yo'
Reputation
1,988
Next privilege 2,000 Rep.
Edit questions and answers
 Mar 2 revised Proving that $\{u_k\}_{k=1}^\infty$, $u_k=\left\{1,\frac{1}{2},\frac{1}{3},\dots,\frac{1}{k},0,0,\dots\right\}$, does not converge in a metric space added 28 characters in body Mar 2 comment Proving that $\{u_k\}_{k=1}^\infty$, $u_k=\left\{1,\frac{1}{2},\frac{1}{3},\dots,\frac{1}{k},0,0,\dots\right\}$, does not converge in a metric space @mercio That seems to be what I'm saying, and it seems to be some bullsh** at the same time. Sorry for that, I'll correct the answer. Mar 2 revised Notation for difference of two dates You can see the code for placing the thingy below. If you like it, you can use it in the other occurences. Mar 2 suggested approved edit on Notation for difference of two dates Mar 2 comment Proving that $\{u_k\}_{k=1}^\infty$, $u_k=\left\{1,\frac{1}{2},\frac{1}{3},\dots,\frac{1}{k},0,0,\dots\right\}$, does not converge in a metric space @Reveillark That's really a nit-picking. There's the metric $d$ which extends to $\ell^*$ and defines the topology. I really don't like this type of proofs. Yes, you can prove that the sequence doesn't converge "by hand". But it's much more natural to thing in general terms; find a natural way that would work for all similar sequences. Mar 2 answered Proving that $\{u_k\}_{k=1}^\infty$, $u_k=\left\{1,\frac{1}{2},\frac{1}{3},\dots,\frac{1}{k},0,0,\dots\right\}$, does not converge in a metric space Jan 28 comment Is there a notation for being “a finite subset of”? @Lehs Even though, if the fact that $A\subset B$ was particularly important and crucial for something, and not obvious at the moment in the current context, I would not hesitate much to say: "... because, from (3.14) we see that $A$ is a finite subset of $B$", or something in that manner. You are right that everything can be expressed in symbols, and it should be used as a good tool! Use symbol when appropriate, and accompany them with words when appropriate. Jan 28 awarded Nice Answer Jan 28 comment Is there a notation for being “a finite subset of”? @Lehs No notation is able to explain an important fact. Only words can. Jan 27 revised Is there a notation for being “a finite subset of”? added mathcal to P Jan 27 revised Is there a notation for being “a finite subset of”? added 28 characters in body Jan 27 suggested approved edit on Is there a notation for being “a finite subset of”? Jan 27 comment Is there a notation for being “a finite subset of”? That's soooooo set-theoretical notation! Jan 27 answered Is there a notation for being “a finite subset of”? Jan 27 comment Is there a notation for being “a finite subset of”? @SteveJessop No. $<\omega$ is not better unless you're a set theorist. As you note yourself, $|A|<\infty$ is the most standard way of writing down that $A$ is finite, if you don't like "$A$ finite". That's what I would actually prefer myself: $A\subset B,\quad A \text{ finite}$. Jan 21 comment Can you be 1/12th Cherokee? @SteveJessop I know. At the same time, it's needed to say that the coins are not $100$ but rather something like $40000$, so the mean deviation is $\sim200 = 0.5%$. I just wanted to point out that it's not $23$. On the other hand, this means that you can get very precisely $1/12$ of Cherokee genes even with 2 or 3 generations considered. However, this model is far from what people have in mind with "I'm $1/8$th Cherokee", right? Jan 21 comment Can you be 1/12th Cherokee? @SteveJessop Needed to say: There's re-combination going on, so you receive 25% of each of your grandpa's DNA. (I'm not 100% sure on this, and a biologist should rather confirm my statement. Still, this is how I understood re-combinations. Jan 18 answered Bijection between sets of ideals Jan 6 comment How to stop forgetting proofs - for a first course in Real Analysis? My favourite quote to the statistics teacher during the exam: "Excuse me, Sir, I don't remember the statement, but if you help me with it, I'll surely manage to show you the proof." Because the basic idea was that the theorem hypotheses need to be used in the proof, and that was usually enough to think out the steps. Dec 23 comment Do we really need reals? However, you can argue that computable numbers have sufficient completeness properties: Each computable sequence of computable numbers has a computable limit.