/sqt/ - Stupid Question Thread: Milnor Edition

Sorry for the crappy diagram. I know in set theory epimorphisms are exactly the same as surjection, but I am unsure if this diagram is an example of a surjection.

Are these diagrams an illustration of an epimorphism?

Let this be the category of Set.
Where you have a function,
f: X->Y
g1, g1: Y->Z

Where X is the first set (reading left to right), Y is the middle set and Z is right most set.

The diagram is suppose to represent g1,g2 mapping the same elements from Y to Z.

an epimorphism is a single morphism, your diagram has three of them

How come definitions define it as

f : X → Y that is right-cancellative in the sense that, for all morphisms g1, g2 : Y → Z if it is just a single morphism from f X to Y?

but no f is not an epimorphism in this picture since its not a surjection

in Set, epimorphisms are exactly the surjections

sorry i couldnt copy paste what i wanted.

Why does wikipedia define it as: en.wikipedia.org/wiki/Epimorphism

if you are just looking at morphisms between X and Y?

In the wikpedia article it makes me think you would map X to Y and then focus on the morphisms g1, g1 between Y and Z in my diagram

that definition says f is an epimorphism
it doesn't say anything about g1 and g2

the definition just happens to involve a condition with two other morphisms

im confused. what makes f an epimorphism?

In category of Sets how many sets are you looking at?

In my diagram would you just be focused on X and Y and the mappings between them for an epimorphism? Or does Z have to be involved?

f is an epimorphism if it's right cancellative

>In category of Sets how many sets are you looking at?
f is a morphism from one set to another, so two sets

>In my diagram would you just be focused on X and Y and the mappings between them for an epimorphism?
not all the mappings, just f

>Or does Z have to be involved?
not just one Z, you involve every other object Z such that you have maps from Y to Z with f g1 = f g2. f is an epimorphism if for every object Z and every pair of maps g1, g2 with fg1=fg2, you have g1=g2

err g1 f = g2 f

How do you apply the definition of epimorphism to this diagram?

let g1,g2 be maps from Y to Z such that
g1 f = g2 f

then since f is surjective, for every y in Y there's an x in X with f(x)=y

by the assumption that g1 f = g2 f, we have g1 f (x) = g2 f(x) , which is the same as g1 (y)= g2(y)

since f is surjective this equation is true for every y in Y, so g1=g2, so f is an epimorphism

what confuses me in what you write is you mention Z. There is no Z in this diagram. Where is that coming from? There is only an X and Y. Earlier in the post you said you don't need three sets and then you include a third set in your proof. Can you explain what the fuck is going on? I am self-learning no professor to ask here so thanks for helping

Whats a decent undergraduate research paper writing service?
Google returns like 100x with poorly designed webpages/live chat support and idk if I can trust them to do a biochemistry paper without getting caught on turnitin.

>Where is that coming from?
the definition for f:X -> Y to be an epimorphism says that you need for ANY two morphisms to another object g1,g2 :Y -> Z satisfying g1 f = g2 f, also satisfy g1 = g2

so if you want to show f is an epimorphism it's not enough to pick a specific Z and specific maps g1,g2 like you did in your diagram

the argument i gave did not depend at all on the choice of Z or g1 or g2, it works for any Z and any g1,g2 satisfying g1 f = g2 f

so in order for the definition of epi to be satisfied then f MUST have an arrow from every object in X to every object in Y right?

THEN

g1,g2 :Y -> Z satisfying g1 f = g2 f, also satisfy g1 = g2

must be satisified for ANY Z you choose.

Is all of that right?

>so in order for the definition of epi to be satisfied then f MUST have an arrow from every object in X to every object in Y right?
in Set, epimorphisms are exactly surjections, so for f to be an epimorphism, every element y of Y has to have SOME element x in X with f(x)=y

>g1,g2 :Y -> Z satisfying g1 f = g2 f, also satisfy g1 = g2
>must be satisified for ANY Z you choose.
>Is all of that right?
yes

what do I need to know before I start learning Number Theory?

elementary number theory, nothing

algebraic number theory, some basics about grops and fields

analytic number theory, a strong grasp on calculus

question i have is for Y to Z does mapping of g1, g2 have to be surjective from on Z? In other words for every element z (in Z) Z has to have some element y in Y with f(y)=z?

no, just look at the definition, it says nothing about g1 or g2 being surjective

it just says g1 f = g2 f

ok that makes sense, so really the only thing that is surjective is f that maps X to Y?

yes

is this book a good intro?

amazon.com/gp/aw/d/0199219869/ref=mp_s_a_1_6?ie=UTF8&qid=1491012386&sr=8-6&pi=SL75_QL70&keywords=number theory

idk dog read the 20 reviews or just download the book...

ok that makes sense. then what the fuck is the point of g1 and g2 mapping the same element to the same shit from Y to Z then if f is the only thing that is of interest here in terms of surjectivity?

using a bad anaology that is like saying if you turn left then the restaurant is there, then if you go 2 miles up you'll see a gas station. while that might be true the gas station is 2 mles up who gives a fuck when you found the resturant?

similarly, if you know f is surjecive then why does what g1,g2 does from Y to Z matter?

>then what the fuck is the point of g1 and g2 mapping the same element to the same shit from Y to Z then if f is the only thing that is of interest here in terms of surjectivity?
because thats the definition of epimorphism? also this is only in the category of sets, in more general categories there's no notions of elements, and so there's no notion of surjective either

what are you even studying this for?

>similarly, if you know f is surjecive then why does what g1,g2 does from Y to Z matter?
knowing f is surjective let's you prove its an epimorphism

studying it out of interest. want to learn group theory and see how category theory applies to it. additionally want to learn functional programming and want to see how it applies to that as well.

started studying group theory on the side and made more progress with that since i am following a structured approach to studying group theory.

the catgeory theory study is hard to structure like my group theory studies.

kind of have to rely on wikipedia articles

you really dont want to rely on wikipedia articles, just get some standard intro texts like aluffi's chapter 0 or leinster's basic category theory or simmons's 'An introduction to Category Theory'

its also really just game of symbols at this point

in groups if you have group elements a1,a2,b with a1 b = a2 b then since inverses always exist in groups you can multiply on the right a1 b b^(-1) = a2 b b^(-1) to get a1=a2. so here an analogous right-cancellative notion of epimorphism would be boring since everything is right-cancellative

in categories inverses of morphisms don't always exist so you can't play the same game, so having this definition on hand is more useful

ok thanks.

Say you have three sets; X, A, and Y. X is unknown, A is given, and the cardinality of Y is given. Y = { f(x,a) : x ∈ X,a ∈ A }

What I'm interested in learning is how plugging in different values for A, different cardinalities for Y, and different functions for f(x,a) affects the range of possible answers for what the sets X and Y contain. Also, I can't figure out how to type this out in latex.

what is the precedence of the sum (sigma) operator ?

Like unary minus, just the term to the right?

im a downie retard and i can't do this questions from courant and john.

Since x can only be rational values, the x value cannot go to any other rational value other than 1/2 without first passing through an infinite number of irrational values. For example, to get to .6 from .5, the x value would first half to pass through irrational values like .534324324564267879657565....
you get the idea. Since the function has to be continuous, and has to always be rational, the value is thus always stuck at 1/2.

Did I make sense? Sorry if this is a bad explanation.

i understand it at that level its more actually writing it out and proving it.

for example i tried supposing there was some f(x) which was not a half and tried to show that that would break continuity at x=1/2, but i couldnt figure it out. think i also tried the reverse to .

Assume f is continuous and 1/2 at 1/2 and not 1/2 for some x1. Then look at the interval from x1 to 1/2, and use the intermediate value theorem

thanks, that works. the problem comes before the ivt in the book so i was trying to not use it. w/e though, im satisfied.

Do the unit vectors transform as vectors or pseudovectors?

Show that with the substitution [math]x^{-1/2}y, \; t = \frac{2x^{3/2}}{3}[/math] the differential equation

[math]\frac{d^{2}y}{dx^{2}} + xy = 0, \; x>0[/math]

is equal to

[math]\frac{d^{2}u}{dt^{2}} + \frac{1}{t}\frac{du}{dt} + \frac{t^{2}-1/9}{t^{2}}u = 0, \; t>0[/math]

I am unsure of how to start this substitution, as u is differentiated to t. Should I write x^(-1/2) in terms of t, and consider y = y(x(t))?

[eqn] 2^{\aleph_0} = \aleph_\omega[/eqn]

In ZFC this can be refuted using Konig's theorem, but is there a model of ZF (without the axiom of choice) where it is true?

I'm not at all a metereologist, but i just had this idea to buy a water thermometer, and go to the lake near my house every day and measure the water temperature, and then make a chart showing the development throughout the year, along with the relation between water temperature and air temperature.
I did a 5 second google search and couldn't find a website that already does this. some of them only have values from May to September, but i want to know the values for the entire year.
Anyway, i will almost certainly do this, but i don't plan to swim out into the middle of the lake every day. Does it suffice if i measure the temperature at the shore? or is that too inaccurate?
also, i just realized i would be measuring the surface water temperature, not necessarily the temperature underwater. but i don't care that much about the temperature underwater

Where can I read Acta Mathematica Sinica online? I can't find it on libgen, my uni only has the English version, etc. Assuming it's not in Chinese...

Sup Veeky Forums, there is something I don't understand in these 2 circuits

In the left one I thought about applying KCL in that node, and that would give me I = 1 + 2 +3 = 6mA and V = 6V. The answer is actually I = 3mA and V = 3V in the resistor but I have no idea why.

Something similar occurs to the right one, but this time he wants the voltage across the diode, so it gives I = 4mA and V = 1. I really can't see this and why in the left one the higher voltage(3V) prevails and in the right one it's the lower(1V)

Thanks

One thing many people struggle with initially is trigonometry, logarithms, and basic algebra. Be sure your algebra skills are acceptable, work with trig, and know what a logarithms is and you should do fine :)

>I thought about applying KCL in that node and that would give me I = 1 + 2 + 3 = 6 mA

why the fuck would it give you that

also

>Figura
lmao

Is there some additional info about the diodes?

judging by the answer from the answer book he clearly looked at, Vt is zero

Download hyperbolic games

I havent done that shit in a while, but wouldn't it make sense that the non-linearity of the diodes cause the resistance of the 1v and 2v diodes be higher than of the 3v one?

I went full retard on different voltages in the same node, shit is impossible,
The section of the book is about ideal diodes so you should consider it an open circuit or a short circuit.

Btw I figured it out, it's batshit obvious, you can only have the higher voltage in the left and the lower one in the right because otherwise it contradicts the whole shit, it can only work that way.

Thanks for your time anyway.

The only real hyperbolic game is 2D.

if there is an uncertainty in position for each individual particle in my body, is there a (albeit extremely low) chance every single particle in my body simultaneously teleports to the moon, teleporting me to the moon as well?

Not if it would transfer information faster than the speed of light in the process.

what kind of shit does the government inject you with in boot camp? is it even something to be alarmed about, like "this will make you invisible to radar" type shit?

It's not a meme, it's extremely important. However, type theory is still poorly understood so it's probably not the "final" version. People are still actively working on it. It will take some major cultural change and more concrete benefits before most mathematicians adopt it.

>People like Lurie opposed it from the start.

Source? Lurie has admitted to not knowing shit about HoTT, even though he made some angry blog comments about it. (PS: Grothendieck toposes are for noobs.)

It doesn't really have one, just use parentheses to make it clear.

Glad you figured it out. Diode behavior is not always immediately obvious. As a general rule, if there are competing possibilities for a shared cathode node in a set of diodes, it has to be the largest voltage of the possibilities. Conversely, the reverse is true for the anode side (it must be the lowest of the voltage possibilities). But you already know that now.

I like math
I like neuroscience and psychology
I like microbiology
I like applied physics
I have nearly completed minors in all of these.
How the fuck do I choose a major?

I've never struggled with an idea as much as I do with matrix algebra systems.
>It's just highschool math! Haha brainlet.
Don't get me wrong, I understand the process of it just fine. But when I go to write it down I fuck up the whole thing. I write 3 instead of -3. I type one of the countless fractions into the calculator wrong and it fucks everything up.
Am I a brainlet, doing it wrong, or is this normal?
I have until Tuesday to get my shit together.

bookkeeping errors will always be more common in subjects like linear algebra where you have to perform a large amount of computations

some things you can do to help minimize this are
>slow down
>write bigger/clearer
>don't try to skip steps by doing them in your head
obviously you need to balance going slow with actually finishing the exam but most tests will give you enough time to be careful

Thanks user.

I feel that pain, brother. Love of math, cogsci, physics, comp sci, economics, actuarial/financial mathematics here. Just pick one and do it. Open up a broad second degree and take courses as you please, you don't even need to finish it.

I've had very slight nausea that hasn't made me vomit at all every day for like 4 weeks. Should I be worried that I have some kind of cancer or something?

It's probably just a side effect from the pollution of living in a third world country.

Puerto Rico isn't third world

Should I major in astrophysics?

This is probably dumb but how do I rearrange this equation to solve for x?

[math]309,000 = 0.1 * 2^x[/math]

I got quite lost after trying to xrt 309,000

You divide .1 from both sides, then take the natural log of both sides and use the natural log rule to bring the x down, divide by the natural log of two to get your answer.

Should look like this

X=ln (309,000/0.1)÷ ln (2)

Thanks buddy.

Is there anything significant about the fact that you can solve the equation
[math]a^x=b^x, a\neq b, x\neq 0[/math]
By using complex numbers? Does anything care about finding this "intersection"?

Did ancient namefags of Veeky Forums actually built a small rocket and shot a squirrel into low orbit in early 2010?

>ok that makes sense. then what the fuck is the point of g1 and g2 mapping the same element to the same shit from Y to Z then if f is the only thing that is of interest here in terms of surjectivity?
because points in CT are arrows 1->X, and generalize dpoints are X->Y (meaning any arrow), but all definitions are meant to work with general arrows, not just points 1->X which come from set theory.

g1 and g2 are the points x and y in the domain of f, but now in CT points are general arrows

>astrophysics
lots of coding, but since it is applied physics, you can find tenure

>>Anyway, i will almost certainly do this, but i don't plan to swim out into the middle of the lake every day. Does it suffice if i measure the temperature at the shore? or is that too inaccurate?
depends on your goal

>>what is the precedence of the sum (sigma) operator ?
Reminder that it is a frnech who used Sigma for sum

What is it like applying for postdocs after PhD? What are all these ``rumor mill'' things?

Seeing as we dont understand how the universe was created why is it generally accepted that matter and antimatter were created in roughly equal amount and CP violation is needed? Why could the universe just not be created with a large matter dominance seeing as we dont understand it meaning that the small CP violation we see is no problem?

>ok that makes sense. then what the fuck is the point of g1 and g2 mapping the same element to the same shit from Y to Z then if f is the only thing that is of interest here in terms of surjectivity?

for monic f, g1 and g2 are points.
fg1= fg2 => g1 = g2
because points in CT are arrows 1->X, and generalize dpoints are X->Y (meaning any arrow), but all definitions are meant to work with general arrows, not just points 1->X which come from set theory.

g1 and g2 are the points x and y in the domain of f, but now in CT points are general arrows

for epic f:X->Y, g1 and g2: Y->Z are any functions
you want f surjective =>[ g1f=g2f=>g1=g2]
the thing to remember is that functions are defined on the whole of their domain, so here g1 and g2 are defined on the whole of their domain say Y
so if f surjective you have g2=g1

for [ g1f=g2f=>g1=g2]=> f surjective

you want f(X) = Y ie X = f^-1(Y)
but with [ g1f=g2f=>g1=g2], you can choose Z={0,1}
Z={0,1}
g2= cst function 1
now you must find a function g1 st g1f=g2f, so that you get for free g1=g2=cst 1 (1 meaning true)
define g1, for any y in Y, g1[y]=1 iff y in the set f(X), 0 otherwise

now g1f=g2f because you did everything to make it so.

what matters is that, when f is surjective, f reaches the whole of the domain g1 and g2, so you clearly see that if f surjective, g1 (any point point of Y) = g2(any point Y) , then it is natural to have to expect g2=g1. surjectivy means precisely that g1 must be equal to g2

>>Reminder that it is a frnech who used Sigma for sum
for the first time

also, read set for mathematics to move from set theory to CT

1. How do we know Na is positively charged and OH is negatively charged? Same situation with 2.

3. Why do we write chemical equations that way instead of other ways? More importantly, how do we know what order to write them in?

Brainlet questions I know but my textbook doesn't really explain this.

[math]\displaystyle\sum_{k=1}^{N}\frac{1}{k}[/math]

Is there a way to find what N would have to be for the sum to reach a certain value?

can someone post the compsci book guide of Veeky Forums

also is there such a thing for pure math?

Let [math]a, b[/math] be two 9-digit numbers made out of all digits from [math]\{1,2,3,4,5,6,7,8,9\}[/math]. Prove that there is no [math]a, b[/math] such [math]a + b = 1000000000 (10^9)[/math]. How do I do that? I have no idea where to start.

Hardly, you need fuckton of power to get to low orbit. It's 160 km high, no amateur rockets made it that high.

Maybe the errorterm of this will help:
[math]\sum_{1}^{s}\frac{1}{x} \approx \ln{x} = \int_{1}^{s}\frac{1}{x}dx[/math]

O is a double electron acceptor.
H is an electron donor.
S is whatever.

I can give you a bound.

recall that [math]\sum_{i=1}^{\infty}{\frac{1}{i}}[/math] diverges because the sum of the second terms is greater or equal to 1/2 and the sum of the next 2 terms is greater then 1/2, the next 4 terms are greater then 1/2 and so on.

So for a bound for N calculate 2v, where v is the value and then take [math]\sum_{i=1}^{2v}{i^2}[/math]

This gives you a (pretty bad) upper bound, which certainly can be improved.

Can somebody recommend a discrete mathematics textbook?
My class was taught using zybooks and my teacher was incompetent, and I plan on going into some cryptology classes later. Would prefer not to be blindsided.