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+--- Thread: A question about the asymptotes of tetration (/showthread.php?tid=625)
A question about the asymptotes of tetration - JmsNxn - 04/17/2011
I hate to be a noob, but am I allowed to conclude that since \( sexp(-2) = ln(0) = -\infty \) that tetration has poles at all negative integers excluding -1?
I think I am, but some part of me is hesitant, I'm wondering if some people argue that the log law breaks down after zero. (Though I think that would be pretty stupid.)
RE: A question about the asymptotes of tetration - tommy1729 - 04/17/2011
you meant log singularities instead of poles ? i hope
what do you mean by " break down ".
sounds like a shrink term rather than math to me
then again , tetration can drive you crazy.
RE: A question about the asymptotes of tetration - JmsNxn - 04/17/2011
(04/17/2011, 05:49 PM)tommy1729 Wrote: what do you mean by " break down ".
Yeah, I thought that sounded kind of dumb.
And yes I meant log singularities.
RE: A question about the asymptotes of tetration - mike3 - 04/17/2011
(04/17/2011, 05:06 PM)JmsNxn Wrote: I hate to be a noob, but am I allowed to conclude that since \( sexp(-2) = ln(0) = -\infty \) that tetration has poles at all negative integers excluding -1?
I think I am, but some part of me is hesitant, I'm wondering if some people argue that the log law breaks down after zero. (Though I think that would be pretty stupid.)
You would be right in concluding there are singularities, but they're not poles -- they are \( \log^n \) singularities, i.e. the first is a logarithmic singularity, the second is a "double-logarithmic" singularity, and so on. In the complex numbers, \( \mathrm{tet}(z) \) is a "multi-valued function" (this term should really be something like multi-valued relation, but this misnomer is so ingrained in tradition it's not funny), like \( \log \) itself.
RE: A question about the asymptotes of tetration - JmsNxn - 04/17/2011
(04/17/2011, 07:25 PM)mike3 Wrote:(04/17/2011, 05:06 PM)JmsNxn Wrote: I hate to be a noob, but am I allowed to conclude that since \( sexp(-2) = ln(0) = -\infty \) that tetration has poles at all negative integers excluding -1?
I think I am, but some part of me is hesitant, I'm wondering if some people argue that the log law breaks down after zero. (Though I think that would be pretty stupid.)
You would be right in concluding there are singularities, but they're not poles -- they are \( \log^n \) singularities, i.e. the first is a logarithmic singularity, the second is a "double-logarithmic" singularity, and so on. In the complex numbers, \( \mathrm{tet}(z) \) is a "multi-valued function" (this term should really be something like multi-valued relation, but this misnomer is so ingrained in tradition it's not funny), like \( \log \) itself.
Okay, alright I'll make sure to not call them poles.
