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A question about the asymptotes of tetration
#1
I hate to be a noob, but am I allowed to conclude that since 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.)
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#2
you meant log singularities instead of poles ? i hope Smile

what do you mean by " break down ".

sounds like a shrink term rather than math to me Smile

then again , tetration can drive you crazy.
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#3
(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.
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#4
(04/17/2011, 05:06 PM)JmsNxn Wrote: I hate to be a noob, but am I allowed to conclude that since 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 singularities, i.e. the first is a logarithmic singularity, the second is a "double-logarithmic" singularity, and so on. In the complex numbers, 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 itself.
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#5
(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 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 singularities, i.e. the first is a logarithmic singularity, the second is a "double-logarithmic" singularity, and so on. In the complex numbers, 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 itself.

Okay, alright I'll make sure to not call them poles. Tongue
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