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Dec 3rd, 2002, 11:06 PM
#1
Thread Starter
Fanatic Member
test for convergence
i need to test for convergence for x^x^x^..., that converges to 2 when x=sqrt(2)
where at it, does anyone know how to solve for x exactly when x^x^x=2?
Massey RuleZ! ^-^__  Cheers! __^-^ Massey RuleZ!
Did you know that...
The probability that a random rational number has an even denominator is 1/3 (Salamin and Gosper 1972)? This result is independently verified by me (2002)!
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Dec 4th, 2002, 12:14 AM
#2
transcendental analytic
if x^y = x^x^x^... then y=x^x^x... and thus you can write x^2=2, x being sqrt(2)
i don't think you can solve x^x^x=2
Use  
writing software in C++ is like driving rivets into steel beam with a toothpick.
writing haskell makes your life easier:
reverse (p (6*9)) where p x|x==0=""|True=chr (48+z): p y where (y,z)=divMod x 13
To throw away OOP for low level languages is myopia, to keep OOP is hyperopia. To throw away OOP for a high level language is insight.
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Dec 4th, 2002, 07:45 AM
#3
Thread Starter
Fanatic Member
if x^y = x^x^x^... then y=x^x^x... and thus you can write x^2=2, x being sqrt(2)
that only works if x^x^x... indeed converges to 2. try this:
x^x^x^...=4
you will get x=sqrt(2) also.
Massey RuleZ! ^-^__ Cheers! __^-^ Massey RuleZ!
Did you know that...
The probability that a random rational number has an even denominator is 1/3 (Salamin and Gosper 1972)? This result is independently verified by me (2002)!
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Dec 4th, 2002, 07:14 PM
#4
transcendental analytic
yeah true, and there's isn't much else I can say, but it looks like it converges to 2, not 4 
Use
writing software in C++ is like driving rivets into steel beam with a toothpick.
writing haskell makes your life easier:
reverse (p (6*9)) where p x|x==0=""|True=chr (48+z): p y where (y,z)=divMod x 13
To throw away OOP for low level languages is myopia, to keep OOP is hyperopia. To throw away OOP for a high level language is insight.
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Dec 5th, 2002, 09:12 PM
#5
Addicted Member
Ok, this is strange...
If x^x^x...=k,
Then k^k is still x^x^x...
Then k^k=k???
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Dec 6th, 2002, 10:15 AM
#6
Thread Starter
Fanatic Member
according to the order of operations,
3^4^5^3^4^5=3^(4^(5^(3^(4^5))))
and not (3^4^5)^(3^4^5)
Massey RuleZ! ^-^__ Cheers! __^-^ Massey RuleZ!
Did you know that...
The probability that a random rational number has an even denominator is 1/3 (Salamin and Gosper 1972)? This result is independently verified by me (2002)!
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Dec 6th, 2002, 01:16 PM
#7
Addicted Member
YL says:"Few are those who see with their own eyes and feel with their own hearts."(Einstein)
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Dec 6th, 2002, 09:50 PM
#8
Addicted Member
Sprite will be the next Fermat.
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Dec 6th, 2002, 11:29 PM
#9
Thread Starter
Fanatic Member
did i mention that according to the rule i mentioned above,
if x^x^x...=k,
k^k then is not x^x^x...
Massey RuleZ! ^-^__ Cheers! __^-^ Massey RuleZ!
Did you know that...
The probability that a random rational number has an even denominator is 1/3 (Salamin and Gosper 1972)? This result is independently verified by me (2002)!
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Dec 6th, 2002, 11:32 PM
#10
Addicted Member
Yes, I assumed that from what you said.
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