1,149 reputation
1411
bio website
location
age
visits member for 3 years, 7 months
seen 53 mins ago

3h
comment Is my answer really wrong?
@user144349, that is not a triviality! Indeed, it is the entire point of the problem, and is not what I think Student was basing his/her answer on. See my previous comment here.
3h
comment Is my answer really wrong?
@Student, There originally was a comment to the effect that: "a Cauchy sequence always converges, just maybe to something outside the set." What does "outside the set" mean for a general metric space $X$? This is certainly true for Cauchy sequences in $\mathbb Q$ since you know beforehand that $\mathbb Q$ sits inside of $\mathbb R$, but why can you view a general metric space as always sitting inside of another complete one? This is the point which my comments were meant to clarify. I appreciate you taking the time to improve your answer.
7h
comment Every compact metric space is complete
Absolutely not. Given a candidate for a complete metric space, it doesn't make sense to say that "every Cauchy sequence converges, the only question is whether the limit is in the space" -- what do you mean by saying that a sequence converges if you don't yet know that the limit is in the space? I think you're confusing what happens in $\mathbb R$ with what happens for metric spaces in general.
7h
comment Every compact metric space is complete
No, that every Cauchy sequence converges is precisely the definition of "complete", so this is what you are trying to show.
7h
comment what key axioms are behind calculus
Adding to the previous comment: and the specific property of the set of real numbers which is crucial is the completeness axiom.
7h
comment Every compact metric space is complete
This is not yet correct, since you haven't yet shown that the original sequence converges. The result which you need to establish first is that if a Cauchy sequence has a convergent subsequence, then the original sequence converges.
1d
comment Calculating a double integral
Use the substitution $u = x-2y$ and $v = x+2y$.
1d
answered How would I evaluate this double integral using change of variable?
1d
comment Why this set is not a vector space?
Have you looked at the rest of the axioms for a vector space?
1d
comment Green's Theorem
Why do you think this "doesn't seem quite right"? The integral of $4x^3+4xy^2$ over the given region is indeed zero: the region is symmetric across the $y$-axis and the integrand is odd with respect to $x$.
2d
comment Completion of metric spaces
$x_n = n$ is most certainly not Cauchy with respect to the standard metric.
2d
comment Significance of an eigenvector being equal to a unit vector?
You're misusing the term "unit vector".
2d
comment What mistake am I making trying to calculate the line integral?
Your method is fine. Double check your double integral computation, in particular your bounds on $\theta$.
Apr
11
comment Calculate Matrix A from eigenvalues, but no given eigenvectors
The matrix is supposed to be non-triangular.
Apr
10
revised Notation question: What does $\langle X, - \rangle$ exactly mean?
deleted 22 characters in body
Apr
10
answered Notation question: What does $\langle X, - \rangle$ exactly mean?
Apr
9
comment What is wrong with the limits of this triple integral?
How did you come up with the bounds on $r$? The upper one is not correct. In fact, it might be simpler if you integrate with respect to $z$ on the inside instead of $r$.
Apr
6
answered Direct understanding of vector projection
Apr
6
answered Homology group of S1
Apr
6
comment Conversion to Spherical Coordinates
What do you get if you differentiate $r=\sqrt{x^2+y^2+z^2}$ with respect to $x$?