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May
1
comment Assigning values to divergent series
I wonder why the downvote.
Mar
28
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.
Mar
16
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.
Mar
16
comment Idempotents and symmetries of Zn
Have you ever heard about quadratic residues?
Mar
16
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" ;)
Mar
16
comment $CD+C+D=0$, show that $CD=DC$
ah damn, stupid me.
Mar
16
comment $CD+C+D=0$, show that $CD=DC$
Are you guaranteed that any matrix here but $I$ has an inverse?
Mar
12
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.
Mar
11
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.)
Mar
11
comment Is there a word similar to “iff” meaning “one and only one”?
Oh no! Symbols everywhere :-(
Mar
11
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.
Mar
11
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.
Mar
9
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! :)
Mar
7
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.
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
@Scientifica The ping from there has reached me! :)
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
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.
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
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
comment Is there a notation for being “a finite subset of”?
That's soooooo set-theoretical notation!