tomasz
Reputation
14,797
Next privilege 15,000 Rep.
Protect questions
 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. Apr11 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. Apr7 awarded Nice Answer Apr7 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. Apr7 revised General polynomial of degree $n$ is irreducible from Gauss' Lemma deleted 8 characters in body Apr7 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...) Apr7 revised Is it necessary for one to understand analysis? added 549 characters in body Apr7 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. Apr7 answered Is it necessary for one to understand analysis? Apr5 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? Apr5 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 $<\kappa$). Apr5 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. Apr4 asked Description of a universal regular space Apr4 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. Apr4 revised Why are $\vdash$ and $\vDash$ symbols from metalanguage? added 970 characters in body Apr4 answered Why are $\vdash$ and $\vDash$ symbols from metalanguage? Apr4 answered When you name an element in an uncountably categorical theory… Apr3 answered Random graphs are not uncountably categorical