one of my earliest pcs had a lcd display showing the clock rate of the cpu. it wasn't any kind of measurement, but set by jumpers. i redid it to display my initials, which helpfully worked at the resolution of the display.
This is a proof that shows $SL_n(\Bbb R)$ is connected. During the proof, it says $\begin{pmatrix} Q & 0\\ w& 1\\ \end{pmatrix} SL_{n-1}(\Bbb R)\to (wQ^{-1})^T$ is a homeomorphism. Why this is true?
I am probably missing the point, but isn't $\begin{bmatrix} I & 0 \\ y^T & 1 \end{bmatrix}$ not an inverse of $y$? (Or rather, the equivalence class thereof.)
@robjohn why would it divide both polys of the combination?
I mean I understood that the polynomial factor with the highest degree divides GCD by definition of GCD but what shows that itself must be Gcd @robjohn
Right so call the (unique up to constant mult.) divisor polynomial which all common divisors divide MCD, clearly it is a divisor with highest possible degree, since GCD is also that, they are equal upto constant multiplication. Hence all common divisors divide GCD @robjohn I didn’t appeal to bezout
I'm trying to solve the following boundary value problem: $$\begin{cases} \Delta u =1 & \{(x,y,z)\in\Bbb R^3:1<x^2+y^2+z^2<9\}\\ u = 0 & \{(x,y,z)\in\Bbb R^3: x^2+y^2+z^2 = 1\}\\ \nabla u\cdot n = 0 & \{(x,y,z)\in\Bbb R^3:x^2+y^2+z^2 = 9\}\\ \end{cases}$$ Here, $n$ is the outward unit normal vector field on $\{(x,y,z)\in\Bbb R^3:x^2+y^2+z^2 = 9\}$. First change into spherical coordinate $u(x,y,z) = v(\rho,\phi,\theta)$. Since boundary conditions are independent of $\phi,\theta$, $v(\rho,\phi,\theta) = v(\rho)$. $\Delta v=1\iff {\partial^2 v\over \partial \rho^2}+{2\over\rho}{\partial u\over…
If $X$ is an infinite set, then the finitary alternating group on $X$ can be defined in the following equivalent ways: 1. the group of all even permutations on $X$ under composition; 2. the kernel of the sign homomorphism on the finatary symmetric group on $X$.
First, what does even permutation mean if $X$ is infinite? Second, how does one construct the homomorphism mentioned in statement 2.
Hello everyone , I have a v important question. I am sure all of you + me love mathematics a lot. I am studying for engineering. So , count physics , computer science into it too. Now , I really do love my subjects. They give me the ability to create sth , I just like it at times to do it. I have my goals as to what goals I want to achieve through studying them. One being creating a rocket ship.
My Q is that there are times while studying that u don’t feel like working , learning that subject at the moment. U feel like doing sth else. I don’t understand this part here. If was work , study is like my passion. Why do I get tired , bored of it ?
It happens sometimes that u just don’t want to study that day but rather play sport or watch a movie or talk with friends.
The problem is that it doesn’t happen when I want it happen. I don’t feel like going to play sport when time comes. I feel like going to sport just after 2-3 hours of study and have entire day left.
There are times when u study for like 8-10 hours , 5-7 hours or sometimes even nothing at all. U just don’t want to do it.
@CalvinKhor I also notice is that we like the end goal but not the process(just everyday but ok sometimes). Let’s say: do u want a body like Chris hemsworth every day. Yes. But r u ready to work for it everyday. It’s a no
do I want to be an astronaut , have a space company. Yes. But r u ready to study about how physics work around it. Not daily
the problem I am having is that: i am finding it difficult to do anything. Knowing that I would get bored of it after sometime. How to live life to fullest - I am finding it hard to manage and discipline myself
When u are studying. Why do u think get bored of your subject which is so significant to you that u want to do sth else
@CalvinKhor When u do really want to study also. U Consider ur work to be even more important than other tasks(Social media,sports,movies) for some time :) but u do consider it.
@CalvinKhor Yes , hypothetically. I get bored of all these things at max - 3days
this is a good point. people also accept a far greater level of rigor in sports instruction (they expect a coach to push them hard) that they might not accept in the math classroom.
a lot of bad math teaching amounts to boiling difficult concepts into something that gives the feeling of instant gratification, but loses something in translation.
scrolling back, it is difficult to maintain motivation at the same thing for a long period of time. and there's no one way to do it, people who are able to do it do so for different reasons.
people sometimes spend many years in therapy to discover that their reasons might not have been the best reasons.
for some people the motivation is external, they want to satisfy their relatives, or a spouse, or some imagined group of peers. wanting recognition or money isn't a bad thing if you know where the impulse is coming from and do not let it consume you.
when i worked in math, mostly i was motivated by curiosity about the subject. but there would definitely be days, sometimes weeks in the summer, where i took a vacation from caring about it.
@leslietownes I was talking about procrastination , discipline , laziness. I was trying to understand what they truly mean. So , if u want. U can scroll up and read. It will be great to continue the chat further with u
well yeah, for some people, what gets them over the procrastination is a desire for recognition. or a desire to be seen by others as hardworking. you have to have something that gets you over the line.
otherwise we'd all just sit around. if i didn't need to earn money i'd probably just play with my cat and my daughter all day. i might end up doing that anyway.
@Asinomás What I meant from it was that why do we really procrastinate ? Maybe we are not or r just tired. Maybe we are down and that’s why. Maybe ur not lazy but just don’t know how to maintain a healthy discipline and why u really get bored. What is boredom exactly ? These kind of points
@S.M.T at the moment, this is lighting the fire under me: everyone has regrets when they die. Try to make decisions so that you can choose what you regret
@CalvinKhor Lightning fire under me - I really don’t know what u mean exactly. I hope I have not upset you or made u feel sad. 2nd point of yours , We r not machines. So , there wil be some regrets but I don’t want them to big regrets. It can be like a small thing where ur business failed but I dont want to regret that I didn’t try
calvin: just the idea of choosing regrets about serial killing. you know, the good kind of regrets. not "why didn't i spend more time with my kids?" but "why did i kill all of those people."
He mostly works on is designing part - the cool part. Why? HE is the boss. It is his team because of which he is Elon musk , not him alone
@CalvinKhor Just like Steve Jobs doesn’t know each and every thing about how an apple device is made. He is mostly there for ideas , motivation and some coding
if i were advising any famous celebrity CEO i would tell them to delete their twitter account and work on not being a celebrity anymore. it has so many potential downsides. satya nadella at microsoft is doing a perfect job.
mark zuckerberg sort of gets it, except he wants to star in promotional videos. i would tell him to stop doing that.
jobs and musk and some of the others, i dunno. some upsides, many downsides.
Video games are just light flickering on a TV screen , that’s all. U can not lose in a video game. They are always made for u in that way u win
I find it incredibly depressing to work on sth like that
@CalvinKhor As of the moment , I only play is car racing game.
If I ask u , Would u like to Run on walls or fight like the guy in prince of Persia video game does OR would u rather learn his skill and use it in real life.
That’s why I don’t play video games anymore
Be the superhero in reality , not in virtuality
Which only uses is a keyboard and controller to work
I want to travel because I want to see how the world looks like. I would rather fall in love with a woman than in love with a video game
Accepting your mortality in a way that u make the best out of it is the goal here
3) What do u need to reach that level ?
Well , I need to study astrophysics. How a rocket is made. I need to exercise(To like amazing and healthy) etc
These are subjects through which the process is done
Now , what we find hard is to work on them , learn the basics
Here , u need to ask urself. Do u want to learn the process or u just like the goal but not process
If u ask me , I enjoy the process some days but I would also like to work on my other goals simultaneously
Not just one goal
Einstein didn’t have just 1 goal - studying physics. He liked communication , violin.
It was a goal too but his physics goal had was more priority
4) Why do I not enjoy the process all the time ?
@leslietownes I pray that u be more productive and achieve what u want - goals. Bye , take care
i couldn't tell if she meant, why did we pick this house, or if she meant what does it mean to own a house, or if she wanted to see our purchase contract and other documents
she's probably too young for a full explanation of secured financing
A manual of moral theology would tell you that you own a house because you bought it and therefore have a qualified ownership of it. You are free to dispose of it within the limits of any civil laws imposed upon you.
I assume you did the calculations and projected that it would be cheaper than renting
Anyways, could I get some recommendations as to how to improve the wording for my question here? There's some things that I could use some help to make perhaps clearer or more succinct: cs.stackexchange.com/questions/150790/…
Over the course of a worst case of 120 years of rent?
As you can see, I don't know how to put it more succinctly for describing that there can be no smaller value than another as the definition of "minimal".
(detailed in the part "we seek to find a common subset ...")
the nesting of quantifiers is making my head hurt, but it feels like it ought to be related to one of the 'big' problems, e.g. the exact cover problem. that's more of a vibe than a well-formed thought.
I'm more of a logician myself, but I'm now more comfortable describing things mathematically than with a bunch of paragraphs given that I lack the terminology necessary otherwise. I didn't even know what pairwise distinct meant before this question.
Huh, now that I read up on exact cover, I think that's exactly what this problem is.
I've done some informal analysis through contemplation. What I have thus far is some unproven theorem(s): the frequency of each unique digit in any column $c_x$ from a given base $n$ is inversely proportional to the logarithmic order of the associated column.
Suppose for instance I have three elements. In base three, the column associated with the order $3^1$ will have digits 0, 1, and 2 occur equally with a frequency of $\frac{1}{3^1}$
So in other words, we'll get any permutation of $[0,0,0,1,1,1,2,2,2]$.
My hope was that I'd catch a break finally and let someone else do the heavy lifting to rest my mind, but I guess thinking upon such fundamental and important concepts as these does not come so quickly and freely.
At least I'll get bragging rights kek
I'll have one of the best and most robust standard libraries in the world for Project Aquinas.
This particular algorithm I'm looking into is for making a hash map that can map anything, but efficiently, specifically a minimal perfect hashing function that maps arbitrary strings to arbitrary strings.
When I say I solve problems once, I mean once
The benefits will then trickle down to everyone else as more people adopt my project (when it becomes available)
I'm monologuing again, so I'll quickly wrap this up.
Indeed, you can get any permutation of that set, but obviously, if we allow permuting columns, the amount of unique information varies as the columns themselves vary, so we have to look at both columns and rows to determine the number of unique values present.
@Asinomás Why's that? lol. Do you even know what my project is?
It's set builder notation, and $:=$ means "is defined as"
S:={s_y|s_y=B_y} in plain English reads (so I would hope): S is defined as the set of elements $s_y$ where each $s_y$ is some object [set of objects] $B_y$.
$B_y$'s definition immediately follows that
I've done things in such a way that I can refer to different rows and columns as indices, e.g. "row 3, cols 4-9": $s_{3,4...5}$".
Yes, but they could be strings of arbitrary length since you can just make them to be the same length because of trailing or leading zeroes. The algorithm is not affected by implicit information.
