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Jan
28
comment What is the oscillation of a function?
You are missing something. Usually it is something line $\operatorname{osc}_f(x) = \inf_{\epsilon>0} \sup_{s,t \in B(x,\epsilon)} |f(t)-f(s)|$.
Jan
28
comment What is the oscillation of a function?
What is $I$? (Not a philosophical question.)
Jan
28
comment Does isometry preserve volume on open sets?
Take $h(x) = x+1$, $A=(0,1), B=(1,2)$ and $f(x) = x$, then $\int_A f = {1 \over 2}, \int_B f = {3 \over 2}$.
Jan
28
comment Does isometry preserve volume on open sets?
Is $h$ an isometry? What is the containing space. You are a little light on detail...
Jan
28
comment Does isometry preserve volume on open sets?
What is the relationship between $f,g$?
Jan
28
comment Is it a subspace or not?
Whatever works. A better take on my example would be the difference $(0,b-\bar{b},0)$, but I always figure out the best solution afterwards :-).
Jan
28
comment Is it a subspace or not?
Well, I think it is easier to guess & verify here. Choose $a=1$ and find all complex $b$s such that $b^3=1$. This will give, say, $(1,b,0)$ and $(1,\bar{b},0)$. Then see if $(2, b+\bar{b},0)$ lies in the set.
Jan
28
comment Help reading a scatterplot
Without more info. I would say that it is hard to infer much other than more lines more bugs. How do you associate a bug with a particular number of lines, how mature is the code, do the bugs arise from a particularly delicate piece of code, etc, etc. It really depends on context.
Jan
28
comment Is it a subspace or not?
The reason that the first one works is that $x \mapsto x^3$ is injective on the reals, so $a^3 = b^3$ iff $a=b$. This suggests a possible way to obtain a counterexample.
Jan
28
answered Prove that $az^n+b\overline{z}^n=0$ does not have any complex solutions except for $0$
Jan
28
comment Help reading a scatterplot
It really depends on context, but assuming this is homework, I would say that here is a strong linear relationship and the ringed point is an outlier. However, in real life, one should take a good look at outliers, especially one that is 'way off'.
Jan
28
comment Math and geometry software to create instructional videos
Your intended sarcasm is hardly concomitant with the wording of the question...
Jan
28
comment Math and geometry software to create instructional videos
Then it is a professional endeavour. And people get paid consulting fees.
Jan
28
answered Is the function complex differentiable at (0,0)?
Jan
28
comment Limits and derivatives - limit of a trigonometric function
Roughly $\sin x \approx x$ for small $x$. So you should expect $x^8$.
Jan
28
comment Math and geometry software to create instructional videos
I don't understand the 'amateur project' and 'to gain a profit'? Which is it? One is a reasonable question here, the other is a shopping suggestion which is not.
Jan
28
answered Is the rank of a matrix unaffected by congruence transformations?
Jan
28
comment Binary to Decimal Floating Point Number
Let $b_n b_{n-1} \cdots b_0$ be the binary digits (zero or one), then the number is $\sum_{k=0}^n b_k 2^k$.
Jan
28
comment Product of matrices of a linear operator and of its inverse
What does multiplication mean here? $\phi(x), \phi^{-1}(x)$ are elements of a vector space?
Jan
28
comment ${f \text{ is differentiable on } I \iff f_{\left|\ [a,b]\right.} \text{ is differentiable }\ \forall a,b \in I}$
For the other direction, note that $I = \cup_{a,b \in I} [a,b]$.