Reputation
2,940
Top tag
Next privilege 3,000 Rep.
Cast close & reopen votes
Badges
6 32 70
Impact
~288k people reached

Sep
29
comment Cubic polynomial and its discriminant
So, I suppose the graph should be read as "has complex roots" vs "has solutions". The shaded area is where there are no complex roots, but the white area does have some?
Sep
24
comment Prove that $2^n>n^4$ for all $n\geq 17$
It genuinely seems like these types of problems come easy with an inordinate amount of practice, and having knowledge of general techniques. I would have never considered many of those inequalities.
Sep
22
comment Proving that $\alpha:\mathbb{R}\to\mathbb{R}$ where $\alpha(x)=\frac{x^{3}}{x^{2}+1}$ is bijective
I'm afraid that goes way beyond my understanding at this level... I was warned by my prof that trying to find an inverse may end up being too messy, so you've just proven that for me...
Sep
22
comment Proving that $\alpha:\mathbb{R}\to\mathbb{R}$ where $\alpha(x)=\frac{x^{3}}{x^{2}+1}$ is bijective
I don't follow how you converted $x^2+xy+y^2$ as $\frac{3}{4}(x+y)^2+\frac{1}{4}(x-y)^2$
Sep
22
comment Proving that $\alpha:\mathbb{R}\to\mathbb{R}$ where $\alpha(x)=\frac{x^{3}}{x^{2}+1}$ is bijective
This seems very strange to me, claiming that it is injective under the constraint that $x=y=0$. Shouldn't $x=y$ no matter what?
Sep
21
comment Give an example of two functions $\alpha,\beta$ on a set $A$ such that $\alpha\circ\beta=\mathsf{id}_{A}$ but $\beta\circ\alpha\neq\mathsf{id}_{A}$.
I was fixated on finite sets.. this is why I was confused.
Sep
20
comment Determine whether the function $\alpha:A\times B\rightarrow B\times A$ where $\alpha((a,b))=(b,a)$ is injective and/or surjective
@SpamIAm I suppose I missed a step. I intended to say $(b,a)=(d,c)$ as these are the images of $(a,b)$ and $(c,d)$.
Sep
20
comment Prove that $(\mathbb{R}\setminus \{0\},\sim):= ab>0$ is transitive.
Ah. For whatever reason I had not considered multiplying them together. I had thought of dividing them out, but was getting nowhere that way.
Sep
19
comment Show that $A\setminus (B\setminus C)=(A\setminus B)\cup(A\cap B\cap C)$
I vaguely recall this from some years ago -- what is this property/equality/law called? I'm referring to the addition of $B$ and $\overline{B}$ to both sides of a union
Mar
3
comment How do I design a generating function to count subsets of distinct objects?
$(1+x)^{250}$ looks like it does not take into account the limitations of at most 3 per state. Given your other advice, however, I came up with $g(x)=(1+5x+10x^{2}+10x^{3})^{50}$
Dec
18
comment How does the triangle inequality work for $|x-y|$?
Yes, that's what I ended up finding. Never occured to me
Dec
17
comment How does the triangle inequality work for $|x-y|$?
Nevermind - I found a proof that shows the inequality using $|x+y|$
Dec
17
comment How does the triangle inequality work for $|x-y|$?
But my question, though, is how $||x|-|y||\leq|x+y|$? My textbook says (without proving) that $||x|-|y||\leq|x+y|\leq |x|+|y|$.
Dec
17
comment How does the triangle inequality work for $|x-y|$?
I have here that $||x|-|y||\leq|x+y|\leq |x|+|y|$... I was able to find several proofs of the "reverse triangle inequality", but they all start off with $|x-y|$ instead of $|x+y|$ like in the upper and lower bounds given. How does this proof translate from $|x|-|y|\leq |x-y|$ to $||x|-|y||\leq |x+y|$?
Nov
3
comment Finding the matrix of a linear transformation relative to two non-standard bases
@Omnomnomnom Unfortunately, all it says is what $T$ is for a given $\langle x,y,z\rangle$.
Oct
28
comment If $\mathbb{Z}_m^*$ is cyclic, and $\mathbb{Z}_m^*=\langle\overline{g}\rangle$, is $\overline{g}$ a primitive root?
@ThomasAndrews I meant to imply when it is cyclic; as in, when $m=1,2,4$, or is of the form $p^{\alpha}$ or $2p^{\alpha}$ where $p$ is an odd prime.
Oct
28
comment What are the generators of $\mathbb{Z}_9^*$?
@JyrkiLahtonen OK, then from the table alone, assuming I correct it to use multiplication instead of powers, can I find a generator from it? Or do I have to test each one individually with the method above?
Oct
28
comment What are the generators of $\mathbb{Z}_9^*$?
@JyrkiLahtonen Wouldn't that mean that every element in $\mathbb{Z}_9^*$ is a generator, save for $\overline{1}$?
Oct
28
comment What are the generators of $\mathbb{Z}_9^*$?
@JyrkiLahtonen But that seems contrary to what I was taught... but again I may have misunderstood
Oct
28
comment What are the generators of $\mathbb{Z}_9^*$?
@coffeemath notice the headers in my table. Are the headers wrong? I listed all the elements $n$ such that $(n,9)=1$