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1d
comment Demonstrate that the two formulas for a scalar product are equivalent.
You have typeset the problem very well in my opinion, but what work have you done to prove the identity?
1d
comment Homeomorphism of a map
You might check your definitions; it appears you are thinking of compactness rather than connectedness (I think you can adapt the proof I had in mind to work with compactness as well, but it will require more effort).
1d
comment Homeomorphism of a map
Continuity is because the component functions are continuous. Bijectivity can be proven directly (if $f(x_1)=f(x_2)$, then show $x_1=x_2$ and show that given $y\in S^1$, there exists $t\in[0,2\pi)$ so that $f(t)=y$).
1d
comment Homeomorphism of a map
Demonstrating the continuity of $f$ itself is straightforward; the continuity of the inverse is a bit trickier, which is where this hint comes in handy.
1d
answered Homeomorphism of a map
1d
comment Find a Four-element Abelian Subgroup of $S_5$
I'm not sure what you mean by "compose $f$ 5x in order to get $S_5$", but if it means $f$ will generate $S_5$, that would be incorrect (because then $S_5$ would be cyclic.
1d
revised Center and angle of complex function
deleted 1 character in body
May
19
answered If $\lvert f(z)\rvert \leq e^{Re(z)}$, then $f(z) = \lambda e^z$
May
18
comment Prove or disprove $\frac{\left(2^{p}-2\right)}{p}\ \in \Bbb N, \forall\, p,\, prime$
This is essentially Fermat's Little Theorem: $2^p-2\equiv0\pmod{p}$.
May
15
comment Prove $||\lambda x_1 + (1-\lambda) x_2 - y|| \leq ||x_1 - y||$
For some intuition, try thinking of the line between $x_1$ and $x_2$ as given by $L(\lambda)=\lambda x_1+(1-\lambda)x_2$. With the condition that $\| x_1-y\|=\|x_2-y\|$, you hopefully can see how to work through it intuitively, then rigorously.
May
14
reviewed Close books about linear algebra, general algebra, analysis?
May
14
reviewed Close Linear transformation to evalute double integral
May
14
revised Evaluating limit of multi variables
minor formatting improvements
May
14
reviewed Approve Partial Fraction Problem?
May
10
comment Square root of height of a paraboloid equal to radius?
The usual formula for a paraboloid is $z=x^2+y^2$. Convince yourself the graph of this equation is the same as the one in the picture; then, in cylindrical coordinates, you have $z=r^2$.
May
7
comment About a field extension and its normal closure
If the extension were normal, it would contain all of the roots of the polynomial $x^5-2$. What are all $5$ roots for this polynomial, though? This will also give you what the normal closure ought to be in this case.
May
6
comment Evaluate the improper integral.
Unless you mis-typed $+20$ for $-20$, Daniel Fischer is right in that you have made a mistake in your calculation of the zeros of the denominator.
May
6
comment Solve $\lim_{x\to\infty}\frac{\sqrt{x-1} - \sqrt{x-2}}{\sqrt{x-2} - \sqrt{x-3}}$
+$1$ Good answer! You beat me to it :)
May
6
revised Solve $\lim_{x\to\infty}\frac{\sqrt{x-1} - \sqrt{x-2}}{\sqrt{x-2} - \sqrt{x-3}}$
added 6 characters in body
May
3
answered Why is $O(n^{km}+n^m)=O(n^{km})$?