Time for a Math Puzzle

[DrPizza]

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

 

[sao123]

Originally posted by: dullard

Originally posted by: DrPizza
9^^^^^^^^9

But how does that compare to my answer:

9!!!!!!!!!

I think factorials grow faster?

no. exponentials grow faster.

 

[dullard]

Dr Pizza, were you using this notation? If so, that appears to grow faster than what I thought you originally posted.

 

[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

8^^^^^^^^8

 

[DrPizza]

Originally posted by: dullard

Originally posted by: DrPizza
9^^^^^^^^9

But how does that compare to my answer:

9!!!!!!!!!

I think factorials grow faster?

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

 

[dullard]

Originally posted by: DrPizza
Here, use this link: wikilink

Look up 2 posts. I misinterpreted your first post, and got the link myself.

 

[DaShen]

Originally posted by: dullard
Dr Pizza, were you using this notation? If so, that appears to grow faster than what I thought you originally posted.

If that is the case,

9^^^^^^^9!


******************************************

Originally posted by: dullard

Originally posted by: DrPizza
Here, use this link: wikilink

Look up 2 posts. I misinterpreted your first post, and got the link myself.

9?9?9?9?9!

 

[dullard]

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

Well, one easy way is:

F^^^^^^^^F

Using hexadecimal numbers. There are other number systems bigger, I just used a common example.

Pages and pages of advanced notations.

 

[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

8^^^^^^^^8

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

 

[giantpinkbunnyhead]

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

8^^^^^^^^8

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

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!

 

[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.

 

[DaShen]

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.

Hahahaa Turing machines... I wouldn't have thought of that.

 

[BlueFlamme]

Originally posted by: sao123

Originally posted by: dullard

Originally posted by: DrPizza
9^^^^^^^^9

But how does that compare to my answer:

9!!!!!!!!!

I think factorials grow faster?

no. exponentials grow faster.

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.

 

[DrPizza]

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?"

 

[TuxDave]

doh.. beaten

 

[sao123]

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

8^^^^^^^^8

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

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

 

[stan394]

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.

fascinating read :thumbsup::thumbsup::thumbsup:

 

[JDrake]

668*2+1

 

[JustAnAverageGuy]

So

2^3 = 8 (3 chars)
2³ = 8 (2 chars)

Or is that considered cheating?

¹,²,³, etc

 

[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!

 

[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!

Charmap.

 

[JustAnAverageGuy]

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!

Charmap.

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.

 

[Syringer]

Originally posted by: JustAnAverageGuy
So

2^3 = 8 (3 chars)
2³ = 8 (2 chars)

Or is that considered cheating?

¹,²,³, etc

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

 

[JustAnAverageGuy]

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

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

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

 

[KrazyBabaGanoush]

999!^9999!