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14h
comment Spectrum restrictions in the signature consisting of just a single binary operation
Have you got any considerations?
1d
comment Prove the set $\mathcal{O}_d := \left\{\frac{a + b\sqrt{d}}{2}:a,b \in \mathbb{Z}, a \equiv b \mod 2 \right\}$ is a ring.
@StVincent: A subring of an integral domain is trivially an integral domain.
1d
answered Prove the set $\mathcal{O}_d := \left\{\frac{a + b\sqrt{d}}{2}:a,b \in \mathbb{Z}, a \equiv b \mod 2 \right\}$ is a ring.
Apr
11
comment Interpreting $n!$ as the volume of a $1 \times 2 \cdots \times n$ box
I don't really understand. What are factorially analogous volumes? And I don't see how this is supposed to answer the question. What exactly is this supposed to illuminate? This does not even look like an answer, more like a question.
Apr
7
awarded  Nice Answer
Apr
7
comment General polynomial of degree $n$ is irreducible from Gauss' Lemma
You shouldn't use mathmode for text formatting. That is not what it's for, and it looks awful.
Apr
7
revised General polynomial of degree $n$ is irreducible from Gauss' Lemma
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Apr
7
comment Is it necessary for one to understand analysis?
@learnmore: If you want to get good suggestions, I recommend asking a separate question with a reference-request tag. I also checked: the preface to Serre's book says outright that the book was originally written for quantum chemists, which is why it is so elementary. (Though it would still be far beyond what my non-mathematician colleagues would usually do in terms of abstraction...)
Apr
7
revised Is it necessary for one to understand analysis?
added 549 characters in body
Apr
7
comment Is it necessary for one to understand analysis?
@learnmore: I don't think I can give you anything like that. Firstly because I have learned basics before I learned about connections between things, and secondly because I tend to study from my notes and only use textbooks for reference. That said, I highly recommend Serre's "Linear representations of finite groups". I've found the book very useful, and easy to read. I vaguely recall some claims that the book was written for non-mathematicians.
Apr
7
answered Is it necessary for one to understand analysis?
Apr
5
comment Why is the construction of the real numbers important?
@MarioCarneiro: Are you deeply perturbed when you read a paper that uses ZFC for its metamathematics? At some point, unfortunately, we have to take things for granted or else treat everything as hypothetical. Or restrict ourselves to ultrafinitism or something, but where's the fun in that?
Apr
5
comment When you name an element in an uncountably categorical theory…
@AlexKruckman: On the other hand, I think it follows by a pretty simple elementary chain argument once you establish $\omega$-stability (or more precisely, stability in cardinality $<\kappa$).
Apr
5
comment When you name an element in an uncountably categorical theory…
@AlexKruckman: The initial statement of the question was ambiguous there, like the second paragraph was a rewording of the whole question, which it wasn't. About the second comment, I guess you're right, it is not as trivial as I had thought.
Apr
4
asked Description of a universal regular space
Apr
4
comment When you name an element in an uncountably categorical theory…
@PrimoPetri: The second question is your "in other words", which is really quite different. The theory I mentioned has two models of cardinality $\aleph_1$ with an elementary map between them which does not extend to an isomorphism. Also, you can only name a set of constants smaller than the entire model. Otherwise, there may be no space left for a back-and-forth.
Apr
4
revised Why are $\vdash$ and $\vDash$ symbols from metalanguage?
added 970 characters in body
Apr
4
answered Why are $\vdash$ and $\vDash$ symbols from metalanguage?
Apr
4
answered When you name an element in an uncountably categorical theory…
Apr
3
answered Random graphs are not uncountably categorical