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Time for a Math Puzzle

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Hmmmm... I can get even larger than 9^^^^^^^^^9 (incredibly larger) using more advanced concepts...
I'll see if anyone beats me first 😛

 
Originally posted by: DrPizza
Hmmmm... I can get even larger than 9^^^^^^^^^9 (incredibly larger) using more advanced concepts...
I'll see if anyone beats me first 😛
Click to expand...


8^^^^^^^^8
😉
 
Originally posted by: dullard
Originally posted by: DrPizza
9^^^^^^^^9
Click to expand...
But how does that compare to my answer:

9!!!!!!!!!

I think factorials grow faster?
Click to expand...

You'd have to understand the ^^^ notation.

3^^2 means (3^3)^3 or 3^27
3^^4 means 3^3^3^3 or 3^(3^27) or 3^7625597484987

3^^^4 means 4 copies of ...

Here, use this link: wikilink
 
Originally posted by: sao123
Originally posted by: DrPizza
Hmmmm... I can get even larger than 9^^^^^^^^^9 (incredibly larger) using more advanced concepts...
I'll see if anyone beats me first 😛
Click to expand...


8^^^^^^^^8
😉
Click to expand...

He said "numbers" 😉 Technically, infinitity isn't a number. I'm still in the lead, holding onto a notation related to a Turing machine 🙂
 
Originally posted by: DrPizza
Originally posted by: sao123
Originally posted by: DrPizza
Hmmmm... I can get even larger than 9^^^^^^^^^9 (incredibly larger) using more advanced concepts...
I'll see if anyone beats me first 😛
Click to expand...


8^^^^^^^^8
😉
Click to expand...

He said "numbers" 😉 Technically, infinitity isn't a number. I'm still in the lead, holding onto a notation related to a Turing machine 🙂
Click to expand...

Yup... numbers only... I also specified "no infinities" to that should clarify that.

Interesting concept... the ^^^ thing. never seen it before. This just gets better and better!

 
For what it's worth, even with the nested ^^^ notation, it can still be beaten by a long shot.
(Ironically, about 2 weeks ago, I read a short paper on the problem of writing the largest number possible - using notation a mathematician would understand - on the back of an index card about 2 weeks ago.)

I found something similar:
here
There's a section that deals with the halting problem and Turing machine...
But as Rado stressed, even if we can?t list the Busy Beaver numbers, they?re perfectly well-defined mathematically. If you ever challenge a friend to the biggest number contest, I suggest you write something like this:

BB(11111)?Busy Beaver shift #?1, 6, 21, etc

If your friend doesn?t know about Turing machines or anything similar, but only about, say, Ackermann numbers, then you?ll win the contest. You?ll still win even if you grant your friend a handicap, and allow him the entire lifetime of the universe to write his number. The key to the biggest number contest is a potent paradigm, and Turing?s theory of computation is potent indeed.
Click to expand...
 
Originally posted by: DrPizza
For what it's worth, even with the nested ^^^ notation, it can still be beaten by a long shot.
(Ironically, about 2 weeks ago, I read a short paper on the problem of writing the largest number possible - using notation a mathematician would understand - on the back of an index card about 2 weeks ago.)

I found something similar:
here
There's a section that deals with the halting problem and Turing machine...
But as Rado stressed, even if we can?t list the Busy Beaver numbers, they?re perfectly well-defined mathematically. If you ever challenge a friend to the biggest number contest, I suggest you write something like this:

BB(11111)?Busy Beaver shift #?1, 6, 21, etc

If your friend doesn?t know about Turing machines or anything similar, but only about, say, Ackermann numbers, then you?ll win the contest. You?ll still win even if you grant your friend a handicap, and allow him the entire lifetime of the universe to write his number. The key to the biggest number contest is a potent paradigm, and Turing?s theory of computation is potent indeed.
Click to expand...
Click to expand...

Hahahaa Turing machines... I wouldn't have thought of that.
 
Originally posted by: sao123
Originally posted by: dullard
Originally posted by: DrPizza
9^^^^^^^^9
Click to expand...
But how does that compare to my answer:

9!!!!!!!!!

I think factorials grow faster?
Click to expand...


no. exponentials grow faster.
Click to expand...


That is if it were a direct comparison of degrees, but remember for each additional ^9 you get 2 factorials.

So for reference, you get 9^9^9 which is 1.96e77
well 9! is 362,880, trying to factorial that again crashes my calculator.
For reference, 5! is only 120, yet 120! is 6.9e198
To better understand, 25000! = 5.4e99,093
And that is still only 6% the size of 9!

EDIT: Thought was first refering to the 9^9^9^9^99 suggestion:

However, going by the definition of ^^ then:
9^^9 = (9^^4)^(9^^5)
9^^5 = 6.0 e6260
9^^4 = 4.4 e695
And you get 4.4e695 ^ 6.0e6260

I don't feel like doing more research on which grows faster, but I give the edge to ^^^ if that notation is allowed.
 
That article that I linked to in the previous post is a pretty enjoyable article to read...

As I've told friends more than a few times, "I don't have time to read fictional books. There are too many enjoyable non-fiction things to read. If I want fiction, I'll get it in 2 hour hunks via the television. Why would I read Shakespeare for hours upon hours when 90% of it can be captured in 110 minutes of film?" That always bugs that English teachers 🙂 None of them have thought of a clever or witty response... they've tried "Yeah, but the style of writing..." but they're so off balance from my comment that I can usually relate whatever they say back to non-fiction. "Are you saying that non-fiction writers can't have style?" "Imagination..." "Ever try to understand a book on quantum mechanics?"
 
Originally posted by: DrPizza
Originally posted by: sao123
Originally posted by: DrPizza
Hmmmm... I can get even larger than 9^^^^^^^^^9 (incredibly larger) using more advanced concepts...
I'll see if anyone beats me first 😛
Click to expand...


8^^^^^^^^8
😉
Click to expand...

He said "numbers" 😉 Technically, infinitity isn't a number. I'm still in the lead, holding onto a notation related to a Turing machine 🙂
Click to expand...



just one more guess....
9 e 9^^^^^^9


dont know how to prove this but along this lines of thinking....
2^2 = 4
2e2 = 200
 
Originally posted by: DrPizza
For what it's worth, even with the nested ^^^ notation, it can still be beaten by a long shot.
(Ironically, about 2 weeks ago, I read a short paper on the problem of writing the largest number possible - using notation a mathematician would understand - on the back of an index card about 2 weeks ago.)

I found something similar:
here
There's a section that deals with the halting problem and Turing machine...
But as Rado stressed, even if we can?t list the Busy Beaver numbers, they?re perfectly well-defined mathematically. If you ever challenge a friend to the biggest number contest, I suggest you write something like this:

BB(11111)?Busy Beaver shift #?1, 6, 21, etc

If your friend doesn?t know about Turing machines or anything similar, but only about, say, Ackermann numbers, then you?ll win the contest. You?ll still win even if you grant your friend a handicap, and allow him the entire lifetime of the universe to write his number. The key to the biggest number contest is a potent paradigm, and Turing?s theory of computation is potent indeed.
Click to expand...
Click to expand...

fascinating read :thumbsup::thumbsup::thumbsup:
 
How the heck did you do that?? Well if you can do it that way... then it counts as 2!

That article mentioned above was quite interesting. Very nice read!
 
Originally posted by: giantpinkbunnyhead
How the heck did you do that?? Well if you can do it that way... then it counts as 2!

That article mentioned above was quite interesting. Very nice read!
Click to expand...

Charmap.
 
Originally posted by: JujuFish
Originally posted by: giantpinkbunnyhead
How the heck did you do that?? Well if you can do it that way... then it counts as 2!

That article mentioned above was quite interesting. Very nice read!
Click to expand...

Charmap.
Click to expand...

I memorized ¹, ², ³, ¼, ½, ¾, è, ®, ?, ©, and ° as I use those quite frequently. 🙂

¢ and ± are useful, but I don't have the codes memorized as I could just look those up when I need them. 😛
 
Originally posted by: JustAnAverageGuy
So

2^3 = 8 (3 chars)
2³ = 8 (2 chars)

Or is that considered cheating? 😛

¹,²,³, etc
Click to expand...

I know it's a math thread, but reading comprehension should not be checked at the door..
 
Originally posted by: Syringer
Originally posted by: JustAnAverageGuy
So

2^3 = 8 (3 chars)
2³ = 8 (2 chars)

Or is that considered cheating? 😛

¹,²,³, etc
Click to expand...

I know it's a math thread, but reading comprehension should not be checked at the door..
Click to expand...

I'm just saying, the whole carrot counting as a character thing kinda sucks 😛
 
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