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1d
comment Show that $x\otimes x+2\otimes2$ is not an elementary tensor in $I\otimes_{A}I$
This has been asked before: math.stackexchange.com/questions/823642/…
1d
comment Galois group of a polynomial and subfields
Find an example or show there are no examples. Use Galois theory to think about properties of such an example as in (b) in terms of group theory.
1d
comment Proving uniqueness of $e$
This argument assumes that the definition of $f(a)$ makes sense, i.e., that $\lim_{h \rightarrow 0} (a^h - 1)/h$ exists in the first place.
1d
revised Polynomials over $\mathbb{F}_2$ without multiplicity 1 factors
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1d
answered Polynomials over $\mathbb{F}_2$ without multiplicity 1 factors
1d
comment If the commutator of a finite group has order $2$, then the order of the group is divisible by $8$
See Qiaochu Yuan's answer (currently it is number 6) at mathoverflow.net/questions/23478/….
2d
comment Quotient field of gaussian Integers
Yes. And the term is equivalence classes, not equivalent classes.
2d
revised Measure Theory Problems
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2d
comment Quotient field of gaussian Integers
Your definition of the quotient field as pairs $[a,b]$ subject to a certain equivalence relation has nothing to do with $a$ and $b$ being integers. It works the same if they are Gaussian integers, or elements of any integral domain at all.
Nov
20
comment Undergraduate Research Ideas?
Oh, transform theory, not transformation theory.
Nov
20
revised What is the meaning of “Hermitian”?
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Nov
20
comment Undergraduate Research Ideas?
While the previous comment is on the mark, I am curious: what exactly is "Transformation Theory"? Every other course title looks familiar, but not that one.
Nov
20
comment A question in Abstract Algebra about cosets
The left or right cosets of a subgroup are not themselves always groups, so I changed your post to speak of a set of cosets, not a group of cosets. Also, learn how to spell the word coset.
Nov
20
revised A question in Abstract Algebra about cosets
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Nov
20
comment Evaluate $\int_0^1 \frac{x^k-1}{\ln x}dx $ using high school techniques
IdrisAddou, asking for solutions that include justification of analytic manipulations like swapping the order of summation or integration is going beyond the pre-university level. The posted solution using differentiation under the integral sign includes no justification for why that method fits this application, and to do so would go beyond the level of high school. To some extent a certain amount of "handwaving" in the derivations should be allowable at the level at which you are asking the question.
Nov
20
comment Evaluate $\int_0^1 \frac{x^k-1}{\ln x}dx $ using high school techniques
The question is not written in antagonistic way, so the sense that it "demands" something seems out of line. Yes, it asks if a problem can be solved without using certain methods, and why is that so terrible? It is not unreasonable to ask if a problem understandable at a certain level can also be solved at that level, e.g., the Gaussian integral evaluation from probability without using a double integral or methods of complex analysis, as the result itself can be appreciated before someone knows such techniques. In summary, I disagree that this question deserves to be closed.
Nov
20
comment Evaluate $\int_0^1 \frac{x^k-1}{\ln x}dx $ using high school techniques
@Integrator: IdrisAddou explained that the interest was in seeing a new way to solve the problem, where "new" means not previously known to the OP. I had already seen the power series method of Adhvaitha before, but evidently IdrisAddou had not, so it counts as new.
Nov
20
comment Evaluate $\int_0^1 \frac{x^k-1}{\ln x}dx $ using high school techniques
FYI, the "Leibniz Integral Rule" is precisely the method of differentiation under the integral sign, which was explicitly disallowed in the question.
Nov
20
comment Evaluate $\int_0^1 \frac{x^k-1}{\ln x}dx $ using high school techniques
This derivation is only valid for $-1 < k < 1$, and perhaps also at $k = 1$ if you are careful, but the result itself is true for all $k > -1$. So this is not a complete explanation. To be fair, though, the original question was vague about the range of $k$ for which the equality was desired.
Nov
19
comment Lower bound on numbers in “extension” to Lagrange four square theorem
Thank you giving me a chance to correct the writing of Shakespeare. Never thought I would be able to do that. :)