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No, that's Panthera. Panini is a clade of sea doggos.
panini? isnt that the violin guy
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proof sketch (this should work unless I misunderstood the problem?)
Uniqueness: every function g may be decomposed into a finite sum of functions g_i with their supports disjoint singletons; just let g_i(x_i)=g(x_i), g(other things)=0 for x_i in support(g). These g_i's values when put through Σ are predetermined by problem statement; thus their sum Σ(g) must be the same no matter the Σ.
Existence: let Σ(g) be the sum over x in support(g) of g(x); this satisfies constraints on singletons.
Let g1 and g2 be functions, let G1=support(g1), G2=support(g2), G=support(g1+g2) for ease of notation, and note G1, G2, G ⊆ G1 U G2; then
Σ(g1+g2) = sum_{x in G} g1(x)+g2(x)
= sum_{x in G1 U G2} g1(x)+g2(x)
= sum_{x in G1 U G2} g1(x) + sum_{x in G1 U G2} g2(x)
= sum_{x in G1} g1(x) + sum_{x in G2} g2(x)
= Σ(g1) + Σ(g2)
so it's a homomorphism too.
A "product" is something you do to a sequence with finite support taking values in a monoid M. A sum is something you do to an arbitrary function with finite support taking values in a commutative monoid M, which you could think of as a "finite M-multiset". I've said this before.
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One of the great things about learning higher math is that a lot of the best resources out there are also available -- often published by the authors themselves! Whatever you want to learn, looking up textbooks for it on Math StackExchange will get you good results.
I personally got a lot out of Hammack's Book of Proof as an intro to sets, functions, and logic; something like it is pretty crucial if you want to know how mathematicians think. It's fairly cheap as far as math textbooks go, and the author's also published it online.
You might also enjoy learning linear algebra if you haven't already? There are a whole lot of different resources for this, but Linear Algebra Done Wrong is probably one of the better ones (albeit a bit proof-heavy; something like Hammack is worth reading before it).
There's also a whole lot of good stuff on MIT OpenCourseWare; they have free courses on pretty much all the math you could want. Here's some good ones for single-variable calculus, multivariable calculus, linear algebra, differential equations, partial differential equations probability and statistics, and real analysis.
if y'all have any other recommendations, reblog with them?
I need to learn more higher math.
Like I took calculus in high school (22 years ago), but it wasn’t well taught. It wasn’t until like 10 years later that I actually grokked what calculus even is (geometry in motion, essentially adding the dimension of time).
And I’m interested beyond that, and enjoy logic and abstraction. I’m just not sure where to start.
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obviously a technicality, unlikely to have a basis in reality, and dependent upon definition of manifold, but you could have e.g. an ultra-long line with 2 copies of [0,1) x (first ordinal with cardinality 2^continuum)? i think that’s a manifold with even bigger infinity you’re not packaging second-countable into the definition
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What? No. The different sizes of infinity have nothing to do with the expansion of the universe. I don't know much about GR but I know enough to know that it says the universe is a smooth manifold, and every smooth manifold has the same infinity of points (cardinality of the continuum). This person appears to be talking out of her ass on this point. I don't think it matters but like, come on.
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was trying to type the letter "C" earlier and accidentally typed "see" instead. how does that even happen? does my brain's "typing lobe" hear words rather than seeing them? why would it do that?
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Augie and the Green Knight absolutely has the vibe of the third one here
Sometimes reading Arthuriana feels like reading Alice in Wonderland.
“Well,” said Alice, “these are a dreadfully strange assortment of objects!”
“They all symbolize different aspects of Our Lord’s martyrdom,” said the Fisher King, casting a line into his teacup.
“Indeed. I am sure everything symbolizes something else, for if everything was only itself I should be very confused. Might I ask what the point of the bleeding lance is?”
Alice regretted asking the question as soon as she had done so, for she saw the pun that would likely be made about the word point. Instead, however, the room erupted in applause and shouts of “The Grail! She has achieved the Grail!”
The next castle she visited, Alice resolved to herself as the inhabitants of this one danced for joy, would be more sensible.
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which of these two would surprise you more if you found them at your doorstep?
Linda, a bank teller.
Linda, a bank teller who is active in the feminist movement.
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English translations of foreign-language poetry be like
My rival dresses to display her legs,
and her shoes are of an alluring fashion;
but my shoes are comfortable
and my tunic is plain.
She holds the most prestigious position in the women’s dance performance,
while I sit in the audience.
I dream that someday when you awaken
you will know that what you sought was always here.
You and I walk together,
you in the coarse and tattered trousers of a common working man;
we sit on a bench in the park, laughing together,
and nothing seems difficult.
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i saw someone use the phrase "this is supposed to be leftism 101" and i think i've fully come around to the idea that "leftism" or "basic leftist principles" are just rorschach phrases for whatever the speaker believes
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loving this StackExchange post. a twist on the classic why-don't-birds-get-electrocuted-on-power-lines question, which ultimately comes down to answering the question "what is the capacitance of an unladen swallow?"
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As a (probably theoretical) math major who'd like to become a professor one day, I'm becoming increasingly aware that actually getting to such a position is...hard. There are, apparently, a lot of people who are very good at math, and many of them would make good professors, and many of them would like to become professors. It's a really big lottery to get into a couple of good positions, and if you're not a really good fit for some college or really really good at teaching, you'll have to settle for one of the intermediate positions.
And it's not a great position to be a starving postdoc forever, and that's a distinct possibility if I throw the entirety of my being into, idk, p-adic analysis or whatever. So I need a backup plan.
Unfortunately, there seem to be roughly two places outside academia that a pure math person will be welcomed with open arms. Those are, uh, quantitative finance and the NSA. So the real question is: do I have ethics?
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conversely, postmodernism started with Robinson's development of nonstandard analysis
this is extremely parochial of me but I think that modernity proper started in 1821 with Cauchy's publication of Cours D'Analyse
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i actually saw a talk recently about using category theory to teach diff. eq to undergrads! it was precisely as horrible an idea as it sounds-- probably the brainchild of some category theorist professor who desperately didn't want to teach diff eq and tried to find the next best thing.
california bans riemannian geometry because it is kinda white supremacist to put a metric on a manifold. florida bans topos theory becuase grothendieck was Woke
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hark how the flames
great golden flames
all seem to play
carols today
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sadly no; it's a finite-state machine. only 50
Is the current US law code Turing complete?
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ok so this is actually...kinda surprising at first glance? and maybe says something about english-friendly genomes?
like, dobsonfly genome is about 500MB. that's big-- but only about a sixth of human genome size, and about 0.03% of the BLAST database as a whole. back-of-the-envelope calculations, assuming these posts pick randomly from BLAST, suggest only a ~1.5% chance that a triple of this kind would have appeared by <100 standard posts in.
this suggests something interesting-- some nonrandomness-- is going on. hypothesis: maybe it's just english letter frequency? t,a are the 2nd and 3rd most common letters in the english language, maybe we're just seeing an over-representation of low-GC-content genomes?
checking dobsonfly now and...yup, it has only about 24% GC content. this is a pretty big outlier even for insects, probably explains most of why this is our champion. so probably not a fluke, expect to see more dobsonfly content in the future i guess?
probably also worth checking how much else this explains in overrepresentation. do moths have low GC content in general?
this is a message to my true love this valentine's day: chocolate
when i come home, still lacking a significant other, there you are, reminding me that i never needed nor wanted one after all. more beautiful and crucially more delicious than any grand romantic gesture by a human could ever hope to be.
chocolate, for all my homies who prefer their valentine's to be about candy and candy alone. y'all are real ones.
String identified:
t a ag t t t at' a: ccat
c , t acg a gcat t, t a, g tat at at a. at a cca c ta a ga atc gt a a c t .
ccat, a t at' t at ca a ca a. 'a a a .
Closest match: Neoneuromus ignobilis isolate Gutianshan chromosome 5
Common name: Dobsonfly
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