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9h
revised Show that $\langle\cdot,\cdot\rangle : E \times E \to \mathbb{R}$ is a continuous function
added 12 characters in body; edited title
1d
comment Are there sets of zero measure and full Hausdorff dimension?
@JulienGodawatta It is a better fit here, anyway.
2d
comment How to find the root of a polynomial function closest to the initial guess?
+1! Though, I fixed a couple typos so that it would run. Why the import of abs from math? There's a built in already.
2d
revised How to find the root of a polynomial function closest to the initial guess?
edited body
2d
revised Roots of iterations of polynomials
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2d
comment Roots of iterations of polynomials
@Watson - No problem! To answer your question, the Julia set is invariant under application of the function, so the Julia sets of $f$ and $f^n$ are identical. The Julia set of $f^n+id$ should be close, but not identical.
Feb
7
comment How do find the numerical average of $x^x$ from $(-4,-2)$?
Have you seen this answer on concerning the $x^x$ spindle? If you choose the principal branch, then you can use ordinary integration to get an average value of $0.00704628 - 0.0121195i$.
Feb
6
comment How to find Misiurewicz Points without solving huge polynomials? (Mandelbrot Set)
The parabolic and Misiurewicz points can be parametrized by the rational numbers between 0 and 1 using the idea of an external ray. The Wikipedia page provides a serviceable introduction, this paper provides a modern account, and Milnor's book is excellent as well. External rays are not hard to compute and you can use one to get close to a Misiurewicz point. I could provide more details over on Mathematica.se, if you like.
Feb
6
comment Roots of iterations of polynomials
@lhf Good point! I used that to help me improve my answer a bit.
Feb
6
revised Roots of iterations of polynomials
added 564 characters in body
Feb
6
revised Roots of iterations of polynomials
edited tags
Feb
6
answered Roots of iterations of polynomials
Feb
4
comment How many values does $\sqrt{\sqrt{i}}$ have?
@DavidC.Ullrich Thank you!
Feb
4
comment How many values does $\sqrt{\sqrt{i}}$ have?
@DavidC.Ullrich The question is tagged wolfram-alpha and expresses clear confusion over the response provided by WolframAlpha. Whether that's the main subject matter of the question or not, it's clear that an answer providing insight into the behavior provided by that specific software is, at least, germane to the discussion. I've edited my answer to indicate that my intention is to address that specific aspect. Incidentally, I personally wrote the code that generates much of the Alpha output, so I think it's safe to say that I know what I'm talking about, at least, in this context.
Feb
4
revised How many values does $\sqrt{\sqrt{i}}$ have?
added 149 characters in body
Feb
4
comment How many values does $\sqrt{\sqrt{i}}$ have?
@DavidC.Ullrich No, I am not claiming that Mathematica is the universal authority. I am answering a question about the behavior of a particular software tool, however, so I think that a proper understanding of that behavior requires an understanding of the conventions employed by that software.
Feb
4
comment How many values does $\sqrt{\sqrt{i}}$ have?
@DavidC.Ullrich As I said in my response to this same comment on my answer, the question concerns WolframAlpha's response, which is built on top of Mathematica's Sqrt function which is well known to return the principal square root.
Feb
4
comment How many values does $\sqrt{\sqrt{i}}$ have?
@DavidC.Ullrich Exactly - and that's what Mathematica's Sqrt function has returned since 1988.
Feb
4
revised How many values does $\sqrt{\sqrt{i}}$ have?
added 57 characters in body
Feb
4
comment How many values does $\sqrt{\sqrt{i}}$ have?
I must disagree with this. The square root function is perfectly well defined as a function. Have a look at my answer if you'd like to understand why Alpha responds the way that it does.