Large Numbers.

[Bullislander05]

Hey guys.  I was just reading up on large numbers, and I thought of a challenge to the tremulous community.

Who can name the largest FINITE number within 100 characters?

Here are some rules:

You may NOT use infinity.  (Hence, finite)
You may NOT write "The largest number here plus/times/whatever X."
You MAY utilize functions that are generally accepted by mathematicians.

I would prefer if these posts weren't just spamming numbers.  It also WON'T win this competition.  It is possible to write a number within 100 characters that would be larger than a number that takes up this entire page to write in simply numbers.  So no "17581367408123870912...etc..."'s.  Try to be as intuitive as possible.

I don't know what I'm going to give to the winner of the contest yet.  I'm looking for ideas.

Good luck.

[Knowitall66]

9999999(etc to 50)^99999999(etc to 50)?

Edit: Opps, forgot you could pile them up. How about 999999(etc to 25)^999999(etc to 25)^999999(etc to 25)^999999(etc to 25)

[Bullislander05]

While that IS large, it certainly is not the largest finite number that can be created within 100 characters.

[Rocinante]

99 9's and a ! ?

Probably not, since I'm sure there's a function out there that would make a set of numbers larger than that factorial.  But even calculus is now a distant memory, and I just had dinner a little while ago so the food coma is setting in.

[daenyth]

In before {graham's number; ackerman's function; busybeaver function; conway chains; knuth arrows}

[The MC Horton Crankfire]

In before {graham's number; ackerman's function; busybeaver function; conway chains; knuth arrows}

Damn, I was just about to do Graham's number. :P

[thirdstreettito]

10,000(+95 0's) It is called a Googleplex!

[Knowitall66]

Tito that's too many characters he said 100 characters (yours is 101 incase you haved realised).

[thirdstreettito]

oops

[player1]

aleph null - 2 = x

(leaves me 94 unused symbols)

cheating?

[thirdstreettito]

@player1: Huh?

[==Troy==]

lim_x->0(1/x) (its not an infinity btw  )

[Taiyo.uk]

A(g₆₄,g₆₄)

[tuple]

Code: [Select]

j = the largest number that can be represented with one hundred characters
Hey, if we can have the square root of negative one, I see nothing wrong with it!

[Eeeew Spiders]

lim_x->0(1/x)+1

[==Troy==]

lim_x->0(1/x) = lim_x->0(1/x) + constant .

You may NOT write "The largest number here plus/times/whatever X."

[thirdstreettito]

Taiyo hacked the largest number files!

[kevlarman]

clarkkkkson
wait no let's overkill it some more: clarkkkkson^clarkkkkson
hm still not enough
f(clarkkkkson!) where f(1)=1, f(2)=2^2, f(3)=3^3^3, and so on
there just right.

[khalsa]

f(clarkkkkson) where f(1)=1, f(2)=2^2, f(3)=3^3^3, and so on

f(clarkkkkson!) where f(1)=1, f(2)=2^2, f(3)=3^3^3, and so on


I would submit that, but it's a copout. If someone truly beats kev's then I'll think.


Khalsa

Edit: ZOMG kev you cheator, dont edit your submission just so I couldn't cop out! QFT ftw!

Edit Edit:

My actual submission:

BB(11111) - Busy Beaver function called on 11111, with standard BB shift of say.. 1, 5, 27 , etc.

[TheEternalDretch]

Code: [Select]

j = the largest number that can be represented with one hundred characters

WIN.

[daenyth]

10,000(+95 0's) It is called a Googleplex!

googolplex compared to some numbers already posted here is so small as to be indistinguishable from 0.

[The MC Horton Crankfire]

clarkkkkson
wait no let's overkill it some more: clarkkkkson^clarkkkkson
hm still not enough
f(clarkkkkson!) where f(1)=1, f(2)=2^2, f(3)=3^3^3, and so on
there just right.

The Clarkkkkson is just a bunch of operators piled onto each other. I don't know much about math, but I know that's not a very elegant way to do things (that, and it's a function that automatically grows with time anyway, which is cheating for this game in my book ). Mr. Graham wins this round. Or maybe tuple.

[Bullislander05]

Wow.  I didn't expect this type of turnout.  Anyways:

@Player1.  Aleph-null, while it is not infinity, is not finite.  You can't give me a number for your expression.  (or can you?  I'm not sure, but if that were the case, I'd say that that would be cheating, yes.)

Also, many of you have posted regarding topics that I do not even know myself, so there is no way for me to determine whose numbers were larger.  I DO know that Ackermann(Grahams number, Grahams number) was on xkcd and many other popular sites, so I'd say that answer, while very large is not very intuitive.  I don't believe I'd give the prize to that one.  I do not know clarkkkkson though.  I know tito is wrong.

Dae:  Is yours even an expression?  I understand that if you used those in conjunction then you will create a fantastically large number.  I do not know conway chains though.

lim_x->0(1/x) isn't infinite?  I was under the impression that it was.

I DO know Busy Beaver is an incredibly fast growing function, but alas, I cannot conclude whose answers are larger given my current knowledge.  Does anyone else who has the expertise required care to help me in the judging of this contest?

[kevlarman]

the general conclusion was that the clarkkkkson is larger than the xkcd number by itself (see this), but even if i chose a different number, f() grows fast enough that defining g(1)=f(1), g(2)=f(2)^f(2), etc (and maybe one more recursion) should be enough to beat the xkcd number (edit: on second thought it would take a bit more effort than that). but since there is no computable function that bounds busy beaver, i think khalsa wins just by choosing a sufficiently large argument.

[player1]

I know tito is wrong.

This is what is known as axiomatic. (j/k tito, <3 ;p)

It's been a quarter of a century since I took calculus and analytic geometry for 1st year electronics, so I basically pulled the aleph null thing straight outta my butt, however:

If 0, 1, 2, 3...infinity = the set of real numbers
then aleph null, representing the cardinality of that set (the number of members of the set, which includes 0) = infinity+1
aleph null minus two, therefore, equals infinity minus one, which I would consider to be finite, since it is less than infinite

[Bullislander05]

Yes, but there are properties of infinity that keep it as infinity.  You cannot take one from infinity and have infinity - 1.  You still have infinity.  A massively huge number minus 1 is still a massively huge number.  It's like trying to take apple seeds out of a zebra to plant a giraffe tree.  The only times when infinity can be reduced down to a finite number is when you have problems that involve limits when the answer is evaluated to be infinity/infinity.  Then you can take the derivative of the top and the bottom until you get something other than infinity/infinity.  Even then it doesn't work all the time.

So pretty much, infinity - 1 = infinity.

[player1]

I will defer to your collective proximity to school-agedness.

Here's a riddle for you:

What song often performed by a famous heavy metal band is actually a cover tune, said to be written by a former lover of Bob Dylan's as a sort of kiss-off/memoir?
a) name the song
b) name the heavy metal band
c) name the original artist

Extra credit:

a) The guitarist who plays on the song "A Whiter Shade of Pale" had a solo career. Name this musician, as well as his old band.

b) The guitarist who plays on the song "Incense and Peppermints" also played in a southern rock band. Name him, and both bands.

c) Before Peter Frampton joined Humble Pie, Steve Marriott said he had plans to work with another famous British musician, whose decline and subsequent death prevented such plans from reaching fruition. Name this musician, and at least three of the instruments which he played.

d) Before Motorhead, Lemmy played with another band. Name this band, and the Canadian city in which he was fired from it.

e) Rainbow was created when the singer's band opened on tour for the guitarist's band. Name the two musicians, and their former bands.

f) What famed heavy-metal guitarist played with Jethro Tull for one gig, and what was the one gig?

all google-able, so don't strain too much...

[Overdose]

I will defer to your collective proximity to school-agedness.

Here's a riddle for you:

What song often performed by a famous heavy metal band is actually a cover tune, said to be written by a former lover of Bob Dylan's as a sort of kiss-off/memoir?
a) name the song
b) name the heavy metal band
c) name the original artist

I only know of a few Bob Dylan songs, so I can't answer this one

Extra credit:

a) The guitarist who plays on the song "A Whiter Shade of Pale" had a solo career. Name this musician, as well as his old band.

Ray Royer? Procol Harum

b) The guitarist who plays on the song "Incense and Peppermints" also played in a southern rock band. Name him, and both bands.

Ed King: Strawberry Alarm Clock/Lynyrd Skynyrd

c) Before Peter Frampton joined Humble Pie, Steve Marriott said he had plans to work with another famous British musician, whose decline and subsequent death prevented such plans from reaching fruition. Name this musician, and at least three of the instruments which he played.

Not sure about this one...

d) Before Motorhead, Lemmy played with another band. Name this band, and the Canadian city in which he was fired from it.

Hawkwind; I don't know the city but I wanna say Toronto?

e) Rainbow was created when the singer's band opened on tour for the guitarist's band. Name the two musicians, and their former bands.

Ronnie James Dio/Elf and Ritchie Blackmore/Deep Purple

f) What famed heavy-metal guitarist played with Jethro Tull for one gig, and what was the one gig?

Tony Iommi on Rock'n'Roll Circus (<3 Black Sabbath)

all google-able, so don't strain too much...
I only used Google once: To try and figure out what city Lemmy got fired in.

[player1]

riddle remains unsolved

xtra cred:
a) Procol Harum is correct (Ray Royer is correct; dangit, I thought Robin Trower played guitar on that, i phail and u win)
b) all correct
c) remains unsolved
d) Hawkwind is correct, Toronto (as far as I know) is correct
e) all correct
f) all correct (me <3 Sabs 2)

when google fails u, try youtube (they never actually say the name of the city, but iirc, it's Toronto)

On Topic: Who won, the kevsternator? Riddle us a riddle, kevman.

[Menace13]

9^^...(G₆₃ up arrows)...^^9

I WIN!!!