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 A question about the asymptotes of tetration JmsNxn Long Time Fellow Posts: 291 Threads: 67 Joined: Dec 2010 04/17/2011, 05:06 PM 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.) tommy1729 Ultimate Fellow Posts: 1,370 Threads: 335 Joined: Feb 2009 04/17/2011, 05:49 PM 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. JmsNxn Long Time Fellow Posts: 291 Threads: 67 Joined: Dec 2010 04/17/2011, 07:19 PM (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. mike3 Long Time Fellow Posts: 368 Threads: 44 Joined: Sep 2009 04/17/2011, 07:25 PM (This post was last modified: 04/17/2011, 07:25 PM by mike3.) (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. JmsNxn Long Time Fellow Posts: 291 Threads: 67 Joined: Dec 2010 04/17/2011, 09:17 PM (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. « Next Oldest | Next Newest »

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