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12:49 AM
Roman numerals 8-segment display concept
mdccclxxxviii seems like a good year for that concept.
i do remember clock radios and such having various variations on the usual 8888888 lcd display thing.
You could reasonably do Chinese numerals (一二三四五六七八九 十百千万亿) on a 5x5 dot matrix
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.
i don't know how i'd do a W.
1:08 AM
looks like they ran out of ideas around ? !
I think that's ? ! @ _ * # $ % & ( ) + - / : ; < = > [ \ ] ^ ` { | } ~
really? that is $?
i sorta see it
i like how with this extremely limited space they still worked in the division sign
nobody has ever used that outside of calculator manufacturing and grades 2-6
I'm not quite sure what that thing before the pound is, or the things after the Euro
Wait, is pound on there twice?
Oh, wait, degrees Celsius and degrees Fahrenheit
1:23 AM
i assume some of those are in there just so doom will render better on whatever display
The last row and the end of the previous one is box-building stuff I guess
Unicode has a symbol, ℇ, for "Euler's constant". Wikipedia adds "It's unknown which constant this is supposed to be."
euler's identity
bernoulli's function
the gauss theorem
just unleashed a cat on a cockroach
worth every bit of cat food
1:39 AM
oh, we try to keep our cat away from them. worried about maybe the cockroach has eaten poison from somewhere outside.
she hates when we take them away.
hmmm....legit concern
she'll stalk the part of the house where she found it, like "i wish a cockroach would show up right now. let's go"
he didnt eat it tho
.......not this time anyway
we usually arrive between the killing and the eating.
cats are good.
1:41 AM
If the cockroach ate enough poison to kill a cat, it ate enough poison to kill a cockroach, I would've thought
I had a dream last night in which I was bitten by a dish-sized spider
i found mosquito coils seem to keep roaches away (not exactly a scientific experiment).
sounds right but cockroaches are hardy
yeah i think you could probably smoke them out
world war 4 will be fought between cockroaches and other cockroaches.
ai powered ones
didn't we just have a president....
1:45 AM
copper: not to my memory, no.
i meant a cockroach
he has become something of a meme
2:24 AM
thank god for air conditioning
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?
3:10 AM
it's a rational function in the matrix entries. one of those 'because we have a formula for it, it is continuous' kind of things, maybe.
3:40 AM
are you asking about the continuity or the invertibility?
3:59 AM
@copper.hat Invertibility. Continuity is easy I think
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.)
4:28 AM
@copper.hat Yea I think it's true. Inverse of $\begin{pmatrix} I & 0 \\ wQ^{-1} & 1\end{pmatrix}$ is $\begin{pmatrix} I & 0\\ -wQ^{-1} & 1\end{pmatrix}$ and $\begin{pmatrix} I & 0\\ -wQ^{-1} & 1\end{pmatrix}\begin{pmatrix} Q & 0 \\ w & 1\end{pmatrix} = \begin{pmatrix}Q & 0\\ 0 & 1\end{pmatrix}$.
4:40 AM
I was thinking more $\begin{bmatrix} I & 0 \\ wQ^{-1} & 1 \end{bmatrix} \begin{bmatrix} Q & 0 \\ 0 & 1 \end{bmatrix} = \begin{bmatrix} Q & 0 \\ w & 1 \end{bmatrix}$.
5:02 AM
Finished The Pedestrian, a fantastic puzzle platformer with stunning art and great puzzles
You control a stick figure - like the figures on bathroom signs - running across traffic signs and the like
Took me about 4 hours, spread over two days, so it's relatively short
3 hours later…
8:02 AM
Is it possible for a polynomial to divide two polynomials and be a divisor with highest degree and yet not be greatest common divisor?
No. Every common divisor divides the GCD.
Write the GCD as a combination of the two polynomials (Bezout). The common divisor will divide both polys, so it divides the combination.
8:20 AM
@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
How can a polynomial divide another of the same degree and not be the same polynomial? At most it can be a scalar multiple of other one.
You know that the product of two polynomials has the sum of the degrees?
Thus, if a polynomial of degree $n$ divides another polynomial of degree $n$, the quotient has to be degree $0$ (a constant).
@VioletFlame You said it was a common divisor.
8:35 AM
So you mean that it must be the GCD because GCD also has highest degree and so they have to be constant multiple of each other.
Am I correct @robjohn? , I thank you for your kind help.
That is sort of it, but it is more that all common divisors divide the GCD
Since the GCD is a linear combination of the two polynomials.
Isn’t that the def of GCD that all common divisors divide it >
@VioletFlame No, the GCD is the greatest common divisor. It requires some work to show that all other common divisors divide it.
8:52 AM
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
How do you show that there is a polynomial that all common divisors divide?
Yes that was my question?
I think appeal to bezout but not sure how
You need to use the Euclidean Algorithm and thus Bezout
It is the non-zero polynomial with the smallest degree that can be written as a combination of the two polynomials.
@robjohn I didn’t understand the details of how to prove existence, can you please give a short sketch?
Do you know how to use the Euclidean Algorithm to write the GCD as a linear combination of the two polynomials?
it is the smallest polynomial that can be written as a linear combination of the polynomials
9:08 AM
I know EA, but not that.
this answer uses the Extended Euclidean Algorithm to find the GCD of two polynomials.
in that case it is $1$
9:29 AM
this message shows polynomial division, but I assume you know how that works.
2 hours later…
11:39 AM
@robjohn I got it, thanks for your help.
1 hour later…
1:07 PM
I'm trying to solve the following boundary value problem:
\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\}\\
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
Did I solve correctly?
i didnt read super carefully but the idea is right @barista
why are you unsure about that step?
I found some error. Let me fix my solution
$n(x,y,z) = {1\over 3}(x,y,z)$ and $\nabla u = \left({\partial u\over\partial x},{\partial u\over\partial y},{\partial u\over\partial z}\right)$. Since ${\partial u\over\partial x} = {\partial u\over\partial \rho}{\partial\rho\over\partial x} = u_\rho {x\over \rho}$, $\nabla u = \left(u_\rho{x\over\rho},u_\rho{y\over\rho},u_\rho{z\over\rho}\right)$. Hence, $\nabla u\cdot n = 0\iff {\rho u_\rho} =0\iff \left(-{c_1\over\rho^2}+{1\over 3}\rho\right){\rho} =0$. Since $\rho = 3$, $c_1 = 9$.
This is where I used second boundary condition.
I wonder if I did it correctly.
because changed cartesian coordinate to spherical coordinate to use it
$u_\rho x/\rho$ <--- here $x$ is the vector $(x,y,z)$ right?
ah i should have read the next line
looks right to me
gradient of a radial function points in the $e_r \propto (x,y,z)$ direction
1:23 PM
1:59 PM
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.
because ur a monkey designed by Higher Management to eat fruit and swing on tree, but some snake told you how to play with fire and now we big brain
But u like it as well right. U think that this is ur passion.
But it just doesn’t work that way,,
Even if u try to sit , u won’t be able to grasp anything & end up with headache
@CalvinKhor What I have noticed is that whenever u r doing sth continuously for a long time. Same thing. U get bored.
let’s say I decide to play football everyday. After a week , I’m like I want to change the sport.
Let’s take into account - Pizza. Though it tastes good but if I try to eat it for like a whole week and nothing else. I get bored of it.
2:19 PM
why do people get bored, why are we never happy with what we have
idk m8 is that not to be human
Thnx for sharing
yw :)
@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
lol. if only every time you saw something, you could immediately ascertain the opportunity cost you would have to pay to get it!
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
2:31 PM
because im lazy, like top 1% of lazy people
But it needs to have is a definition
well, monkey brain tells me, why feel good in 5 years, when u can feel good now
Yes. It is mostly noticeable like for a student
but , think about this.
lets say u get onto watching a movie
ur monkey brain has said that watching a movie is a feel good now thing
but , u can’t watch movies ur entire life. Can u ?
u can’t search social media entire day , every second. Can u ?
Similarly , u can’t study all day
nah, but I can waste a whole day (or more...) on doing nothing useful
A day is ok. Understandable
2:37 PM
entire summer? :)
@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
Worst I have ever been
unless interrupted by hunger, tiredness, or a certain sense of duty, i can spend the rest of my life playing video games
Notice Sth here.
I have been an avid gamer. I have played for like 8 hours a day
Lets say you’re playing GTA 5. Amazing game. Now , u have finished all the levels
There are 2 things here
8 hours a day of gaming is considered a lot?
@Asinomás hahaha
2:41 PM
1) U will want to switch to a new game since all ur levels are finished now. U wont play it. Agree?
@Asinomás How much is a lot for u ?
16 hours
is a decent number I think
2) Notice. Ur point @CalvinKhor is good that u can play video games entire life. But u want to switch to a new game
Just like any other thing monkey brain does.
@Asinomás Wow. When do u sleep or eat man :)
you eat while you play
and you sleep when you don't
It is the monkey brain that tells u to study now because of ur bored of every other thing
It happens at its best after a lot of procrastination or a nice vacation
@Asinomás LEGEND. Ur my god :)
glad to hear it
2:47 PM
So , what do u think about this point
Also , study is more harder when it is mostly textbook type than visual type. Why? Instant gratification
Same concept u said at first
People are able to be disciplined at sports as a career since it is mostly an instant gratification job
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.
Exactly. Being a professional cricketer myself , I know it
i have felt it
@leslietownes nice to meet u btw
good morning or, as i suspect, evening.
yes that sounds true @S.M.T
@leslietownes What do u think about the points I have made so far now
2:55 PM
i've only read the most recent one.
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.
@leslietownes Hmm K
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
@leslietownes Exactly the point
what do you mean what they truly mean?
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.
3:02 PM
@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
greatness should not be expected
50 years ago you could be an alcoholic baker and have a family
For me , it is like if I achieve this goal. How great would be its outcome ?
That's what I like
Example: If I am playing football , my goal is to win or score goals.
@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
@S.M.T no, you misunderstood, and didnt do anything wrong
if you have a fire under you, you can't sit down :)
3:08 PM
A regret to fail after trying is ok but its not if u have not tried at all for it
U feel like to work I think is what u mean
better about what?
@CalvinKhor Sorry , not right word
no problem
calvin: "why did i do all of those killings? most of them didn't even ask for it, it wasn't fair."
Thank you for your beautiful comment @CalvinKhor
3:10 PM
@leslietownes dont bring your work home
@S.M.T yw
@leslietownes If u notice , I would be happy to make a space shuttle but not work on it like every second
@leslietownes actually im feeling rather dense i think im missing a joke
I would be happy to have written the calculus (When mathematicians were trying and failing) but maybe , I would not working on it everyday
So , we understand that we need a break from anything were doing after some time
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."
unless ur elon musk
3:13 PM
Since we like to live our life in creativity , do different things , experience different things
yikes lol @leslietownes
I don't like to experience different things or do different things
@CalvinKhor It is interesting to see how that guy works. He does take breaks. He goes to party , met gala(He was there) , SNL(TV SHOW).
He finds his work like instant gratification
He is on twitter every 3 hours
He has even gone to NBA seasons
Understand Seth really important. He does not create everything going on in his companies
p sicc
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
3:17 PM
he's mostly deceased, at present
It’s an example
i deliberately misunderstood :)
Do u guys agree with me on that ?
i think you are right in the techinical detail but i don't see your point
3:19 PM
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.
What is our goal of this entire conversation ? To always have control over our motivation in a way that u can work whenever u like
U can enjoy the process so do u fantasize about the goal
hey man if we could solve that we'd be bigger than elon musk
We can be. Always believe in yourself
trying :)
I got a scholarship of 1000 dollars from my institute
So , it is small steps. We can do it
3:22 PM
1) What is ur goal in life ? What do u want ?
I want to travel different planets
I want to create cars. I want to go into designing clothes
I want to write a song. I want to do sky diving
These are just few of mine
@CalvinKhor @leslietownes U can prepare yours
writing "a song" is easy. Writing a song you like, that's another thing
i wanted to be the greatest rapper of all time. having achieved that, i don't know what else to do.
No , its v hard to write a song depending on what u r creating
right, you can add interesting constraints, but the unconstrained problem is easy
3:25 PM
I want to create on gun violence , drug abuse , racism. Many things. That song has to be sth like people can groove to and also understand its depth
It’s poetry , I find it hard
U have to go deep in thoughts
yup thats hard
@leslietownes K
2) Why do u want it ? Would u want to play video games instead ?
MY answer: I have only 1 life. I will not live it again
I want it to be special. Video games is fun but is it your highest potential ?
Is that the only highest amount of courage in you ?
I will say no
Then , I decode video games
Video games is a fake reality. Life doesn’t work on the clicks of your keyboard , controller
but what if i get a sick hiscore
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
3:57 PM
i'll have what he's having
my daughter stumped us this morning at breakfast. she kept asking "why do we own this house?"
we could not figure out what, exactly, she wanted to know, but she was very insistent
good question hahaha
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
so that you're dry when it rains and warm in the winter wasn't good enough?
it wasn't. she somehow realized that someone must have lived in our house before we did, and also asked why they were doing that.
i really don't have answers to these deep questions
4:11 PM
Long time no see, guys!
hi AMDG. why do i own this house?
yeah, that's my reaction too.
i was hoping somebody would know
There are a number of answers. The issue is knowing the question.
yeah, we were trying to figure that out. what is it that she wanted to know? there must have been something
4:15 PM
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.
why do we own this house? why do we own this house? why do we own this house? those are only three of many alternatives in the multiverse.
why do we own this house? because it was cheaper than renting.
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/…
our mortgage payment is maybe $1000 below market rent for equivalent housing.
this may be more a reflection of inflated rents than the deal we got, but i'll take it.
looking at the question now.
4:17 PM
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 ...")
It works but I don't like how convoluted it feels
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.
What does quantifier mean in this context?
exists subset forall indices there does not exist ...
the goofy E and A
oh that lol
as you can tell, i am a logician
4:24 PM
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.
knuth is a good reference for that stuff.
and for tons of other stuff.
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.
I will never adopt your project
4:40 PM
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 a project to fix all the problems we have in information technology, mostly oriented towards us programmers and software engineers.
I am not a programmer
I am a mathematician
Do you use python for making computations, or some other form of calculator perhaps, or mathematica?
No, I use programming languages for smart people
4:44 PM
Ah, so C and assembly?
no, wolframalpha
big brain
Well, if it's software, my project is applicable. That's all you need to know, then :)
Given strings S and T find the shortest substring of S that is not a substring of T
oh nvm
I can't read your problem
$S := \left\{s_y | s_y = B_y \right\}$
Yes, an $s_y$ is a set $B_y$
S is a set
4:49 PM
oh, it should be y | s_y = B_y
How does that make sense?
I don't know
what is $s_y$ and $B_y$
They're defined...
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": $s_{3,4...5}$".
in the example algorithm we have 4 strings of the same length
that is the only input?
4:56 PM
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.
you just want to find $l\leq r$ that minimizes $r-l$ such that no pair of input strings coincide on all of $l$ to $r$ ?
What does coincide mean, please?
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