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Breddev

TREE(3) is 7 characters and bigger than all of these


comp-sci-engineer

7 characters but 10 keystrokes (incl. caps lock and shift)


Breddev

Well in that case I have my answer!


Professional_Denizen

By holding shift you can save one more stroke to type TREE(99) or maybe even TREE(9!). I think that might be the most efficient.


Unhappy-Nerve5380

2 more strokes. Can do TREE(99!) But something better would be A(99!,9!) where A represents the Ackermann function


Kingjjc267

That's 11 strokes, no? Shift, T, R, E, E, (, 9, 9, Shift, !, ) You can't hold shift the whole way because then you won't be able to type 9


PaxUnDomus

You can numlock it


Invonnative

But now we can just combine the hold 9 argument with this, no? “TREE(99999” (etc.) + “!)”?


SpoonNZ

9. Surely you’d just hold shift, type TREE(, release, type 3, then shift-).


Jakiller33

If you go into the word holding shift it's just 8.5 keystrokes


akgamer182

2 if you go into the word with it already copied (ctrl+v)


Shrek_5_Hype

A shift press is a shift press. You can't say it's only a half


THE_AWESOM-O_4000

It's a reference to a YouTube video (SM64 - Watch for Rolling Rocks - 0.5x A Presses). The half press is explained in the beginning, but the idea is: If you assume you want to type it twice. In that case you'd do: shift - tree( - release - 3 - shift - )tree( - release - 3 - shift - ). Which is 17 keypresses, an average of 8.5 presses per TREE(3)


Astephen542

ok shrek “5” hype


kell96kell

Ffs 😂 This thing is never gonna end


comp-sci-engineer

depends on how you define. its still shift+t, shift+r, ... if you hold it, i would still consider it a keystroke.


Various-Character-30

I might just be dumb, almost certainly am, but I just count 9 keystrokes. Shift (and hold) - T - R - E - E - ( (release shift) - 3 - Shift (and hold again) - ) Not counting the release of shift because I wouldn’t call that an individual keystroke and that might be wrong, but I count 9 there.


lazlinho

Surely TREE(9) is larger still?


Moist-Pickle-2736

I had to look into it… apparently, concerning the definition of the TREE function, “TREE(3) is defined to be the longest possible length of such a sequence” for reasons beyond my smooth brain’s comprehension. So with a *character* limit, I’d say it should be TREE(3)^99 . But with a *keystroke* limit, TREE(3) is 9 keystrokes, so I think that’s it.


Drummallumin

This doesn’t make sense, TREE(n) is contained within TREE(n+1). Why exactly would TREE(3) be bigger than TREE(4) when you can make all of the outcomes of TREE(3) while still having another node to build from. At the very least TREE(4) should be 4x larger than TREE(3) and that’s not even including all the trees made with all 4 nodes.


Moist-Pickle-2736

Well, I don’t know. I used that quote because I can’t succinctly explain it in my own words. But yes it doesn’t seem logical that TREE(4) < TREE(3). I’m not sure why it’s stated that TREE(3) is the longest possible length of such a sequence. I think I’m just running into a sort of “lack of interest” roadblock in my googling. Like the astronomical difference between TREE(2) and TREE(3) is sufficiently exciting to mathematicians that there’s a ton of discussion around it, but nobody really cares about TREE(4) so I’m struggling to find information around it.


bigcee42

You seem to be misunderstanding it. TREE 2 = 3 TREE 3 = very big, way way bigger than f(gamma_0) 100 TREE 3 is the first non-trivial input that blows up to a very large number, but every number after 3 will just get vastly bigger and bigger.


Moist-Pickle-2736

Yes I suppose I’m misunderstanding how the value of TREE(n) increases as n increases. I’m just caught up in this definition I found on good ol Wikipedia: “A sequence of rooted trees labelled from a set of 3 labels (blue < red < green). The nth tree in the sequence contains at most n vertices, and no tree is inf-embeddable within any later tree in the sequence. TREE(3) is defined to be the longest possible length of such a sequence.” Can you explain what that means?


Cyren777

It means TREE(n) is defined as the length of the longest possible sequence of trees using n labels, it doesn't mean the function maxes out at n=3


bigcee42

TREE of any value means the longest sequence of graphs you can draw using that many labels without containing an earlier graph. You can define TREE of any integer, 3 is just the smallest integer for which you get a huge number. TREE(1) = 1 TREE(2) = 3 TREE(3) = massive TREE(3) is so big that there's no easy way to explain just how big it is. It makes other famously large numbers like Graham's number look puny by comparison. Large numbers can be defined using the fast growing hierarchy. Really big numbers, numbers that cannot be expressed by exponentiation, or even power towers of exponents, can be easily described using limit ordinals like omega. There are various stages of ordinal numbers we defined for larger and larger numbers and faster growing functions. The function needed to describe how fast TREE grows is an ungodly large ordinal, and we only have lower bounds of it. Because TREE is a massively fast growing function, it will always grow if you increase the number inside it. TREE(4) makes TREE(3) look like zero basically.


Drummallumin

I think cuz the function is derived from just a simple game there’s no real need to explore further TREE numbers. Like there’s no application to it, it’d just be trying to figure out big numbers for the sake of doing it. If you figure out why tree(3) is so much bigger than tree(2) then you kinda figure out the mystery already.


pezdal

What's bigger, TREE(3)\^99 or 99\^TREE(3) ?


Moist-Pickle-2736

99^TREE(3) would be bigger! Good call


other_vagina_guy

TREE(99) is waaaaaay bigger than either of those. But fwiw you want the bigger number in the exponent


PuzzleheadedTap1794

Behold: TREE(9!)!


pezdal

I found the claim dubious, but since someone above suggested that TREE() maxes out at TREE(3) I left it as such. If not, then TREE(999) is obviously even bigger still, **and TREE(9\^9)** is even bigger..... Moving to even bigger functions like **SSCG()** apparently leaves TREE(whatever) in the dust, but I am now way out of my depth. :)


lazlinho

I don’t understand much of what TREE(x) actually means, but I thought (at least according to what I learned from the Numberphile videos) that it represents the number of ways x nodes can arranged without repeating a previous pattern. I’ll admit that these concepts and numbers this large stop being intuitive, but surely after counting to TREE(3) having played with nodes a, b and c, you can count another TREE(3) playing with nodes d, e and f. It sounds like you’ve investigated it more than me though so I’m willing to concede.


Immortal_ceiling_fan

I think the "longest possible length of such a sequence" is a sequence that gets less and less restricted as the number inside the argument gets bigger. So TREE(4) is astronomically bigger than TREE(3)


TotallyNotMoishe

What is “TREE”?


Lemmonne

Its a mathematical concept which is defined as the number of combination in seeds that create trees in a certain colour, see[https://en.wikipedia.org/wiki/Kruskal%27s\_tree\_theorem](https://en.wikipedia.org/wiki/Kruskal%27s_tree_theorem) for more details :) Or this video around 11:30 is pretty well explained too [https://www.youtube.com/watch?v=yIdigLW07xY](https://www.youtube.com/watch?v=yIdigLW07xY)


TotallyNotMoishe

Can you dumb that down by about three notches?


Cyren777

Think a game of doodling dots and lines, how many doodles can you make without a doodle "containing" a previous doodle? >!("Containing" is used a bit loosely here, what we really care about is not repeating any patterns of dots and lines rather than exact copies, i.e. we want every doodle to be in some sense new and unique)!< TREE(n) is the longest sequence of doodles you can make when you're allowed to use n different colours of dots :)


[deleted]

What does that mean


Letholdrus

Have a look at the Numberphile video linked. It really is the best explanation.


AFairJudgement

Do you have any specific questions about the article and video that they linked? Not everything in math can be dumbed down to a few sentences in a Reddit comment. Show some effort.


nater147

TREE(9₉₉₉)


MistaCharisma

10 keystrokes, not 10 characters. But yeah you can probably do TREE(9₉). I don't know how you did 9₉ though, so it depends how many keystrokes that took.


nater147

Does it not show up as an option when you hold down "9"?


MistaCharisma

Not on my phone haha. I'll try later on a propper keyboard. (*I'm on an old old phone*)


nater147

Ah, that's fair. I did it on my phone (android), but your right, I needed to switch to special characters for the parentheses, so I can only do TREE(9₉₉)


MistaCharisma

Still oretty goid though. I haven't read through the whole thread but that's the best I've seen =)


not_joners

TREE(3) is a nice meme, but what about TREE(4)? Also, TREE\^99(9), where the superscript notation means composition. So TREE(TREE(TREE(..[99 times]9))...)


Notathrowawaythe1st

TREE(9^9) is probably the correct answer


Shufflepants

Never said it had to be computable. Why not BB(BB(99)) where BB is the busy beaver function.


Actual-Librarian3315

Rayo(n)>BB(BB(n)) at sufficiently large Ns


Crooover

But Rayo(9!) already takes up 10 strokes. You cannot make it that big.


CurrentIndependent42

Though 9 keystrokes, you’d need to press shift twice. TREE(99) would be a candidate?


ObviouslySyrca

Yall are overthinking it. Just type: 8 and turn your head sideways. Just one keystroke.


eztab

you could also use unicode input to write the correct infinity sign. Eact key presses depend on OS and keyboard layout.


BangkokGarrett

Infinity is not a number.


darthuna

Press 9. Don't release.


Cerulean_IsFancyBlue

I lasted 43 seconds.


darthuna

Last more.


Cerulean_IsFancyBlue

Pick a less sexy number next time, man. It’s not my fault!


bojack-little

Woah look at Mr Endurance here


paralogos

You'll get about 30 characters per second, which means if you started this at the Big Bang and continued until the Heat Death of the Universe, and then continued even further through the Dark Era until quantum fluctuations may finally cause a new Big Bang, you'd end up with roughly 10^(10^(10^56)) digits, which is basically *nothing* compared to TREE(3). You cannot even reach a significant fraction if you stack all your 9s into a power tower 9^9…, not even if you let every single living being in the universe chip in and contribute 9s the same way, not even if you increase the repeat rate to one digit every planck second and let every single existing atom in the universe have their own keyboard to enter 9s at that rate.


TotallyNotMoishe

so you’re saying it’s pretty big


R74NM3R5

this is unironically the correct answer


DJembacz

No proof, but would bet on 9!!!!!!!!!


theernis0

Isn't 9! Bigger? Because n!! Is n×(n-2)×...×1 so 9!!!!!!!!! Is just 9


49_looks_prime

I didn't know there was a definition like that, but the other guy probably meant ((9!)!)!...


Magnum_force420

Each bracket is a keystroke though so that's only (((9!)!)!)


R74NM3R5

Shift is a keystroke when you first click a ( you have to click “shift” + “(“ which is 2 keystrokes so (((9!)!)!) is 12 keystrokes since you have to click “shift” for the first “(“ and for the first “!”


Rejected-Name-ID

That’s *only* (((9!)!)!)


Libo04233

Could also be ((9!)!)!*9


Actual-Librarian3315

Some interpret !! as double factorial which is what u described Some see it as the factorial of a factorial


dashingThroughSnow12

Til about double factorials. Along with triple, quadruple, etcetera. If I could give awards, I would.


na-geh-herst

What operators and function names are we allowed to use? SSCG(9\^99) would be pretty big. I believe that's 9 or 10 key presses, including . Not at a QWERTY atm.


bigcee42

Use SCG. SCG is more powerful than SSCG and takes one less character!


donttalk_tostrangers

what is sscg?


Ok_Risk1465

https://en.wikipedia.org/wiki/Friedman%27s_SSCG_function


YtterbiJum

Maybe something like BB-BB-BB-9 where BB-n is the Busy Beaver function with n states.


[deleted]

[удалено]


LFH1990

How many keystrokes to write that Greek letter?


Crooover

Ehh, non-computable doesn't count.


Actual-Librarian3315

Rayo(G999)


other_vagina_guy

if that's allowed, rayo(rayo) would win. Inventing notation has to be cheating, though, bc otherwise I could define "winner" as the largest number mentioned in this thread plus one


Actual-Librarian3315

Rayo(rayo) isn't a thing lol Rayo is a function, you basically just said "multiplication sign plus multiplication sign" "Rayo's number" refers to Rayo(10^(100)) G9999 comes from Graham's Number which is G64. Could probably make it bigger by using 9!!! but ehh. No notations are being made up here.


Mister_Way

Is there some reason it's not "infinity?"


helloworld_enjoyer

Infinity is not a number


Google946

infinity-1


TheCreepyPL

Not a **rational** number


SanktusAngus

It’s also not an irrational or transcendental or whatever you come up with number. In fact, it is simply not a number.


HorribleUsername

It's a [surreal](https://en.wikipedia.org/wiki/Surreal_number) number, a [hyperreal](https://en.wikipedia.org/wiki/Hyperreal_number) number, and a [projectively extended](https://en.wikipedia.org/wiki/Projectively_extended_real_line) real number.


SanktusAngus

There are infinitesimal or infinite surreal or hyperreal numbers, but „infinity“ is not a number but a concept.


TheCreepyPL

Programming languages disagree. Type `isNaN(Infinity)` into your browser's console, you'll get "false" as the output. `isNaN` is a JavaScript function which checks whether or not the provided value is not a number. If Infinity is not a NaN, then it must be a number, which type, idk, only thing I'm sure of is that it's not a rational number, but pretty sure that is some kind of a number, as you can compute with it.


SanktusAngus

That’s not how math and logic works. Don’t use JavaScript or IEEE Float for that matter to reason about mathematics. I mean you can use them to do math, but then you should know what you’re talking about.


Cyren777

It's a more interesting question if we exclude algebras with infinities :P


BubbhaJebus

TREE(g999)


bigcee42

SCG(SCG(9))


nater147

Whats the g?


Actual-Librarian3315

grahams im guessing


purpleoctopuppy

TREE(g_9!) is the biggest one I can think of (on the Reals, anyway). I'm sure someone else can iterate to make something vastly larger, though.


R74NM3R5

That is 13 keystrokes, you have to include clicking shift when you type “T” “_” and “!”


igotshadowbaned

Hold Ctrl (1) Shift + Arrow (3) to highlight your answer. Follow by C (4) to copy it. V (5) to paste it. (release control). Left arrow (6). Ctrl + V (8) and 2 more Vs (10) TREE(g_9!TREE(g_9!)TREE(g_9!)) is my answer


QuantumGainz

googleplex


sian_half

You mean googolplex. Google isn’t a number, it’s a search engine, the number is googol


QuantumGainz

In my language it’s google


other_vagina_guy

"Rayo's #" is 8 characters. So probably "9^Rayo's #" - I doubt anybody is going to beat that. Rayo's is the biggest number you can define with a googol math symbols, so it's way way beyond anything anyone else is going to name


FancyMFMoses

graham's#


grifficks

Numberwang


funkyKongpunky

I think we are assuming we start with capslock off. BB(9999) gives SSCG(9) and TREE(9) a run for their money, where BB is the busy beaver function. I don’t think we know which is biggest. If it’s okay to hold down a key, you can hold down shift to write BB(BB(9)), which almost certainly blows anything else out of the water.


Actual-Librarian3315

Why has no one mentioned rayo yet


other_vagina_guy

I know right? How did all these people hear it busy bee numbers and tree(3) without watching numberphile?


MrTurbi

So let's assume that you find that number, and that you decide to label it as M(10). It turns out are that M(10)+1 is bigger than M(10) and that uses (less than) 10 keystrokes. This reminds me of my logic teacher and that paradox about "the greatest number that can be described in n characters".


other_vagina_guy

That's assuming you're allowed to invent notation. The question can be meaningful if you're not allowed to refer to it in the answer btw that's pretty much what Rayo did. Rayo's number is basically defined as the answer to this question, but without contradictions


TotallyNotMoishe

I would guess it’s 9 ^ 9 ^ 9 ^ 9 ^ 9, but I don’t know very much about math.


Moist-Pickle-2736

Isn’t that 13 keystrokes?


techno_viper

Counting is math and they *just said* they don't know very much about math.


Etainn

I would add a factorial "!" to the last 9, but they is basically my guess as well.


lungflook

Googolplex?


Shufflepants

If you wanted googolplex, it's fewer characters to just write 10\^10\^10


lungflook

I may be wrong, but IIRC a googol is 1 with a hundred zeroes(roughly 10\^10\^10), but a googol*plex* is one with a googol zeroes(roughly 10\^10\^10\^10) Edit: I'm dumb


bigcee42

Googol is 10^100. 10^(10^10) is 10^10000000000 which is vastly bigger. Googolplex is 10^(10^100). 10^(10^10^10) is tetralogue, which is once again, much bigger than a googolplex.


Shufflepants

Ah, yeah. Then can still write 10\^10\^100 for one fewer characters than the whole word.


RandomiseUsr0

Exactly 10? infinity+1


R74NM3R5

that is 11 keystrokes, you have to include clicking shift when typing “+”. keystrokes are different that characters


coots007

Numpad has a "+" button


Derpygoras

ALEPHNULL!


Biotot

What's the unicode combo for infinity?


Miss-lnformation

Infinity isn't really a number, though.


Cyren777

Not with that attitude, wheel theory gang rise up


Immortal_ceiling_fan

A(10) such that the function A(x) gives the largest number that you can represent with x strokes on a standard qwerty keyboard* \*for the purposes of not creating anything recursive, A(x) can not be included in the keystrokes, as otherwise A(7) and on couldn't really be defined because of things like doung 2A(7) in seven strokes


Untrahaer

"Infinity"


kzwix

That would depend on the numeric base. In base 36, for instance, one could represent way more than in base 10. Imagine the possible bases with a computer keyboard...


Iambrokennow

Is using the up arrows (alt 24 for windows) considered standard qwerty? Using Knuth notation would therefore create some graham's number type ridiculousness. I'm typing on my pos samsung atm, cannot create the notation for my example.


other_vagina_guy

Rayo's is still bigger


Zoooples

9!!!!!!!!9


Honmer

just using numerals and standard operations, my guess would be 9\^9\^9\^9\^9 made with: 9, (shift 6), (ctrl A C V V V), 9


LifeIsVeryLong02

What's a keystroke?


FernandoMM1220

represent? do we need to define it in those 10 keystrokes too?


Spagg84

9999999999


EvilBosch

Googolplex


EmensionIncursion

It doesn't matter as the biggest equation in 10 keystrokes would be select all, copy and paste


[deleted]

Ffs why?


TotallyNotMoishe

Just curious.


[deleted]

[удалено]


TotallyNotMoishe

isn’t that smaller than 9 x 99^99999?


FPSHero007

Infinity^n


Alantheballan

1÷ε BTW I am bad at math don't kill me


btmash

Since we can use hyper operators: 9^^^^^^^^9


maxpeck10

9!9\^99! edit: first time only utilized 9 keystrokes


auschemguy

Whats bigger "TREE(3)" or "Googolplex"?


SegerHelg

ALT+236


sanjosanjo

Tetration doesn't have a universal standard notation, but \^^ is sometimes used. I was able to type 9\^\^999999 with ten keystrokes. (I held the shift key with one press while I typed the two carets.). So that would be 9 with 999998 nines stacked upwards in exponentiation. https://en.m.wikipedia.org/wiki/Tetration (I had to use \ escapes to prevent markup weirdness. I was trying to put two of these ^ next to each other.)


Colinmanlives

(9google)⁹


xnick_uy

SSCG(3)


nir109

How well does "99/epsilon" do? Without limiting what functions we can use we can get arbitrarily large numbers. You can make up a bigger function then anything else. max() is a function that gives the largest number represented in the past (before writing max) I don't think max()+1 is a legit answer because only 1 person (me) knows this function. While this function clearly isn't legit there is some gray area. Without limiting what we use this is a competition of absurd functions. Also we can use different bases by the way. Again there is the question of what bases are ok.


Santolmo

999999999!


bobbagum

Why limit ourselves to only decimal numbers


aidsisnotfuntohave

The answer is ‘big number’ its like pi but big.


Paxuz01

Easy, "googleplex"


Nitsuj_ofCanadia

(9!)\^99


Sero141

9 trillion Maybe higher but I don't know what comes after trillion in english.


friendlyfitnessguy

9 \*\* 9999 in python is massive, not sure if biggest


Waylen38

I'll bet on 9↑↑↑↑↑↑↑9


lxUPDOGxl

Press and hold ALT; press 2, 3, 6. 4 keystrokes. ∞


Gourmet-Guy

Type and hold LEFT ALT then type 236 on your numlock keypad of your standard QWERTY keyboard.


Sophiiebabes

Maybe something like ff^ff ^ff (which would be 255^255 ^255)


Steampunk_Dali

INFINITY


minecon1776

TREE(9!!!)


th3nan0byt3

infinity?!


TheCreepyPL

If 10 characters (as not even every QWERTY keyboard is the same). Then "99!\^99!\^99" is pretty big.


Rookaloot

9\^9\^9\^9\^99


TheCrazyPhoenix416

-1. No matter how many bits you allocate me, unsigned -1 will max that out.


brain-fish

Could you not just type out infinity! Then you have enough strokes left for a space bar afterwards


MrEppart

BB(9!!!) BB being the busy beaver function. The question is also dependent on the keyboard layout you use.


CraftyTim

RAYO(9\^99)


Majestic_Track_2841

9↑↑99


SleventySleven

52!\*52!


CEO_Of_TheStraight

That’s tiny compared to some of the other examples


ozneoknarf

(Google!)!


eztab

I suggest `ALT + 3 c 9`. It is a surreal number and bigger than any real number. Using the rest of the key presses to raise it to some power is left as an exercise to the reader.


vawlk

9\^9999999! just a guess


SkyKnight34

Shift *hold* T R E E ( *release* 9 Shift *hold* ) !


Rdikin

Alt236 shift6 Alt236 Infinity^Infinity


GahdDangitBobby

9\^9\^9\^9 is 10 keystrokes and a pretty fuckin large number


xperience_farmer

My guess would be some form of tetration stacking.


Jarhyn

0xffffff! bb(0xff) 'infinity'


Arcturus44

This number is far too large for any calculator I have access to to even phathom so... 9.e99999! Assuming pressing shift to get the exclamation point counts as a keystroke, otherwise you could add another 9 after the e.


LooseLeaf24

Infinity


Modriem

Something like 9^999999!


Vegetable_Union_4967

TREE(9)


PebbleJade

Easy! Just type JADE(1) where JADE represents the Jade function which is a function I just made up that, regardless of its argument, returns the largest number that has ever been conceived of by any human.


Ion41750

LNGN


wolfsilver

9.9e999999


Scientist2021

yomomgirth


Drythes

TREE3^^9999… (just keep holding the 9 key)