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 Mar28 comment Average Frequency of 1's in an Infinite Binary Sequences Can be Anything Between 0 and 1 I was just about to post the same thing. No need for complicated formulas. Mar16 comment Denoting bijection (conjugation) in a commutative diagram @IbrahimTencer Well, in the right one, the direction is clear; the inverse would be put on left from the double arrow. Mar16 comment Idempotents and symmetries of Zn Have you ever heard about quadratic residues? Mar16 comment Confusion with a function being “onto” and 1-1 correspondence. Yes, it means that $f$ is a bijection, and this is one of the definitions of "equal in size" ;) Mar16 comment $CD+C+D=0$, show that $CD=DC$ ah damn, stupid me. Mar16 comment $CD+C+D=0$, show that $CD=DC$ Are you guaranteed that any matrix here but $I$ has an inverse? Mar12 comment Is there a word similar to “iff” meaning “one and only one”? @MarioCarneiro The question doesn't need more than 2 answers. But that may be only my point of view. Mar11 comment Is there a word similar to “iff” meaning “one and only one”? I hope I'll never meet a person willing to write "exists a unique" as $(P\oplus Q\oplus R)\land\lnot(P\land Q\land R)$. (I don't speak about computer algebra, but neither the OP is.) Mar11 comment Is there a word similar to “iff” meaning “one and only one”? Oh no! Symbols everywhere :-( Mar11 comment Is there a word similar to “iff” meaning “one and only one”? @SteveJessop No, it is not equally sensiitive. It's much easier to overlook a typo in a word than in a number. Mar11 comment Prove that the complex expression is real @CiaPan "You don't need an induction in this case" sounds to me like "the story is not complete". I don't buy this. Mar9 comment Induction - Examples where the induction step is correct but the base case is always wrong This is soooooo good! Thanks for it! It'll go in my Discrete Mathematics problem sessions! :) Mar7 comment Would you ever stop rolling the die? @luegofuego However, as I show, this is not the case, since the series behaves like $~n^2 (1-p)^n$, which is convergent. Mar2 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 @Scientifica The ping from there has reached me! :) Mar2 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. Mar2 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. Jan28 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. Jan28 comment Is there a notation for being “a finite subset of”? @Lehs No notation is able to explain an important fact. Only words can. Jan27 comment Is there a notation for being “a finite subset of”? That's soooooo set-theoretical notation! Jan27 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: $A\subset B,\quad A \text{ finite}$.