#serious-discussion
1 messages · Page 142 of 1
so one might think its better to start with known examples and then have students notice more esoteric behavior from that
ring are a pretty good playground for this
Oh
you have this entire zoo of rings with increasingly "less nice" structure
and you could introduce them one by one
and students can notice this structure via examples themselves and actually play with it
I guess that could play out nicer
groups seems simpler but computations in them are actually more esoteric than multiplying and adding polynomials
Certainly since group is more abstract, in that they are usually something which acts on spaces
Not a generalization of numbers
personally by the time I started looking at groups, I already was familiar with like, matrices and some of the matrix groups
so it just seemed to make sense i guess
Opinion: High school should continue to teach matrices
It gives taste of noncommutative cases, showing that world is not nice even with math
its also worth noting that historically the abstract definition of a ring is older than of a group
yes, (permutation) groups were already studied previously but not in an abstract setting
the field of abstract algebra really started with the invention of ideals and then soon modern ring theory followed
Interesting
What would you cover in an intro abstract algebra course starting with rings? @surreal sapphire
check out aluffi's Algebra: Notes from the Underground for some inspiration

what high school is this about
yeah, i would probably follow that book, at least roughly
what isMAtrices why do we need to study this
pretty general question, cant really be answered like that
you can read the wikipedia article on matrices
they're important because they can encode important data about many different mathematical objects
and at the same time they are very easy to compute with
any high school
@visual breach, bold of you to assume that every country even starts discussing matrices
Hence what I said: High school should
you said "continue"
thereby assuming that they did it earlier, worldwide
My bad, wording error
High schools should teach matrices
is that what you meant?
Yep
can i spam ?
40 years ago or so, they even taught the type of linear algebra you'd do in the first semester here
Did you at least read the rule
"they" is who, "the type" is what and "first semester" is when
no (yeah i know i cannot)
Then do that, read the rules
- German high schools (atleast in my Bundesland/region)
- not only gaussian elimination that we still have, but actually rings, fields, ..., vector spaces, dimension, base, ...
- First 6 months of the first year at uni
I wonder what high school you're learning under
Though this was 40 years ago, as I said
It's no longer like this
My teacher had it like this
Must've been great
their high school better start at 19 years of age
Also, my teacher had set theory in elementary school (venn diagrams, cardinals, ...), this was some experiment or something 40 years ago and it has been discontinued
Apparently they decided it's too abstract for elementary schoolers
I really need to know for what age these schools started
high school was from grade 5 to 13, now from grade 5 to 12
ζ(s) = 1 + 1/2s + 1/3s + 1/4s + …
Oops
Wrong
Simplify the following algebraic expressions. A) -2x + 5 + 10x - 9. B) 3(x + 7) + 2(-x + 4) + 5x
I need help
With mah homework
Wait
and the corresponding years of age for typical students?
grade 12 is around 18
Lmao what
Nani
Maybe it is true that mankind's intelligence is on downtrend
Common sense isn't really common
I have to be clarified what school definitions are being used
Wait there is grade 13?
There was, yes
By high school, I mean the one you go to before university
Assuming uni at 19
Now it's to grade 12
Oh it got debunked in 2020
But some school districts in Oregon offer a grade 13
And in Canada grade 13 was replaced with OAC for students starting high school Grade 9 in 1984
so last stage before undergraduate, got it
New message!!
huh
is there a way to keep track of the sig figs in binary?
what do you mean by that exactly?
binary number system
there are different levels at which you can "keep track of significant figures" and it also depends on what you mean by "in binary"
by definition every rational number can be represented in binary given enough bits
i am learning about conversion from binary to hexadecimal (in digital electronics)
i learned that for the fractional part of the binary number, we need to add trailing zeroes in order to make convertible into a hexadecimal
for example 0.1000010 is the fractional part of a binary number
fractional part of a binary number?
numbers in binary system don't have decimal representation, they're integers
by definition the number in decimal system can be converted to it's binary representation by counting the amount of powers of two that make up that number
yeah
and placing 0 and 1 in proper places
yeah
numbers of the form 100101101 are all integers, there's no such thing as fractional part
there is
this is why i'm asking
like 0.1 in binary is 0.5 in decimal
it's a one in the place holder of 2^-1
so, we get 1/2
thus 0.5
you can just assign 1 in proper position if the number has 2^{-1} in it
repeat the same thing for 2^{-2}, 2^{-3}, etc
yup!
but my question is different
it's about conversion from binary to hexadecimals
surely that doesn't require using any of that fractional business, it's just regular binary to hexadecimal conversion of integer to hexadecimal number
no, i think my question may seem stupid, but it is valid considering the method adopted to convert binary numbers to hexadecimal numbers
hexadecimals are used to conveniently represent binary numbers
for the integral part of binary numbers, we group them in sizes of 4 from right to left
Integers or rationals?
integers
Or irrationals I suppose, but that’s just turning it from a power series in one to a power series in the other
Euclidean division
for example 10001010 would be 8A in hexadecimal
Your decimal number is actually a “polynomial” but with x = 10
?
$\sum_{n = 0}^{N}{b_n * 10^n} = x$
i didn't understand
Mizalign
oh okay
I am on mobile right now, let me grab my computer to type this out easier
Actually btw this is why polynomial division is like long division, because numbers in base 10 are kind of like polynomials
i am actually more interested in the problem i posed in the beginning
yeah
Gimme a second
back
just to be clear, this is not an exact mathematical translation of a binary number to hexadecimal numbers
it's the way it's taught in digital electronics
I mean the algorithm can be done in arbitrary bases, but it's nice because 2 divides 16 (many times actually)
So if you have your binary representation, like 10001010, we know that 16 = 2^4, so we can break it into blocks of 4 digits, or pad it to a multiple of 4
(1000)(1010)
oh!!
so, this is an exact translation
this is quite literally the standard conversion from binary to hexadecimal
i had a belief this is wasn't the case
to do the reverse, you just take a hexidecimal number, like 8AF, and reverse it into (1000)(1010)(1111) aka 100010101111
what did you mean when you said keep track of significant figures in binary?
yeah
Sig figs are in respect to the base, usually, and it's kind of how many digits your mantissa in your "scientific notion" has
so what about when the number is such that there's an incomplete group
I.e floating point doubles have 53 significant figures in respect to base 2
we add zeroes right?
yes
That works because our base is a power of the other base
this works if we had like ternary (base 3) and like, base 27
same principle
0.(01011)(0000)
the dot doesn't change the fact that the number is still being interpreted as a regular binary number
dot == zero?
it's a matter of convention how you mark where the bit related to 2^0 is
you might not even mark it or put a bar or any other symbol
It's because any real number in base N is:
$\sum_{n = -\infty}^{m}{c_n N^n}$ where $c_n \in {0... N-1}$
So we can break it into blocks
observe that we added zeroes here
Mizalign
that's when i started thinking about the loss of the actual number of sig figs in the original number
significant figures are NOT conserved between base conversions, usually
but because 16 is a power of 2, you can kind of take your sig figs of binary, and divide it by 4 and round down, or up
your choice
idk if there is a standard for it
Since you're essentially breaking up your binary number of the form x.xxxxxxx * 2^P
you're welcome lol
you made me realize basically floating point doubles have explicitly 53 sig figs as there are 52 bits for the mantissa, plus the 1
i don't what i did but i'll take the credit
Double-precision floating-point format (sometimes called FP64 or float64) is a floating-point number format, usually occupying 64 bits in computer memory; it represents a wide dynamic range of numeric values by using a floating radix point.
Double precision may be chosen when the range or precision of single precision would be insufficient.
In t...
People with imposter syndrome HATE this trick!
oh this is good
🤝
I mean I didn't consider sig figs in different bases before
yeah got it! just had a look at the wiki
Hello
hello
Yeah but I wouldn’t understand the transiston from rings to groups
how is it better then to start with groups
i would motivate groups by just looking at groups of units in number rings 
just motivate groups by going
"you like symmetries right? you won't after this course"
then start with definitions immediately after
uh tbh though
i think i would struggle more with rings first
because rings are similar enough to something familiar
that i would probably be more prone to making assumptions that aren't actually true
groups from 0 is like almost forgetting everything you know
which is hard
but once you do it i think its good for you
the thing here is that its very easy to notice that some things arent true
bcs you know how to compute with polynomials
with groups its kinda weird bcs an intro group class has a lot of "meaningless symbol pushing"
its also very easy imo to build a ring that behaves in a certain way
say you want a ring that isnt an integral domain, you just take Z or wtv and build Z[x,y]/(xy)
this is very intuitive because you add 2 new elements that are zero divisors
say you want a ring that isnt a ufd, what do you do?
||Z[x,y,z,w]/(xy-zw)||
you add some elements and build 2 factorizations that agree
this gives you infinitely many examples and also teaches you how to build objects that behave in a way you want
and at the same time its very easy to do computations in those objects
This is the 2nd time this has come up recently and I honestly wasn’t aware that people found basic groups conceptually challenging, I didn’t and to the best of my knowledge, most people in my intro group theory course didn’t either (it was bundled in with analysis 1 and everyone found the groups side of the course far easier, group actions were like the hardest part to grasp maybe?)
I feel like rings first would be a lot from the start, like starting with abelian groups and monoids (obviously you don’t have to use those words) and for polynomials you then have equivalence classes and stuff to worry about, but if you start with groups, everyone knows permutations and symmetries and matrices (obviously nxn matrices also form rings and vector spaces but still)
I’d be interested to see a rings first approach though, but I just don’t really see how that way would be easier conceptually
pls tell whats 2+2
My issue is that even if rings are very familiar, the "special kinds of rings" are a lot more confusing
$suc(suc(\emptyset)) + suc(suc(\emptyset))$
we is typing, they
this is your first post in the server? is there a reason you joined this server just to post dumb stuff?
STOP being mean
stop feeding trolls.
I'm feeding them knowledge
I would actually propose that one teaches abelian groups first
Yeah while rings have a lot of nice properties, like modular arithmetic is easy, but people don’t describe them as a zoo for no reason, stuff like zero divisors and the lack of inverses can just feel weird for people
They will be like "what's suc" then start a career in number thoery resarch
Because then you can learn quotients without having to worry about normality / ideals
in my mind everyone taking algebra did a year of linear algebra first which introduces groups and rings first (but doesnt really do much with them)
this includes basic math stuff like equivalence relations
To me the one benefit of teaching rings before groups is that ideals are more inuitive IMO than normal subgroups
my algebra class also did basic constructions (quotients mostly) for both at the same time
I would agree with that
I actually immediately dont think i like this anymore
But
i would only teach comm rings
I do think the focus should be on abelian groups after a first section of the course on general group theory
and then introduce groups where this breaks
broo
cant i just joke
i am just schooling
My school takes a totally different approach group theory before anything else, then a course on LA which actually uses quite a bit of rings and modules
so idk these complex maths
Like every third user that joins here makes that exact post first thing they say
i mean an intro algebra class should classify fg abelian groups right
gross
I kind of like the artin approach of groups + lin alg simultaneously
i feel like you need more LA later then though
But I also think knowing lin alg well before any other algebra is pretty important
I mean you take an introductory LA course before either of them, but it’s much more computational (not fully, but it’s not exactly an algebra course either)
so idk
why u are the only one , being angry
group theory many mathematicians dont need too much
but LA is quite important everywhere, so i really want a year long class on it
just giving you a heads up so you dont get yourself banned, sorry for being rude about it
human please just read the channel topics and try to read the room, there is a serious discussion going on rn
I mean it’s not far off the approach of Artin or DF it’s not that weird lol
ok
can this server help me with maths of like 10th standard
yeah, read #❓how-to-get-help
But I think they are actually planning to switch it up in the future since there’s such a long gap between the intro la class the fully general one
frontloading a class on groups seems like you do it just to hit students with abstraction
what are even the standard examples of week 1 group theory
I think we started with basic graph theory to introduce the idea of isomorphisms
Then just started with the axioms
i think if you focus on matrix groups its fine
those at least allow computations
I think it was mostly just groups of symmetries of geometric objects and the basic examples from elementary number theory
the main struggle for algebra students is not having enough examples imo
and then a few matrix groups
I would subscribe to that.
the issue with matrices is that computing with anything beyond 2x2 is torture
one thing i would definitely do if i ever teach algebra is use CAS early on
this could fix many issues
My LA/rings and modules class teaches sage with it
Which I do think is helpful, because on the rare occasion you actually have to compute something, like inverting and multiplying some matrices, you definitely don’t want to do that by hand
i compute things every day!
I mean the rare occasion for this course not generally, I know lots of people use it lol
The commalg and alggeo courses next year uses sage quite a bit afaik
based
But yeah it’s not typically useful in the LA class since the goal of it is to do everything as generally and abstractly as possible, so the coding assignments are generally quite separate
You'd probably want to mandate some sort of programming experience
Or use something like cocalc to offload the programming setup
Because teaching basic programming + algebra at the same time would probably require cutting corners on both
(luckily i will never teach algebra)
I think teaching algebra could be fun
This is where the strict prereq system in Europe helps, everyone doing the course has taken at the very least 1 very good programming class so you can assume that
They’re not even teaching us programming in this class, it’s much more just that we have coding assignments in sage in addition to our regular homework
what do you mean by that
my highschool computer science class was certainly not a very good programming class
yeah im not sure where the very good comes from 
well i guess i'm not european actually
Yeah this is worded confusingly, I mean everyone at MY uni has taken at least 1 good programming class because it is a prereq to the algebra class
Haskell
I think the strict prereqs thing can be good because it means you can safely assume things like that
meow

I don't like this because I could have learned programming well but not have taken that class
I feel like in general there should be recommended prereqs, but let people take what they want with the knowledge that they might fail (i.e. don't slow the class down for people who don't have the recommended prereqs)
i find professors have difficulty in not slowing down because they habitually explain things
My school has like an over-a-month period to drop classes though, I'm not sure how y'all's schools function w.r.t. dropping classes?
So i vote for having preliminary tests prior to taking classes
maybe its too hardcore idk
This is probably just too much effort on the prof's part/too stressful for students who are probably shopping around for classes during this time
I'd be in favor of having a preliminary HW assignment to check prereqs though
It worked well for my calc 3 class but i can see how this is rough for other classes because they can't know well what the prereqs actually cover in full
Yeah this is good too
of course i am also only talking undergrad math classes
Just let me test out of all the credits I should have anyways
I think a preliminary HW assignment is even more useful for grad math classes actually when the prereq system is usually less clear, but in that case the prof can tailor the course more to the students' needs and interests based on the preliminary assignment
we have 8 weeks
It is probably the thing I will miss most once I leave this university to begin grad school

having 8 weeks to drop a class without it going on your transcript is so so so so nice
I genuinely cannot fathom a 1 week deadline, or even 2
when I took the upper level algos class, there were too many students and not enough graders
so the prof gave a prereq check HW that everyone had to work on solo
enough people dropped
wasn't even that hard tbh but if you weren't comfy with the prereqs then yea it would be rough
this is what proficiency exams are for
anyone from toronto
why?
doesn't exist
i didnt get u
I asked why

I'm guessing you're planning for uni or what
sorry sorry i just dont have much friends and stuff coz i am an introvert so finding some
kind of sad, can u dm me
sure go ahead
i dont know how to, plz u dm me
Hello, I've been working through the Natural Numbers Game and I've gotten stuck on the LessOrEqual world level 8 (x <= y or y <= x). Is there a good channel here to ask for help with this?
<@&268886789983436800> troll
joy in the world
metal bishop moment
While I do get that and it’s why I’m generally iffy about the strict prereq system, the class actually wasn’t bad if you already knew how to code, you could just do the assignments, the weekly ones were trivial and the 2 large ones were actually of a decent level
If it got fully bogged down in the real basics it would have been shit, but they didn’t so it wasn’t too bad.
Since I did physics too though I had to take their mandatory coding class and that was insanely basic, but luckily everything assigned was available week 1 so I just did everything right off the bat and didn’t worry about it for the rest of the semester, so like it can be made to work as long as they recognise there’s a range of coding abilities in the class
We only get 2 weeks making it essentially pointless 
I can relate that
In a question where i have to find the value for X would it count as a valid answer if i just plug in different numbers for X until i get the correct value?
No because you’d still have to show you found all values of x, plus it’s just an inefficient way to solve problems
my best friend wrote me into a short story and i just read it and its about someone stalking me 😭
A 'Perfect Blue' fan I suppose
Somebody in the Christ centered discord just claims that 2019 was their personal best year because fortnite was at its peak.
It's official, the church has fallen into apostasy.
the christ centered discord??
It's a Christian discord.
quite the juxtaposition
seriously the average age of my congregation is like over 60
not just that, this app in general tends to be quite far from god
Hey, now it think about. If I post invites to the Christ Centered discord here, and I get banned for adverting. Can I count myself as a martyr?
lmao
Lmdao
why is the fortnite thing apostasy but that fine
Fortnite is cancer
but discord isnt
No
lol
No
Yes there are many good things to do instead of playing that
any one on collatz conjecture
Damm that's something interesting
also known as 3n+1 rule
Yup there are two rules in it actually
kakutanis problem
Yeah
Is there a section for stats of psych
what?
no one has either proved the conjecture or disproved the conjecture
anyone's on it
Not really, it’s both incredibly hard to prove and would offer nothing particularly useful so there isn’t really anyone working on it actively
Not that it's incredibly hard, just that we don't know how to approach it effectively
We don't even have any meaningful partial results
Unlike, say, RH, where it has been proven for many other fields iirc
Use the help channels here: #❓how-to-get-help
Question 0f what topic?

Yea but read how to get help page first
How old is too old to get into a Math PhD program?
21
50
Average mathcord prodigy
bleak
you're under 21 though you got time
so true bestie
I'm also in a program
6 years till too late for me 😔
Guess I just need to skip the last year of my degree if I want a chance 
Never mind it’s actually just too late for my I’ll be 21 before next apps season 
last year of undergrad = applying for grad
congrats, best luck.
are you in pure or applied mathematics?
I'm not talking about myself, if that helps
Im planning to do a masters first so i wont be applying next year, id still be 21 while applying even if i didn’t do the masters though
ah, I see, I misunderstood the sorry
the virgin "applying for grad school while finishing undergrad" versus the gigachad "take a gap year and read 100 papers"
the gigachad doing uni as a side task with learning and doing everything you like (with honor degree)
Irl do you think this ever works?
Not gradschool but anything
Not good enough or low confidence -> study up informally, no institution -> achieve goal
Like job or school or hobbies
I feel like these things value institutionalize knowledge significantly more than independent
Fk I am doomed
pen users, do you prefer black or blue ink?
black
always black
whatever color the pens i find on the ground are 🤷♂️
I could accept red
for the sole purpose of pissing her off
Opinion discarded, watch this instead: https://www.youtube.com/watch?v=F4_j5W8-L3g
Santa Clara, CA | 1st place | 98.625
2018 DCI World Championship CD, Blu-ray, audio, & video downloads now on sale!
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big fan of doing the main notes in black but having 3 other colors on hand for highlights and diagrams
I’m year 12 college now (Australian), and I’m taking what is the second highest level of mathematics behind specialist. My final year has just started and I just don’t think I can do it. Our teacher is very foreign, and respectfully almost completely unhelpful. She’s lovely but I can’t see myself even scraping a pass together. I really do want to drop down a level, but my parents are refusing as I’ve done “well” in previous year (consistently top 20 among around 200 students ish excluding specialist), but even then I’d only really be getting Cs which is about 55-60~ percent on tests. I just don’t know what to do. It’s my first day with the new class and I’ve spend an hour on the first textbook page. I just don’t understand. In addition it just drags down all my other classes as I can’t give them time. I just don’t really even know what to do
Ignore your parents, drop down a level
it sounds like youve already made up your mind about the class
also this is probably a bit of an early/overreaction
give it a few more days and stop being a debbie downer
if it still sucks
then switch

Thank you I appreciate that :).
I haven’t, it’s why I’m asking for advice.
what are your three other colors
this was my interpretation as i read it, it sounds like you've given up/accepted defeat to this class
blue, red, green, purple. just the colors that came as a set when i bought it
which certainly wont help in succeeding in it
perhaps this is the first time a class hasnt gone smoothly from the getgo
but still
keep a positive attitude, maybe talk to a prof, and if you arent making any progress, then switch
bro got a 50 on all their tests, how is it an over reaction
not US grading system... pls use eyes and reading comprehension. C is 55-60 which is... a C
aka
C is still awful
You would get academic probation with Cs
you are dislikable
You are clueless
Thanks for the help guys 👍
Thank you for sticking up for me, means a lot champion
I’ll stay for a bit longer :).
...what kind of school do people go to where C's get you on academic probation
Not familiar with academic probation. Grades < 2.0 give academic probation. I thought it was grades <= 2.0 until looked it up again. C is still just 2.0 not that far off
this is a high school
i have never heard of a high school giving any sort of probation for anything besides outright fails
(or plagiarism)
"year 12 college" means high school
what?
why are you commenting on the australian system without understanding it
i thought college was college sorry
Thank you, sorry should have tried making things a bit clearer
(theres a technical difference but the point is that theyre both secondary level)
anyway reading your post i would not be concerned at all
for one, if your teacher is genuinely incompetent, then thatll probably factor into your class' grade distribution
but regardless of that point, most learning in mathematics happens during exercises, not during lecture
plenty of students have passed university courses without attending a single lecture just by doing textbook exercises
im not saying you shouldnt try to pay attention in class or anything, just that theres ways to overcome these obstacles
i think youre kinda overstressing yourself
I do stress a lot especially about school work. Big concern of mine is not dealing myself appropriate amounts of time for other classes. The way the gaps work and from even doing practice work/tests from classes below, I'd be so unbelievably fine to just drop down a level. I'm just worried because i believe that times I've done well have been a result of some really good teachers. Comparatively I've actually done well in past our school has just had some really hard units.
I really have appreciated the advice from people, it has meant a lot
also fwiw all high school math courses have 10 gajillion resources on the internet
so if you really do find the lectures inscrutable, you can go on khan academy or pauls math notes or whatever
might not align completely with the topics covered in your lecture but it should be close enough (probably a superset)
oh yeah. i used prof leonard every now and then for multivar in hs, not that our teacher was bad, but i didnt really pay attention a lot
why tf and how tf am i more stressed about school now than when it was exam time like two weeks ago
every day during exam time i could go to bed and sleep within like 10 or 15 minutes and get 8.5 hours or so of sleep, now i'm so jittery i can't even go to bed until like 7 hours before wake time
do you work out?
perhaps you should work out
i fall asleep instantly, haven’t had trouble sleeping for a decade
mostly just doing physical activity forces sleep
Gave you the studying! selfrole.
the food at my uni is way too freaking good
i ate @frail lagoon today, mwahaha
and some gulrot (why are there no carrots in here?)
olives 
How was it
Looks nicee
I just had dinner at my college lol
the one on the left was filled (i’ve no idea with what but it was nice) and baked
Like uhhh what do you call it
I don't even know the name lol
Oh well paella anyway
Very tasty
sounds lovely
I wasn't sure what kind of rice it was lol
the food aside, bruh the color grading is amazing, the picture looks awesome
i found a good spot in my library building, there was some lovely evening sunlight outside
Yea I see
i wanted to discuss a different version of halting problem
so (idk how rigorous this version of the proof is) but basically the halting problem proof relies on
def g():
if halts(g):
loop_forever()
i was wondering if you could just replace halts() with has_property() for some arbitrary property?
for example i could do:
def g():
if does_not_print_helloworld(g):
print("hello world")
if g doesn't print hello world, then it does; if it does, then it doesn't (there's no 'hello world' to be seen)
is this correct?
as a generalization of halting problem
sure but theres an easier way to see this
is it basically
'we dont know if the program will halt so we dont know any property until it shows up'
define a function f by
function f(g):
if g returns [value]
loop forever
and then apply the halting problem to f
the point is that "its impossible for a computer to determine whether an arbitrary program will halt" applies if you replace "halt" by any other criteria
"halt" is just used because the original formalism was turing machines
i just thought they thought halting was a particularly interesting property
by apply halting problem, do you mean to say 'we dont know if f will halt'?
correct
we apply the halting problem to f
"we dont know" is misleading though
thats not what the halting problem says
the halting problem doesnt say its impossible to dteermine whether a program will halt
its for arbitrary programs
just that a computer algorithm cant determine whether an arbitrary program will halt
The interesting question would be what are properties that can be proven (to not be decidable) through this method?
all of them
to be a bit more formal, define a turing machine whose accept states correspond to the property you care about
this turing machine, by the halting problem, cannot determine whether arbitrary input will halt
Arent all of these properties just equivalent to some turing jump though?
why are we focusing on what g returns?
don't we care about any arbitrary property of g
also since g is the only arbitrary program here, surely we can only apply halting theorem to g?
i mean, replace g by a function g' that just returns true/false if it satisfies [property]
ok fine
the halting problem establishes the nonexistence of a program that accepts arbitrary functions as input and returns true if it halts
yes
the contradiction in the proof of the halting problem is that the program cannot accept itself as an input and return the correct value
the point is that, if it was possible to computably determine whether g satisfied a certain property, we would have a function/procedure f that does this
but such an f cannot exist (for arbitrary g)
if you mean for a SPECIFIC g, then thats fine
its "usually" possible to determine the properties of a SPECIFIC procedure by just running that procedure
i say "usually" informally here, i am not aware of any combinatorial arguments or anything
i just mean like, in terms of questions youd want to ask
<@&286206848099549185>
can you help me ?
noo its not a math ?
it is
just ask your question in a help channel and follow steps in #❓how-to-get-help
the pictures at least helps
Fat and proud
how do you do weighted averages
$$\sum_s w_i v_i$$
we is typing, they
something like that
Stop thinking!
I've been awake for 27 hours
What have you accomplished?
Team selection tests
I tried to sleep
But all I can think about is polynomials
Bro
Based hodler
harpz The
(i messed up the capitalization and omitted the last 5 characters)
Which country?
How would you prove that the best solution is to just order the digits from least to greatest?
You are given a positive integer N consisting of exactly four digits. Split N into two new integers new1 and new2 by using the digits found in N. Leading zeros are allowed in new1 and new2, and all the digits found in N must be used.
For example, given N = 2932, you have the following digits: two 2's, one 9 and one 3. Some of the possible pairs [new1, new2] are [22, 93], [23, 92], [223, 9] and [2, 329].
Return the minimum possible sum of new1 and new2.
Hmm, sell time I guess
Given 4 digits, one could try to show that for any other arrangement A, the way you order the digits sums to no more than the sum of A.
Is that what you meant by "best solution"?
sorry for being too cool for you, sorry
Okay I'll accept
really no, its fine, we can be freunds again
im SO glad our friendship stays unrocked
Are you trying to come up with an algorithm?
My brain just goes:
Take like 398273, sort into [2,3,3,7,8,9]. num1's digits is the evens, num2's is the odds
so (238,379)
I think you can prove this relatively simply
fr like
infinity is a concept or like a direction
its not really a number
the same way
its too vague
and whatnot
it has to be a number to be subtracted at all generally
problem is infinity is really vague
id have to answer 0 in general
but like
it gets odd
yes
that
doesnt contradict what i said
because thats the point
it isnt being subtracted by a number so it doesnt make sense
right so what subtraction is at that point becomes vague
it isnt
and subtracting a tree from a tree is vague in process
sure you can pick up a tree but do you need to take away every molecule of the tree? what constitutes as a molecule of the tree? is the moss a part of the tree? is the bark apart of the tree? some bark fell off of this tree, is that bark a part of the tree?
subtracting infinity from infinity is also vague
is integer minus integer 0?
i will relay that answer to you
yes, if its the same infinity
but infinity is vague
What is really vague is what is meant by subtracting infinity from itself

its not vague
if the infinities in question are the same number then the answer is zero
if they aren't the same number then it depends on their value

Have you learnt something today?
Nope
Me neither
I know that now. Thank you for this information. It truly is such a wonderful world that we live in that we can grow and gain more knowledge at the push of the button. We should really thank all our ancestors for working so hard to keep the human race surviving and thriving. Without their dedication to the cause of popping out babies we would not be where we are today. I hope to one day contribute to man kind and allow our future generations to learn even more things. Maybe they will know what percentage your phone is at before you even know yourself. What a time to be alive!
lmfao
this is a chatgpt esque reply
idk y, maybe its the baby popping that makes it seem that way
Alright if you're just gonna be condescending and mock other people, you're not welcome here.
nono its fine lmao
was a nonsense message so any reply to that doesnt really mean much
just jokes
Thank you for this information. It truly is such a wonderful world that we live in that we can grow and gain more knowledge at the push of the button. We should really thank all our ancestors for working so hard to keep the human race surviving and thriving. Without their dedication to the cause of popping out babies we would not be where we are today. I hope to one day contribute to man kind and allow our future generations to learn even more things. What a time to be alive!
humor is such a thin thread to balance on sometimes
yea lmfao
been banned far too many times
friends cant take my jokes man
ends up with me making alts
alts for free expression
im worried on day i might cross the line
i probably already have to someone w/o realizing it
lmao youre good
prbly
hopefully
lmfao
Wait what recommended chat messages??
Like it pings u and says “xyz is talking about [smthn]”
ive never heard of this feature
OHHH
thats like the snapchat notifications ive been starting to get
x is on snapchat
For example “Jay [panda smthn smthn hurricane] is talking about differentiating matrices”
No that’s something else
I mean like a discord thing
like who tf r u, and y r u telling me youre on
but its similar right_
Weird, I don't have that
Yeah
Ooof
"Matrixes"??
how do u get this
maybe theyre talking about hypothetical universes in the matrix series?
hacker
aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa 2>100
sos
hati
what
discord told me you were talking about college degrees and trolling this morning
LOL
Let’s see if can trigger more for people
You know what I love? Fish and chips
Gosh fish and chips are just amazing. The preparation is so fire
i have actually never had fish and chips
Dann
thinking sp
Blade of justice
gg
is this blade of justice
I thought it was Spacelocked II for a second
hi
Who did you bite?
I love telling people something like "I'm scheduled to be dead between the 14th and the 17th, but I could squeeze you in on the 13th or the 20th"
go troll somewhere else
daily 1+1 poster
Squeeze 
Yo guys question
In probability
It takes me like
5 mins
To solve a 3 dices question
Is there an easier way?
no
Do more practice to increase speed
Wait actually?
There is no like formula?
Cuz bro it rlly takes 5 mins
In my final exam
I need the 5 mins
As the question worth only 2 marks
lmfao
1000009>11000000000000
Damn
Is there a formula tho?
For probability
Or no?
This is the only way?
wtf is a "3 dices question"
wym "3 dices question"
do you mean solving something to do with the distribution of a 3d6 roll
12 fold path
Its the way
Learn it and you will be better than all your peers at counting
In combinatorics, the twelvefold way is a systematic classification of 12 related enumerative problems concerning two finite sets, which include the classical problems of counting permutations, combinations, multisets, and partitions either of a set or of a number. The idea of the classification is credited to Gian-Carlo Rota, and the name was s...
To become counting god learn to decontextualize counting problems instantly into a graph or function format
Literally read this wiki article and spend a week coming up with different examples of viewpoints and youll be better than most
create a 3 sided polyhedron
@neat lintel It'll be cheaper just developing a software for something that can run your program
instead of making hardware for it
anyone know physics here?
maybe some but check this channel #old-network you will find a physics server
ook
I know I was warned to check my stocks just once a year but I’m tempted to check it every day
Depends on how much money you have in your account and your goals
Its normal to check stocks every 15 minutes if you're balling like that
also depends on your temperament
if you're investing long-term (like most people probably should) and you're liable to panic sell then yea lol
dont check every day
Yeah
Honestly would you guys rather invest in buulding companys who got tons of land claimed for building or the smp500?
I wouldn't use this place for investment advice
so poor, can't even invest in oneself
Way so many remarks about investing in mathematics server?
Honestly it seems like I should enter a short position soon
some people are into math for the money
Sure, but IIRC it was not like this for about a year.
one time when i was a music major i ran into my high school friend who was doing a master’s degree in financial mathematics
and he was like “music? nah, get that shit outta here, do math and make money”
i wonder how much the server has grown
In a year?
yeah
how long does it take to make money with fin math like how many books do i need to finish
fin math is pretty boring
idk im still less than 1/3rd through my first book after several months 
if it's fin math already done, someone's already made a simple decision boundary for it
though i also put it down for a couple months because it was causing too much pain
is it like bifurcation theory and stuff
if it's fin math not already done, then it's probably not very relevant
at what point do you "make" money
when you join a company as a quant
more likely than not, most of the technical knowledge won't be very relevant
all my life ive struggled to grasp the concept of where money is made like in an mmo game you cut down trees and sell the logs and the shop magically prints money, but irl i can chop down every tree in the US and if someone with money doesnt want a log all my work is for nothing
my leading theory is everything ties back to the military sector, and its defense related tasks that "print money"
what
nowadays many jobs are many layers removed from actually selling stuff to customers, especially in tech
there are jobs where your job is to help people in other jobs do their job better
etc
but that feels so fleeting, once the customer learns then you lose the customer
what
get a job for the government or something then idk
but that too may be fleeting
when your department gets budget cuts and you get laid off 
but the government wont be around long, ya
maybe farming is another source
food i guess
people need to eat always
but look at france mdr
i let the businesses worry about how to make money
they have all sorts of plans and tricks
as long as i get paid im good
do you not question if you are underpaid
what would happen if you asked to have the ceos job
they sound cool
ceos in general? or mine
i agree, tho im not sure what made u think that
well i work remote so i don’t have access to the snacks anymore 
but yeah we have some good stuff
does your country have a postal service?
yeah
ask your boss to ship you a regular supply
i feel like people avoid talking to bosses like they are people, and it translates subconsciously and bosses subconsciously pick up on it and act crappier because of it
Interesting
Wat
I do think some kind of "worth" is generated by farming, yea
you should remind them with direct human questions like "The office has a snack room but my house only has a pantry that i hab to pay for myself. Can you ship me a box of snacks biweekly and bury the cost in the company books? If not, out of the ceos income works too." Remind them sharing is caring.
I feel like if you cant ask that in a meeting then the company doesnt value you
i genuinely believe this
workers having quality snacks would becof very high importance if i was a ceo
Why do you think company would truly value any employee
It all comes down to money for them
It quells the rebellions
Wdym "quells the rebellions"
yeah no thanks, id rather be paid in cash money than in snacks
Hey, I have sometimes problem to "snap" my focus to topic I am learning from book. Its like: I start in conscious state and then I go to automatic non conscious mode and I have to reread multiple times. I bet anyone can relate in some way. What are your thoughts on that?
I do this so much
legit just read more
and take breaks
id like answers to this too (that aren’t ADHD meds)
you don't want to learn
compare with listening to music
you learn the lyrics without trying
because it's enjoyable
like ark says drugs solve it by force making it enjoyable
If you got moving particles infront of you it gets your attention maybe? The best way is to study infront of a white wall
hello
helo
Yeah, I have noticed that helps me a lot in the long run
You mean placing moving particles somewhere on the desk can help me focus?
No i meant avoid them at all costs so ypu have no distractions
What your having is stimulation distress
Your addicted to dopamine or something so you keep looking at stuff, make as many less dostractions so your only stimulu is the math question
Thats interesting, i will read about this
Well you missed the part of where the CEO pays for the snacks because they can afford them
You need to tell the ceo you cant afford the extra snacks
the snacks are implicitly out of your salary
instead of asking the ceo for snacks ask for their value in hard currency
Well you see, ceos care about money, and they dont want to share hard money. But they innately can understand the importance of snacks and will gladly supply them, which if you are smart you can barter elsewhere.
how are you
they care about roi, snacks have hella roi
finally someone who understands
ordered mine today 
noice
how long till it arrives?
uhh i havent checked
lemme see
i cant find anything?
regular shipping is 3/6 days, so im assuming next next week
idk the order -> build -> ship turnaround
what specs did you get again?
7800x3d 4090 
what are you upgrading from
from 2018*
let me get the specs
okay its
i7 8565U
intel UHD graphics 620
yeahh
mega potato
damn your mind is gonna be blown with your new pc 
anyone good at basic algebra
actually can you please help
awwww
what is it lol
#help-48 message
@worthy mortar: No. The message that invited action warranted far more serious repercussions than a mere time-out. And actually, that person was probably removed from the server (hopefully for ever). You were timed out separately for whatever reason applicable.
Just done my math exam, I failed my mom again ;/
If only I concentrated in chapter functions
Yo! Don't feel low, I'm sure that this exam has prepared you better for your next ones. Now, at least you know where your skills lack. You can work hard on improving yourself there. 🙂
Hopefully 😕

No need to get upset man you didn't failed your mom.
YOU FAILED MATH.
im doing great
can i ask u ?
ho is watching anime
ask what
u gotta do what u gotta do
Just ask your question. Anyone who knows will definitely help you.
what does the role emeritus mean here on the server?
people who used to be active but currently arent

ex-activists
slacktivists
I thought they are retired professors 
Can somebody help me
where did u get that profile picture
when you are new to discord it should shows you one of these
if you don't have a pfp
ohh alr
$\int_{0}^{\infty}{\frac{\cos(t)dt}{t^x}}$
Mizalign




