 26, 2015 9:35 pm UTC
Location: Somewhere cosy.

Re: My number is bigger and smaller!

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
Posts: 126
Joined: Wed May 09, 2012 6:02 pm UTC

Re: My number is bigger and smaller!

FE5 = 10↑↑10↑5

(can also be called "giggolgong")

emlightened
Posts: 42
Joined: Sat Sep 26, 2015 9:35 pm UTC
Location: Somewhere cosy.

Re: My number is bigger and smaller!

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
Posts: 126
Joined: Wed May 09, 2012 6:02 pm UTC

Re: My number is bigger and smaller!

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

patzer
Posts: 431
Joined: Fri Mar 30, 2012 5:48 pm UTC
Contact:

Re: My number is bigger and smaller!

(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
Posts: 126
Joined: Wed May 09, 2012 6:02 pm UTC

Re: My number is bigger and smaller!

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

emlightened
Posts: 42
Joined: Sat Sep 26, 2015 9:35 pm UTC
Location: Somewhere cosy.

Re: My number is bigger and smaller!

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
Posts: 126
Joined: Wed May 09, 2012 6:02 pm UTC

Re: My number is bigger and smaller!

FE6 = 10↑↑1000000

Fejfo
Posts: 5
Joined: Fri Mar 31, 2017 6:51 pm UTC

Re: My number is bigger and smaller!

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
Posts: 126
Joined: Wed May 09, 2012 6:02 pm UTC

Re: My number is bigger and smaller!

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
Posts: 5
Joined: Fri Mar 31, 2017 6:51 pm UTC

Re: My number is bigger and smaller!

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.

thunk
Posts: 480
Joined: Sat Apr 23, 2016 3:29 am UTC
Location: Arguably Exiled

Re: My number is bigger and smaller!

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

Meowers
Posts: 6
Joined: Wed Apr 06, 2016 1:35 am UTC

Re: My number is bigger and smaller!

(10^^9876543)^21

Daggoth
Posts: 52
Joined: Wed Aug 05, 2009 2:37 am UTC

Re: My number is bigger and smaller!

10^^16,000,000

Meowers
Posts: 6
Joined: Wed Apr 06, 2016 1:35 am UTC

Re: My number is bigger and smaller!

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

threetwoone
Posts: 19
Joined: Sun Apr 22, 2018 2:35 am UTC
Contact:

Re: My number is bigger and smaller!

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

SuperJedi224
Posts: 16
Joined: Thu Apr 16, 2015 4:19 pm UTC

Re: My number is bigger and smaller!

Using Hyper-E Notation:

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

PsiCubed2
Posts: 13
Joined: Tue Apr 02, 2019 8:55 pm UTC

Re: My number is bigger and smaller!

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)

Meowers
Posts: 6
Joined: Wed Apr 06, 2016 1:35 am UTC

Re: My number is bigger and smaller!

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
Posts: 13
Joined: Tue Apr 02, 2019 8:55 pm UTC

Re: My number is bigger and smaller!

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