Reputation
11,027
Next privilege 15,000 Rep.
Protect questions
Badges
2 23 49
Newest
 Good Answer
Impact
~147k people reached

1d
comment How to get intuition in topology concerning the definitions?
@user153330 That's extremely generous of you. I can only hope that you've enjoyed the experience of building up reputation and that it's inspired you to keep contributing to the site.
Jan
27
answered Torus topological space
Jan
27
comment Compute explicitly a fundamental group
The OP says in the comments that they're not allowed to use the fact that fundamental group is a homotopy invariant.
Jan
26
comment Compute explicitly a fundamental group
Which book are you using?
Jan
26
comment Compute explicitly a fundamental group
Do you mean $[-1,1]$? Remember that the fundamental group is a homotopy invariant, so if two spaces are homotopy equivalent, then they have the same fundamental group.
Jan
25
comment Contrapositive - Convergence of a sequence
Do you mean the contrapositive or the negation? The contrapositive only makes sense if you explicitly formulate the definition into an if/then statement, as Alex says.
Jan
22
comment Conjecture $\sum_{n=1}^\infty\frac{(1/2)_n(-1/6)_n}{n!(2/3)_n}H_n\overset{?}={\pi\over 6}+2\sqrt{3}\ln(1+\sqrt{3})-{7\over\sqrt{3}}\ln 2-6+2\sqrt{3}$
I don't know much about the subject, but I'm curious how you cam across this possible identity. Might there not be some clues there that might help show it is true?
Jan
20
comment For any subset H in a Group G, does H necessarily share the same binary operation as G?
@Mathematicing Perhaps your book could have stated this a bit more carefully. The full statment is: if $G$ is a group and $H$ is a non-empty subset of $G$ such that $ab^{-1}$ is in $H$ for all $a,b\in H$, then $H$ is a subgroup of $G$ if we equip it with the operation inherited from $G$.
Jan
20
answered For any subset H in a Group G, does H necessarily share the same binary operation as G?
Jan
19
answered Is the power set of a set a definable set?
Jan
19
comment Homeomorphism of 2 spheres
Try computing the fundamental group of $S^2$ minus $n$ points.
Jan
15
comment How should I understand the probability space $(\Omega, \mathcal{F}, P)$? What does “hidden” mean?
To show that we can consistently define Brownian motion using measure theory, we use something called the Kolmogorov existence theorem. In this case, the $\Omega$ we end up with is the set of all functions from $[0,\infty)$ to $\mathbb R$. Each possible Brownian motion gives us such a function and the measure of a subset of $\Omega$ corresponds to the probability that we end up with that particular function.
Jan
15
revised How should I understand the probability space $(\Omega, \mathcal{F}, P)$? What does “hidden” mean?
added 5 characters in body
Jan
15
answered How should I understand the probability space $(\Omega, \mathcal{F}, P)$? What does “hidden” mean?
Jan
13
revised Can we use Atiyah-Macdonald Proposition 1.11(ii) to prove the Lagrange interpolation theorem?
added 336 characters in body
Jan
13
comment Can we use Atiyah-Macdonald Proposition 1.11(ii) to prove the Lagrange interpolation theorem?
@user218931 Ah yes, you're right. Let me rewrite the proof.
Jan
13
revised Can we use Atiyah-Macdonald Proposition 1.11(ii) to prove the Lagrange interpolation theorem?
added 336 characters in body
Jan
13
comment Can we use Atiyah-Macdonald Proposition 1.11(ii) to prove the Lagrange interpolation theorem?
@user218931 I'll add some more details to the proof so you can see how it works.
Jan
13
comment Can we use Atiyah-Macdonald Proposition 1.11(ii) to prove the Lagrange interpolation theorem?
@user218931 No, my proof is right. And I'm don't see how you're so sure that such an $x_i$ exists.
Jan
13
asked Can we use Atiyah-Macdonald Proposition 1.11(ii) to prove the Lagrange interpolation theorem?