02/26/2013, 11:19 AM
(This post was last modified: 02/26/2013, 11:27 AM by Balarka Sen.)
Hi, it's me again,
I made an observation : for very small values of z, it seems likely that as b tends towards infinity, b^^z grows to infinity too, but rather slowly. I mean \( \lim_{b \rightarrow \infty} {}^{z} b \rightarrow \infty \) for all \( z > 0 \). It's quite obvious for z > 1 because tetration grows much faster than exponentiation there. So, it would sufficient to consider z on the interval [0, 1]. Questions : 1) Is it straightforward from the definition of superexponential? If not, 2) Is it true/false? I am interested in a proof for both cases of #2, however.
Also, can somebody give me a plot of sexp'(x, 0.1) where x is the base( and the plot variable of course) and 0.1 is the height. sexp' means the derivative of superexponential function. It would be much appreciated.
Balarka
.
I made an observation : for very small values of z, it seems likely that as b tends towards infinity, b^^z grows to infinity too, but rather slowly. I mean \( \lim_{b \rightarrow \infty} {}^{z} b \rightarrow \infty \) for all \( z > 0 \). It's quite obvious for z > 1 because tetration grows much faster than exponentiation there. So, it would sufficient to consider z on the interval [0, 1]. Questions : 1) Is it straightforward from the definition of superexponential? If not, 2) Is it true/false? I am interested in a proof for both cases of #2, however.
Also, can somebody give me a plot of sexp'(x, 0.1) where x is the base( and the plot variable of course) and 0.1 is the height. sexp' means the derivative of superexponential function. It would be much appreciated.
Balarka
.
