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 Dec 18 comment If $u$ is a unit in $S$, then $u$ is a unit in $R$ Just simply use $S ⊂ R$. If for some $u ∈ S$ there is some $v ∈ S$ with $uv = 1$, then – as $S ⊂ R$ – both $u$ and $v$ are also in $R$. Dec 18 answered If $u$ is a unit in $S$, then $u$ is a unit in $R$ Dec 18 comment How to explain that null $A$=(row$A$)$^\perp$? That doesn’t give you a description of the kernel of $A$ now, does it? Could be anything of the correct dimension, right? Dec 14 comment Calculate $\:\lim_\limits{ \Large_{z \to c}}\:\:{\frac{z^n - c^n}{z-c}} ~~ c,z \in \mathbb{C}\:$ without L'Hopital's rule I edited your question: I corrected the problem statement and deleted your edit where you corrected it (as is customary for corrections on this site). I also erased the 
tags before and after the math formula, for they are not needed there, and I deleted the “thanks” (as is customary for this site). Hope that’s okay. Dec 14 revised Calculate $\:\lim_\limits{ \Large_{z \to c}}\:\:{\frac{z^n - c^n}{z-c}} ~~ c,z \in \mathbb{C}\:$ without L'Hopital's rule corrected the problem statement according to the edit Dec 14 comment Find a family of open sets whose intersection is compact. Or even $∅$, right? Dec 14 comment Find a family of open sets whose intersection is compact. Well, actually, $­­­­­∅$ is compact as well, … Dec 14 comment Find a family of open sets whose intersection is compact. It is (if you use $3-1/n$ in the lower bound instead of $3+1/n$). But you can even find a more minimal example (exploiting the same idea). Dec 14 comment Are Standalone Introductory Linear Algebra Classes Bad? I don’t think this question is off-topic, but it’s definitely a soft-question, so you should use this tag. Regarding the question, maybe the author just means that a whole course on linear algebra might be unnecessarily much for a introductory course to differential equations? I can’t see why it might be bad – it surely helped me a lot with studying the basics of (linear) differental equations. Dec 12 accepted What does the theory of the empty set look like? Dec 12 comment What does the theory of the empty set look like? This is actually where the question came from – a friend and I realised that the inference rules for first order logic are inconsistent with the empty set and we were wondering if the theory of the empty set is truly an extension of first order logic. Only after asking the question we realised that the inference do preassume nonempty models. Gonna accept this one now. Dec 11 revised What does the theory of the empty set look like? added 143 characters in body Dec 11 comment What does the theory of the empty set look like? 1. Did you mean to say “$∀x∀y(x = y)$? 2. If so, if the model contains exactly one element “$∀y∀x(x = y)$” should be true as well. 3. Else, “$∀x (x = x)$” should be the axiom of reflexivity, no? Dec 11 asked What does the theory of the empty set look like? Nov 22 comment Proving that the diagram commutes In case you aren’t already on it, fixing it: You have a math processing error in your upper latex code. Nov 21 comment Why is the union of two closed sets again closed in the Scott topology? So it turns out that it’s easier to think of it as the intersection of open sets being open. Okay. Nov 21 accepted Why is the union of two closed sets again closed in the Scott topology? Nov 21 comment Why is the union of two closed sets again closed in the Scott topology? (Sorry for all the edits. I’m in a state of utter confusion right now.) Nov 21 revised Why is the union of two closed sets again closed in the Scott topology? added 63 characters in body Nov 21 revised Why is the union of two closed sets again closed in the Scott topology? added 63 characters in body