2,415 reputation
934
bio website
location Canada
age 32
visits member for 1 year, 11 months
seen 14 hours ago

I hold a diploma in Network Administration (along with many industry certifications) and am currently studying Computer Science and Pure Math in University.


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 $(n,9)=1$
Oct
28
comment What are the generators of $\mathbb{Z}_9^*$?
@coffeemath but I thought I had to take $2^4=16\equiv 7\mod{9}$
Oct
28
comment What are the generators of $\mathbb{Z}_9^*$?
Where are my errors? I've gone over this twice and I got the same thing each time.
Oct
25
comment Solve for n: $\varphi(2n)=\varphi(3n)$
@lhf Updated the math
Oct
25
comment Solve for n: $\varphi(2n)=\varphi(3n)$
@lhf I think you may be right, but I don't know how to show it... My math above used the assumption that if $(3,n)=3$, then $\varphi(3n)=\varphi(3^2n)=\varphi(3^2)\varphi(n)=3(3-1)\varphi(n)$... but now I see that I didn't factor the $3$ out of the $n$, so I should probably have $\varphi(n/3)$ instead...
Oct
24
comment Solve for n: $\varphi(2n)=\varphi(3n)$
All I was taught was that it's multiplicative.
Oct
23
comment What is an “incongruent” solution?
@labbhattacharjee Why is it not called "congruence" then, not "incongruence"?
Oct
23
comment What is an “incongruent” solution?
Does this mean that there are 11 different equivalence classes?
Oct
22
comment Let $ABC$ be a well-defined product of matrices. Suppose that $A,C$ are both invertible. Prove that $rank(ABC)=rank(B)$.
@AgustíRoig Ahh.. I think I see how I might do this, then... If $A$ and $C$ are invertible, they can be reduced to $I$... and $I$ has the same rank as $A$ and $C$. So if I have the product $I_mBI_n$, then I get $B$...
Oct
22
comment Let $ABC$ be a well-defined product of matrices. Suppose that $A,C$ are both invertible. Prove that $rank(ABC)=rank(B)$.
@AgustíRoig What do you mean? "rank" is the dimension of the column space... so if $A$ and $C$ are invertible, and $A$ is an $m\times m$ matrix, then the columns of $A$ are linearly independent, meaning the dimensions of the column space is $m$, thus the rank of $A$ is $m$... simmilarly for $C$.