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11h
comment Is a pattern proof?
No, this [post][1] contains many examples [1]: math.stackexchange.com/questions/514/…
15h
comment Prove that this set is open
@drhab - I think you should keep it, it can be interesting for future readers as it is a confusing matter
15h
comment Prove that this set is open
@drhab - It is prove! If $X=\Pi_{i=1}^{n}\mathbb{R}$ one can consider two topologies on $X$ - The product topology and the topology induced by the metric on $\mathbb{R}^{p}$. I proved that $A$ was open without relying on the fact that the two topologies on $X$ are the same since I assumed the OP does not know that
1d
comment Topology, maps, continuity
@smits - then $f^{-1}(U)$ is closed. This condition is equivalent for the continuity of $f$
2d
comment Subgroups of every order dividing the order of the group imply the group is abelian?
Thank you for your answer, Can you please rephrase or explain the theorem you are taking about "if divides the order of a group with a prime, then the group has a subgroup of order " it seems to be missing a word or two and it sounds like Cauchy theorem..
2d
comment If $f^2$ integrable, then $|f|$ is integrable?
Don't you need to know that $|f|$ (or $f$) is integrate to begin with ? The space of which this inequality is deduced is the space of integrable functions $f$
2d
comment Subgroups of every order dividing the order of the group imply the group is abelian?
@Timbuc - I see your point. But this seems to answer only (2), can you also give an example for (1) ? thanks!
2d
comment Groups with “few” subgroups
@mathmandan - Very interesting, I'll be sure to read it. thanks!
2d
comment Groups with “few” subgroups
@mathmandan - How do you know such subgroups of $T$ exist ?
2d
comment Groups with “few” subgroups
How do you know that $P$ exist ?
Apr
20
comment Finding all possible pairs of positive integer values
Because I can assume without loss of generality that x>=y (otherwise y>=x and we change their names ). I have used this in the first equation, the LHS is positive and by that assumption the RHS is also positive
Apr
19
comment Proofs shorter than the statement of the theorem
Does "this is a direct consequence of the previous theorem" counts? :-P
Apr
18
comment Combination formula?
Do you mean the number of ways arranging $n$ items ?
Apr
17
comment What would be a value of $X$ under an automorphism of $F(X)$ over $F$?
Why do you believe that $p,q$ have degree $1$ ?
Apr
11
comment Elementary proof for $\sqrt{p_{n+1}} \notin \mathbb{Q}(\sqrt{p_1}, \sqrt{p_2}, \ldots, \sqrt{p_n})$ where $p_i$ are different prime numbers.
can you explain about the existence of $a,b$ ? why does the linear combination does not include combinations of the other roots of $p_1,...,p_{n-1}$ ?
Apr
7
comment Are there any irrational numbers that have a difference of a rational number?
@Quincunx - you mean irrational numbers, not imaginary numbers
Apr
6
comment Finding the singularity type at $z=0$ of $\frac{1}{\cos(\frac{1}{z})}$
@JessePFrancis - thanks
Apr
2
comment Prove the extension to be a Galois Extension
Maybe see what are the roots of $t^{p}-x^{p}$. $x$ is a root, so $t-x\mid t^{p}-x^{p}$ so you can divide and see what are the other roots..maybe all are easily seen to be in $K$
Mar
7
comment show if a sum is uniform convergent
@toothandcup2 - that statement doesn't sound right - but probably you are misinterpreting what the lecture stated
Mar
7
comment show if a sum is uniform convergent
The first sum doesn't have an $x$ on it, and if $\zeta$ is a constant then the sum is diverges as the harmonic series does