What about x between the bounds ~0.066 and ~1.44? How do we know sqrt(1) and sqrt(2) are the only solutions?
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Replying to @johnnygreavu @InertialObservr
It looks like the 'infinite power tower' only converges if x is in [e^(-e), e^(1/e)] :https://math.stackexchange.com/questions/1089458/how-can-i-prove-the-convergence-of-a-power-tower …
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Replying to @AndrewM_Webb @johnnygreavu
yea! i tweeted about this a while ago!
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Lambert-W function!
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Replying to @Derektionary @InertialObservr and
Now when does z^z^z^... converge if z ∈ ℂ? ;)
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Continuing my horrible empirical approach to this problem: it looks... complicatedpic.twitter.com/omn0BHJ4Zl
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that's a neat fractal!
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I've gotten different python graphs but yours is probably more accurate. Need to check it later sometime and compare with you! How are you determining convergence and divergence? And your doing a linspace thing to get points?
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Replying to @Derektionary @AndrewM_Webb and
WAIT A MINUTE, THERE'S A NUMPY.ISFINITE??? WTF?
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Doesn’t the sequence need to be decreasing anyway for convergence?
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I don't think it decreases for complex values. Definitely could oscillate...
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Right forgot we were in the complexes..
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End of conversation
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