Archived threads in /sci/ - Science & Math - 1561. page

>>8183461
There's water in it.

>>8183461
there's more water in the ocean than my bathtub

>>8183461
it's wet

>>8183297
drink more water

>>8183299
also check your pee color, if it's clear you're good

Sorry for the bad englisch im typing on My phone, and the auto corection is laggy

>>8183273
which field?

>>8183278
communications

>>8183286
Why are you on /sci/?

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spoiler alert.....
.....dirac was probably autistic

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>>8182845

>>8182723
Edema is just excess fluid. It depends on what you have.

>>8182743
it doesnt look like edema, more two pea sized bumps on my neck

>>8182754
Not particularly educated on physiology but as far as I understand, lymph nodes swell up all the time, especially if you are at all sick. The lymph system is for "cleaning" and so there are endless reasons it could be overloaded.

A category C consists of a U'-small set of objects, which I will denote C_0, and a U'-small set of arrows or morphisms, which I will denote C_1. This notation should remind you of objects being 0-cells, and arrows being 1-cells. We will handle this generalization later on.

There are parallel functions s,t: C_1 -> C_0. We call s(f) the source or domain of f, and t(f) the target or codomain of f. A pair of arrows (f,g) is called composable if s(g)=t(f). There is a binary operator called composition ∘: {(f,g) : (f,g) is composable} -> C_1 which is associative. We will write g∘f for ∘(f,g). Furthermore, we impose the following relations: s(g∘f)=s(f) and t(g∘f)=t(g).

There is always an injective function Id : C_0 -> C_1, satisfying f∘Id(X)=f whenever s(f)=X, and Id(X)∘g=g whenever t(g)=X. We call Id(X) the identity arrow of X, or just its identity. (Exercise: show that identities are unique (ie, that if two arrows exhibit the properties of an identity, then they are equal).)

Given objects A and B in C, we will denote the set of arrows {f : s(f)=A and t(f)=B} := C[A,B]. This is the set of arrows going from A to B. We write f:A->B if f is in C[A,B]. Generally, C will be clear from context in this case.

A morphism f:A->B is called an isomorphism if there exists a morphism g:B->A such that f∘g=Id(B) and g∘f=Id(A). We call g a two-sided inverse to f. (Exercise: show that two-sided inverse are unique.) With this, we will simply call g "the" inverse of f, omitting "two-sided."

The elements of C[X,X] are called endomorphisms of X. The subset of C[X,X] consisting of the isomorphisms is called the set of automorphisms on X, Aut(X). (Exercise: show that Aut(X) satisfies the group axioms.) With this, we call Aut(X) the automorphism group of X.

If r∘s=Id(X), we call r a retract of s (a left inverse), and we call s a section of r (a right inverse). A morphism f is called idempotent if f∘f=f. (Exercise: show that, if s is a section of r, then s∘r is idempotent.) We say that such an r and s split this idempotent.

A monomorphism is an arrow f:A->B such that, given any two arrows g,h:C->A, f∘g=f∘h implies that g=h. Dually, an epimorphism is an arrow f:A->B such that i∘f=j∘f implies that i=j. Later, we will provide a more concise and elegant way to characterize epimorphisms and monomorphisms. (Exercise: show that the composition of two monomorphisms is again a monomorphism, and that the same holds for composable epimorphisms.)

If f∘g is an epimorphism, then f is an epimorphism. Indeed, suppose we had some i and j where i∘f=j∘f but i=/=j (such a pair must exist for f not to be an epimorphism). Then, after composing with g on the right, we have (i∘f)∘g=(j∘f)∘g. By associativity, we have i∘(f∘g)=j∘(f∘g), but by hypothesis, f∘g is an epimorphism. We thus have that i=j, a contradiction. So, f must also be an epimorphism. A similar argument applies to monomorphisms, so that if f∘g is a monomorphism, then g is a monomorphism.

Clearly every isomorphism is both an epimorphism and a monomorphism, but the converse need not hold in general.

A category C is called small (by our use of universes, this is technically U-small) if C_0 is a small set and C_1 is a small set. It is locally small if C[A,B] is a small set for all A,B in C. (Exercise: show that a small category is locally small.)


We will now examine some of the categories which we will be working with most heavily.

The category Set has for objects U-small sets, and Set[A,B]=B^A, the set of functions from A to B. (Exercise: check that Set indeed forms a category. Is it small? Locally small?)

The category Grp has for objects (small) groups, with group homomorphisms between them.

Vect_k has for objects vector spaces over a fixed base field k, with linear maps between them.

CRing has commutative rings (with multiplicative identity) for objects and homomorphisms between them.

Top is the category with objects topological spaces, and with continuous functions between them.

>>8182142
It makes you just smart enough to qualify to be my sandwich maker.

Can you prove the formula for volume of sphere

If yes then you're probably a fucking genius

>>8182142
nah, not just browsing... you have to fight with someone, and believe that your right

>>8182075
>What's gonna happen at CERN?

Protons are gonna get smashed together.

>Are the worries of a black hole forming or the world exploding valid?

No

>>8182075
>What's gonna happen at CERN?

Particles are going to be accelerating

Are the worries of a black hole forming or the world exploding valid?

No.

>>8182088
Why not?

>>8180110
there are naming conventions you have to learn. in chemistry there is currently a discrepancy between generations, as the old fucks had a system put into place, but the fresh meat redesigned the standard to be more intuitive.

most everyone knows the new notation because its really easy. i dont know why old people insist on using the older words to cause confusion. some are just easier to say I guess.

>>8180136
You happen to know the name of the two notation sets? Would like to find out which one I'm being taught.

>>8180139
IUPAC handles the naming conventions for current chemistry education and is named "IUPAC notation" accordingly if i remember correctly. I dont know what the old notation is called, but sure tell me what you are being taught.

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one of these space balls?

>>8178608
Pipe bomb?

>>8178608
>space balls
Piece of satellite.

i like the video

>>8172611
Finally someone standing up against this nuts concept? I'll watch your videos later

>>8172611
Good OP!
Sick and tired of people taking a mathematical equation as proof that black holes and dark matter exist. All fucking nonsense.

i have no idea about chemistry, but i summed the amounts of letters in your picture and googled it
https://en.wikipedia.org/wiki/Capsaicin

>>8161859
basically it says "hot." don't wear it around your in-laws.

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I couldn't get into Spivak Calculus, and Apostol's introduction to proving Archimedes just left me confused and I have no idea of what these guys are doing.

So I am obviously too dumb for these two. Is there some other book that kind of gives me the type of thinking required for this type of math? Induction, proving, etc.

>>8183754
Be a nigger
Say "you didn't build that"
Get a Nobel Peace Prize

Passive facilitation versus direct impact.

https://en.wikipedia.org/wiki/M%C3%BCnchhausen_trilemma

>>8183201
>is it just a metaphor?

No, it's literally the answer to everything. Every single constant can be reduced to pi.

>>8183211
what

>>8183201
No mathematician ever said that, the closest thing will have been a math undergrad who will probably drop out.

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>>8183195

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>>8183197

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>>8183199