lentic catachresis
Reputation
5,223
Next privilege 10,000 Rep.
Access moderator tools
2 24 72
Impact
~178k people reached

# 962 Actions

 Dec 11 comment Components in the Euclidean plane? This is very similar to what is called comb space: check this out en.wikipedia.org/wiki/Comb_space Dec 11 comment Is the axiom of universes 'harmless'? @CarlMummert: Great! I'm looking forward to it :) Dec 11 revised Is there a less ad hoc way to find the degree of this extension? added 112 characters in body Dec 11 answered Is there a less ad hoc way to find the degree of this extension? Dec 10 comment Importance of Least Upper Bound Property of $\mathbb{R}$ The conclusion of Bolzano's theorem (intermediate value theorem) would be false if $\mathbb{R}$ weren't complete. Now think of all the times you say "since $f$ is a continuous function, negative here and then positive, it must be zero somewhere in the middle"! Dec 10 comment Are free modules injective? @Manos: I edited in a reference for the stated result. I recommend you learn it, it is very useful. Dec 10 revised Are free modules injective? added 229 characters in body Dec 10 answered Are free modules injective? Dec 10 awarded Benefactor Dec 10 comment Is the axiom of universes 'harmless'? This answer is very interesting as a comment: since the bounty is coming to an end, I will award it to you. I do not consider it really answers the question, as you point out in the first paragraph yourself, hence I will still leave this question without a checkmark. Dec 9 comment Is the axiom of universes 'harmless'? @Asaf: The bounty expires soon. Perhaps you have something relevant to say about this question? Dec 9 awarded Disciplined Dec 9 comment “Submissions in TeX” I think the answer to the question would depend on the journal... Why don't you ask them? Dec 8 comment Is the axiom of universes 'harmless'? ... metamathematically and heuristically about the boundaries of the consequences of this axiom. I know this may all be a bit too fuzzy; I'm sorry I can't be more precise, but I lack a more profound set theory formation to be able to formulate the question more precisely. To conclude, anything there is to be said that is related to the concerns expressed in the OP and in these comments, will surely be welcome :) Dec 8 comment Is the axiom of universes 'harmless'? @AsafKaragila: I agree the question, as stated, may be a little bit broad. Of course, we will never be able to list all consequences of the axiom of universes. However, surely some of them must be known. Now, I know that the consequences necessarily will have to do with cardinality issues, and probably a plethora of consequences are known in the realm of set theory; I ask what are the consequences outside the set theory concerned with large cardinal axioms, and what are the consequences in the rest of mathematics. More ambitiously, perhaps something can be said (continues)... Nov 26 comment Motivation behind the definition of GCD and LCM With this definition, gcd and lcm are pullback and pushout, if you see $\mathbb{Z}$ as a category where $m\to n \iff m\mid n$ (every preorder is a category in this way). See en.wikipedia.org/wiki/Pullback_(category_theory). I don't think this is why this definition is preferred, but some (such as myself) find definitions that are categorical quite satisfying. Nov 13 comment Is there any difference between a math invention and a math discovery? Nov 12 accepted A ring with IBN which admits a free module with a generator with less elements than a basis Nov 10 comment A ring with IBN which admits a free module with a generator with less elements than a basis @Mariano: Oh, I may have heard about them in Córdoba, in any case ;) A lot of things flew over my head there, unfortunately! Nov 9 comment A ring with IBN which admits a free module with a generator with less elements than a basis @t.b. There it is, in page 11! Great. As expected, the example is quite nasty :) Thank you once again, Theo. You can perfectly post is as an answer, I'll accept it if in a safe time from now no one offers another (perhaps simpler?) example.