11/27/2015, 12:36 AM
Not so much related to tetration but I just wanted to warn about limits.
Limits , induction and infinity are imho poorly used and understood.
For a simple example
1/1 + 1/4 +1/9 + 1/16 + ...
The truncated sum after n additions is
Always rational. No matter how Large n is.
However the (complete) Sum = zeta(2) = irrational.
But that is Well known.
Tommy's limit paradox
Quiz
F(1) = 1/3
F(2) = 1/3 + 1/9 + 1/27
...
Is
(-2) ^( F(oo) ) =
A) sqrt(-2) = sqrt(2) i
Most students say " Yes ofcourse ! "
B) the solution set {sqrt(2) i , - sqrt (2) i )
C) (-2)^0,499999...
D) - 2^(1/4 + 1/8 + ...)
E) - sqrt(2)
F) cant say
G) other.
Regards
Tommy1729
Limits , induction and infinity are imho poorly used and understood.
For a simple example
1/1 + 1/4 +1/9 + 1/16 + ...
The truncated sum after n additions is
Always rational. No matter how Large n is.
However the (complete) Sum = zeta(2) = irrational.
But that is Well known.
Tommy's limit paradox
Quiz
F(1) = 1/3
F(2) = 1/3 + 1/9 + 1/27
...
Is
(-2) ^( F(oo) ) =
A) sqrt(-2) = sqrt(2) i
Most students say " Yes ofcourse ! "
B) the solution set {sqrt(2) i , - sqrt (2) i )
C) (-2)^0,499999...
D) - 2^(1/4 + 1/8 + ...)
E) - sqrt(2)
F) cant say
G) other.
Regards
Tommy1729
