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#1 2006-10-14 18:41:35

Registered: 2005-06-28
Posts: 20,909

Two special numbers

(1) 1.444667861...............
(a) This is the maximum value of xth root of x for any value of x.
(b) This number is also the maximum value such that
x^x^x^x^ infinitum is finite.
The number is eth root of e, the Natural logarithm base.
e is approximately 2.7182818284.

2. 1787109376
It is known that the square or any higher power of a number ending in 6 is always 6.
This holds good for 76, 376, 9376, etc.
The ten digit number given also has this property.
This can be continued indefinitely, and you get more and more digits.

PS:- Try searching with Google for these numbers. You'd be surprised by the result cool

It is no good to try to stop knowledge from going forward. Ignorance is never better than knowledge - Enrico Fermi. 

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#2 2006-10-15 00:16:55

Registered: 2005-06-22
Posts: 4,900

Re: Two special numbers

I remember that 2nd number! There was a topic about it a while ago.
Then further investigation revealed that there was a similar number to that, but it ended in 5.

8212890625 was the last bit. And there was the very peculiar property that if you added together the last n digits of both numbers, you always got 1000...0001, with (n-1) zeroes.

Why did the vector cross the road?
It wanted to be normal.


#3 2011-07-24 19:06:00

Registered: 2011-07-23
Posts: 16

Re: Two special numbers

I agree with (a) but I thought that x^x^x... would be infinite if x>1 because x^x^x>x^x>x, and time ^x is added the amount by which it increases also increases.


#4 2011-07-24 20:28:49

From: Bumpkinland
Registered: 2009-04-12
Posts: 104,227

Re: Two special numbers


Which is approximately


Welcome to the forum!

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
A number by itself is useful, but it is far more useful to know how accurate or certain that number is.


#5 2011-07-24 20:50:46

Real Member
From: Harlan's World
Registered: 2011-05-23
Posts: 16,015

Re: Two special numbers


actualy the value of x^x^x^x^...:
Let s=x^x^x^...
So once we can sole this equation in terms of x then we get the value of s.

“Here lies the reader who will never open this book. He is forever dead.
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.


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