12/01/2015, 11:58 PM
@andrew
Congrats with your result.
@gottfried
The thing is solving (x_m ^ x_m)^[m] = y is only close to solving
X_n^^[n] = y ( n = m in value )
When
Y is large and n (or m) is small.
For instance x in x^x^x^x = 2000 is close to
Y in (y^y)^(y^y) = 2000.
But a in a^a^a^a = 2,718 is different from
B in (b^b)^(b^b) = 2,718.
This is logical considering the fixpoint
X^x = x
Gives x = {-1,1}.
So one method is attracted to eta and the other to 1.
For y > e that is.
For y < e its even worse.
Since we are mainly intrested in small y and Large n ... This idea seems not so practical here.
Guess it might be more usefull for the base-change .... Well Maybe ...
Regards
Tommy1729
Congrats with your result.
@gottfried
The thing is solving (x_m ^ x_m)^[m] = y is only close to solving
X_n^^[n] = y ( n = m in value )
When
Y is large and n (or m) is small.
For instance x in x^x^x^x = 2000 is close to
Y in (y^y)^(y^y) = 2000.
But a in a^a^a^a = 2,718 is different from
B in (b^b)^(b^b) = 2,718.
This is logical considering the fixpoint
X^x = x
Gives x = {-1,1}.
So one method is attracted to eta and the other to 1.
For y > e that is.
For y < e its even worse.
Since we are mainly intrested in small y and Large n ... This idea seems not so practical here.
Guess it might be more usefull for the base-change .... Well Maybe ...
Regards
Tommy1729