lentic catachresis
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 Sep 27 comment Why is any compact metric space the union of a countable set a subset which is a perfect space under the induced topology? Sep 19 comment Is there a more efficient method of trig mastery than rote memorization? @GiuseppeNegro: I think you should expand your comment into an full-fledged answer, expanding on your claim. I would certainly vote you up ;) Sep 16 comment free $R$-algebras: when does $R\langle X\rangle\cong\!R\langle Y\rangle$ $\Rightarrow$ $|X|\!=\!|Y|$ hold? +1 for a well-posed, motivated question. Sep 11 comment Motivation for Eisenstein Criterion @Qiaochu: In Gallian's book, he states the "Mod p irreducibility test" with an additional hypothesis, which is that the reduced polynomial mod $p$ must have the same degree as the original polynomial in $\mathbb{Z}$ for the implication "irreducible over $\mathbb{Z}_p\Rightarrow$ irreducible over $\mathbb{Q}$" to work (and it seems an important point to the proof). Why don't you require it? Can it be proven without that hypothesis? Sep 11 comment Showing $\sup \{ \sin n \mid n\in \mathbb N \} =1$ Sep 8 comment Methods to see if a polynomial is irreducible ...if $a$ is a unit. Sep 7 comment What's the index of a subfield? As a comment, I'd like to point out that using the same notation for different notions (degree of a field extension and index of a subgroup) is useful, the Galois correspondence theorem being its prime evidence. Sep 7 answered Finding $\lim\limits_{x \to \infty} \sqrt{9x^2+x} - 3x$ Sep 4 awarded Nice Question Sep 4 revised What's bad about left $\mathbb{H}$-modules? added 233 characters in body Sep 3 comment Quotient objects, their universal property and the isomorphism theorems Thank you for your answer. What about considering a category with zero morphisms and normal monomorphisms? This would cover at least the category of groups. At any rate I'm still not fully satisfied, as per your comment on your last paragraph... maybe category theory is not the right language to express what is at hand? Sep 2 revised What's bad about left $\mathbb{H}$-modules? added 307 characters in body Sep 2 comment What's bad about left $\mathbb{H}$-modules? @Soarer: In general, you can define the tensor product of two $R$-modules over a commutative ring, and get a new $R$-module. If your ring is not commutative, then the tensor product does not naturally have the structure of an $R$-module, and thus remains only as an abelian group. If you accept bimodules, you can get a module structure without the ring necessarily being commutative, see en.wikipedia.org/wiki/Tensor_product_of_modules "Additional structure". Sep 2 revised What's bad about left $\mathbb{H}$-modules? added 74 characters in body Sep 2 comment What's bad about left $\mathbb{H}$-modules? @Soarer: sure, sorry, sometimes I first post a draft of the answer and then repeatedly edit it to add more content. Sep 2 answered What's bad about left $\mathbb{H}$-modules? Sep 1 revised Quotient objects, their universal property and the isomorphism theorems added 2 characters in body; edited tags Sep 1 comment Quotient objects, their universal property and the isomorphism theorems @Noah: right. I changed $Top$ to $TVS_k$. Sep 1 revised Quotient objects, their universal property and the isomorphism theorems added 9 characters in body Aug 31 comment Quotient objects, their universal property and the isomorphism theorems @yoyo: I know what an abelian category is. What does it have to do with this? The category of groups is not abelian, for example, and all that's stated in the question applies to it.