/sqt/ - Stupid Question Thread: Sheaves Edition

5/6 Part c

6/6 Part D
T-t-thanks guys.

I have 20 chickens
Every 10 minutes, every chicken lays an egg, 1/10th of the eggs become chickens after 10 minutes (the rest don't develop into chickens)
1. How many chickens do i have after 8 hours?
2. What's the equation for this? I'm assuming something is integrated and it seems really simple but i guess i'm too tired to understand it.

Explain this to me as I don't understand it.

How is the probability that there are two of the same die be 90/216? I understand how that value is produced by subtraction of the probability that all the dies are different and that all the dies are the same however I don't understand the reasoning for

>(If you want to convince yourself of this, think of it this way: There are six possible values that A could be, five possible values of what B could be, and three possible choices of which die could be B. This is 6 x 5 x 3 = 90 combinations out of the 216).

Shouldn't it be 6 possibilities for the first die, 5 possibilities for the second and two possibilities (either the same as the first or the second die) for the last, ergo, 6*5*2 = 60 and the probability for exactly two being the same be 60/216?

>Shouldn't it be 6 possibilities for the first die, 5 possibilities for the second and two possibilities (either the same as the first or the second die) for the last, ergo, 6*5*2 = 60 and the probability for exactly two being the same be 60/216?
youre not counting the 30 cases where the first two dice are the same

That possibility is excluded because the second die cannot have the same value as the first. The third die is the one that makes the pair.

>That possibility is excluded because the second die cannot have the same value as the first.
why not?

Six probabilities for the first die (any number from 1-6). Second die is constrained to 5 values (1-6 exempting the value of the first die).

>Second die is constrained to 5 values (1-6 exempting the value of the first die).
why? youre just not counting these valid cases of 2 matching dice for some reason
(1,1,2) is a 2 match just like (1,2,1) or (2,1,1)

there are 6 3-matches (A,A,A)

you can change any of these 3 to one of the 5 values of B =! A to get a 2-match

so 3*5=15 'switches' of a 3-match give a 2-match

and there's 6 3-matches, so 6*15=90 2-matches

Got it.

It took me 4 posts to get the Sheeve joke

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anyone know of some decent videos/online notes for babby model theory?

What is the meaning of that goofy looking O?

So am I all good? Sorry I can't read some of the writing properly. Thanks for helping out!!!

iirc its order

so in your pic, it means terms of order at least dx^2

i.e. Adx^2 + Bdx^3 + Cdx^4 + ..... for some A,B,C...

How can I scientifically last longer in bed? Yesterday I came just from my girlfriend rubbing on me and then I pretended not to want to have sex to hide the fact that it happened. We're supposed to have sex today instead and if I don't cum at insertion I'll do so in like 10-30 seconds. What do I do?

tactical wank m8

care to explain?

Thanks that would make sense in the context

What said is partially correct, but it's not the full story. In general, [math]f(x) = \mathcal{O}(g(x)) \text{ as } x \rightarrow \infty \Leftrightarrow \exists M > 0 : \exists x_0 \in \mathbb{R} : \forall x \ge x_0 : |f(x)| \le M|g(x)|.[/math] Basically, at some point [math]x_0[/math] the ratio [math]\left|\frac{f(x)}{g(x)}\right|[/math] can be approximated by the positive real number [math]M[/math] once we pass the point [math]x_0.[/math] If we're only interested in this around a point [math]a,[/math] in which case we write [math]f(x) = \mathcal{O}(g(x))[/math] as [math]x \rightarrow a,[/math] what we should be able to do is we say that there should exist positive real numbers [math]M[/math] and [math]\delta[/math] such that [math]|f(x)| \le M|g(x)|,[/math] when [math]0 < |x-a| < \delta.[/math] In other words, if we're sufficiently close to [math]a[/math] but not at [math]a[/math] then we can approximate the quantity [math]\left|\frac{f(x)}{g(x)}\right|[/math] by the positive real number [math]M.[/math] Usually though, we're mostly interested in the case where [math]a = 0[/math] because then we can do nice things with infinitesimally small things etc..

I appreciate your effort and rigour but there are more symbols I don't recognise or fully appreciate. I'm coming at this maths from a physics perspective and they only teach us the maths we most immediately need

Check out the trollface on PBS youtube infinite series video. I LOLLED.

Hey guys,

I'm parsing files (Wiki pages, basically) using the re package in python (might not matter) and I'm having problem with the following. The structure is as such

=== Header1 ===
[[link1]], [[link2]],
[[link3]]
=== Header2 ===
[[link3]]
=== Header3 ===
[[link1]], [[link2]]

This is read in as a STRING, i.e.
STRING = "=== Header1 ===\n[[link1]], [[link2]],\n[[link3]]\n=== Header2 ===\n[[link3]]\n=== Header3 ===\n[[link1]], [[link2]]"

Here the names are dummies. Names and quantity of headers and links is basically random

I'd like to get the data, e.g. in a dict.

d = {"Header1": ["link1", "link2", "link3"], "Header2": ["link3"], "Header1": ["link1", "link2"]}

And here is the reference for the re package I use to try and assemble some code

tutorialspoint.com/python/python_reg_expressions.htm

Absolute uneducated plebian here, I need help with neuroanatomy and neurotransmitters. My best friend is a unifag and he's under a ton of stress right now, he needs to get an A in this class but he tells me that he doesn't know enough about "neuroanatomy and neurotransmitters". I've only taken biology courses, but I really want to help him out, take away some of the insane stress he's got.

Can any of you recommend some books on the subject I could read, take notes from, then give to him? Hopefully it'll be like he's reading two books at once.

I should mention also that apperently it's a class about drugs and how they affect the mind.

I'm attempting to be an active learner by taking notes from the math textbook that I'm reading, but I want to know the best method of taking notes.

I am already doing all of the practice problems at the end of the book, however I'd like to combine this with an effective note taking method (since I am doing this self-didactically.)

Can anybody help me find the azimuthal angle phi in which the planes x-z=0 and z+y=0 intersect? My math is telling me it should be phi=arctan(y/z)=arctan(1)=pi/4 but when I put that into my software it is not quite right, it in fact is tangent to the middle of those planes. The close I got was about 0.95, but I want an exact answer and the math behind it.

jerk off some time before going so that you can stay cool for a while

more of a request, but does anybody have that image where a guy tells how he taught some 4th grader he tutored algebra? If I remember he used things like times tables, gave the kid structure because his mom was always away, etc

Anyone know what this is?
I was just playing some vidya, looked down for some reason and noticed this on my forearms. Both, nearly identical pattern.

Looks like burst blood vessels. I assume I was just sitting weird and blood flow was not ideal or something.

Only time this ever happened was sometimes when I have sex or masturbate my chest flushes. I dont have leukaemia

DO I HAVE CANCER? ITS WHAT GOOGLE TELLS ME

Anybody know of good sites to help get through Physics III course. It's over relativity, quantum mechanics, and nuclear(? vague on syllabus). Anything helps thanks

Anyone?

what does Veeky Forums have against Stewart calculus?

G-g-guys what do you think?
Here's a rare gif for you.

They look like abrasions.
The major blood vessels don't go that way.

Do you get sweaty their often? Does it rub?

I think ilectureonline is pretty good. Haven't used it for physics III though so dunno.

Why does the categorist cross the road?

I'm doing a project with under water water communication. I am using this article as a reference file.scirp.org/pdf/JEMAA20110700001_18390291.pdf
I'm confused what conductivity for the water they are using. In the abstract he say average conductivity is 0.01 S/m for fresh water, but in (3) the Debye parameters of water is 17.1 S/m. Any guess what the conductivity of water is being used for the charts?

Thanks bud looks like a useful site

How often are useful contributions made by those who did not go on to grad school (autodidacts)?

I think I'm droppin' outta the race boys

Is (∃x)(¬P(x) ∨ Q(x)) equivalent to (∃x)(P(x) → Q(x))?

freshman cs student here please be nice

TA for logic here, that is correct. My textbook calls that the material conditional rule and the replacement should hold regardless of the main operator. (i'm rusty so if i'm wrong pls don't bully.)

in math specifically, btw

I just don't see going into a PhD being a great idea desu, academia seems to be a big circle jerk and grad students are slave labor tier

what are the objective benefits of grad school? certainly I could learn it all outside of the classroom, right?

P implies Q
is (classically) equivalent to
(not P) or Q
and sometimes "implies" is even defined in that way.

The \exists-spiel is unrelated here, and extra.

SOMEONE PLS HELP

∃x)(∀y)(¬y = 0 → L(x, y))

What about something like this?

"Suppose our domain of discourse is all natural. Assume L(x, y)
represents the claim “x is less than y.”"

still a little confused about the order of the two quantifiers

Unfortunately my brainlet class doesn't use that notation, maybe the other guy knows. I haven't fallen for the CS meme yet so we didn't work with numbers, just truth values.

I assume there should be parantheses around "y = 0", so that the: ¬ applies to the proposition 'y=0'.

The way to try and comprehend nested qualifiers is to look at them one at a time, so in fact the statement you have said means:

"There exists an x such that:" (∀y)(¬(y = 0) → L(x, y)).

Meaning, that every time we try to substitute a number into y, there exists a number x such that the proposition holds. Now, from what we know about the natural numbers, this is in fact true.

Since the statement is saying, that when y is non-zero, there exists an x such that x is less than y (which is true, if y = 2, then there exists an x less than it, i.e. 0 or 1, if y =1 then x = 0, and so on).

This is correct.

2 questions about hydrogen -

I've read that a protium atom can theoretically decay, so if it were to decay what would it break down to? I've read that quarks cannot just e it by themselves, right?

Also, how come protium is more common that deuterium?

>what are the objective benefits of grad school? certainly I could learn it all outside of the classroom, right?
You _could_. You could probably do it more or less for free. But you won't.

Doesn't seem right. I'll make my scribbles and post hold on.

Sorry,no time to solve our right now. Gotta run.

## IMPORTANT ##

Actually I have soon my exam and I don't know much about predicate logic. Can someone mention and link some good ressource(s)? I need to get the basics and the general idea/concepts down, rather fast.

Why does pic related not work. Know I probably made a mistake, just wondering where.

me to haha

You have to change it to [math]\sum_{n=1}^\infty n^s[/math] first before manipulating it, then you can sub back in s as 0 later.
It's valid since it does converge for [math]s < -1[/math].
For example it's equivalent to
[math]\displaystyle \frac{1}{s+1} \frac{d}{dx} \left. \sum_{n=x}^a n^{s+1} \right|_{x=1}[/math]
which you can evaluate at positive integers at the very least.

Anyway when you have the n^s it's clear that the steps you took no longer work, since, for example, 2^s =/= 1^s + 1^s and 3^s =/= 1^s+1^s+1^s and so on.

Wouldnt it just be 20 times 1.1^48?
This is assuming you are never rounding to the nearest whole chicken

...

I know how to do matrix multiplications (with whole numbers at least), but I'm not sure about this one question.

A =
[-1 3]
[4 -2]
[5 0]

B=
[-3 2]
[-4 1]

The question asks me to find the product for a) AB and b) BA. a) is easy enough, but what do I do with b)? It can't just be switching the two around because you can't the columns in 2x2 is less than the rows in 3x2.

Sorry if it's a very stupid question...

the question has to be written wrong

you can only multiply a mxn matrix A with a axb matrix B if a=n (# of columns of first matrix needs to equal # rows of second matrix)

I have a flat 8x6 inch object that weighs a pound. It's rectangular with rounded corners

I need a plausible way for this to generate a small amount of lift enough to cause it to momentarily move upwards if it's moving fast enough horizontally. It can be rotating or spinning or not.

I just need some explanation of how it could have moved in an upward arc and not simply forward and downward

The other user already answered your question but I'd still like to reiterate, elaborate, and suggest a MNEMONIC.

Consider two matrices [math] Y [/math] and [math] Z [/math] , whose entries are all complexes (that is, complex numbers, of which natural numbers, real numbers and so on, are all specific examples) and thus the crunching is amenable to the usual arithmetic. Let us reiterate along the lines of what the above poster wrote: Let us specify that the number of rows in Y is m, the number of columns in Y is n, the number of rows in Z is a, and the number of columns in Z is b. We may if we wish, write a subscript for any matrix at our convenience, to specify these quantities. By convention, a matrix's number of rows is ALWAYS written first, and a matrix's number of columns is ALWAYS written second. Thus our two matrices can be written as [math] Y_{m \times n} [/math] and [math] Z_{a \times b} [/math] . By definition (hopefully, obviously) all of m, n, a and b are natural numbers.

As the other user as-good-as-said, matrix multiplication is only defined when the number of COLUMNS in the first (left) matrix, is equal to the number of ROWS in the second (right) matrix. Thus, in order for the the product [math] Y_{m \times n} Z_{a \times b} [/math] to be evaluated, defined, worth doing and not looking stupid in trying, we immediately require that n = a, just as the above user said. This allows the arithmetic to work out in a well-defined way, you just have to be careful to do your boring bookkeeping while crunching.

FURTHER, continuing with the above, the RESULT of such a matrix multiplication, IS a matrix whose number of rows is EQUAL to the number of rows in the first matrix, and whose number of columns is EQUAL to the number of columns in the second. Thus, if n = a, then the above product is indeed defined, and may be expressed thus, as some matrix [math] W [/math] : [math] Y_{m \times n} Z_{a \times b} = W_{m \times b} [/math]

cont.

If I have a (pseudo)random number generator that outputs numbers uniformly distributed between 0 and 1, how do I play with these numbers so the distribution fits an arbitrary PDF?

I want to study physics. Do you guys knows some good textbooks?

I don't know calculus, but I can learn if necessary, but I don't want to take like 6 months on it

Now for the mnemonic which I recommend to you: if you know to write basic information for matrices out in this way, then you can do a little "cancellation" trick to simplify and know what you're driving towards, ahead of time. Sharper anons should know where I'm going with this.

Continue with the above example, where n = a and the matrix product W is defined. In determining the product W, I like to imagine (as a slight abuse of notation) that the inner two dimensions n and a "cancel", or whatever word you prefer. In any event they "go away" in the course of evaluating W, so that (again, abusing notation), you might write something like:

[math] Y_{m \times a} Z_{a \times b} = Y_{m \times \rlap{/}a} Z_{ \rlap{/}a \times b} = W_{m \times b} [/math]

where I simply replaced n with a because, after all, they're equal and you could have done the other if you'd pleased. As you see in my notation, the two inner dimensions "vanish", and the real point of this type of activity (which is so dumb-simple that it can of course be done mentally once you understand the motivation, which is to have a clear idea of what a matrix product is going to look like in terms of dimensions) is simply to look at what's in front of you and figure out whether what is proposed is a defined multiplication, or a trick question where the proper homework response would be "undefined".

Let us now turn this elaboration to the concrete example. You provide [math] A , B [/math] and are asked to evaluate AB and BA. We have

[math] A_{3 \times \rlap{/}2} B_{ \rlap{/}2 \times 2} = C_{3 \times 2} [/math]

[math] B_{2 \times 2} A_{3 \times 2} [/math] is undefined, as [math] 3 \neq 2 [/math] .

I don't recommend writing the mnemonic down on a homework assignment (a professor might be pedantic about it), just use it mentally. The above is how you answer this type of question properly - there is sufficient context in the line for the professor to be confident that you get it.

do those buttons at crosswalks actually do anything? the ones you press when you want to walk across

in my personal experience they never seem to reduce the timespan between light changes

A-a-anyone? ;__;

You cant subtract infinity from inifinty

at (relatively) busy crossings no, they are purely placebo. infrastructure planning is tough to get right, why would a city planner say "eh fuck all the logic behind how i designed this intersection, let the pedestrians always have priority", especially on a major street?

on smaller streets where there may not be much traffic (or rather, where traffic is very variable, for example a residential area where people go to work at 9 and come back at 5, but almost no cars in between), the buttons are pretty much guaranteed to let you through real soon.

Is a natural law (ex. the speed of light) comparable to a school schedule in terms of how it could change? Related to uniformitarianism.

>9
look at the truth tables and see for yourself jackass

You usually do not need to take notes as if it were some life science course. Do the exercises and when you get stuck, that is what the handful of examples in each section are for.

is the product of two hermitian operators itself hermitian?

I want to be a badass chemist. Which upper year chemistry courses are necessary for this? I'm assuming Organic and Biochemistry are mandatory since those are prerequisites for everything.

If your only good skill is memorization, then you should be in Veeky Forums.
looks like someone failed their logic class and realized that computer science isn't vidyagame making degree. go to /a/

are you not already a chem major at your uni? organic is like intro chem for chem majors. even after undergrad and you take some higher level courses you've still got a long ass way to go.

study hard in your physics and math classes so you don't die in physical chemistry. learn programming because computation is really important. you kind of sound like either a freshman or someone who just finished breaking bad

I need to combine linear falloff of explosion force with distance and inverse square falloff of explosion force with distance.

Obviously it's impossible to have true inverse square that is zero when distance = blast radius, but what would be a good imitation?

The points (1, 3) and (−2, 6) lie on a line. Where does the line cross the x-axis?

Ik how to do this easily with y =mx+b, but I'm in a linear algebra course and I need to do it using a matrix.

I set up the matrix
1 -2
3 6
But then what? If I try to make it go to reduce form, it just becomes
1 0
0 1

you have the equations
3=m+b
6=-2m+b

so the matrix equation is
[1 1][m]=[3]
[-2 1][b]=[6]

invert the matrix on the left to solve for the vector
[m]
[b]

or i guess you want to solve
(1,3)+t[(1,3)-(-2,6)]=(x,0)
(1,3)+t(3,-3)=(x,0)
(1+3t, 3-3t)=(x,0)
so need t=1
so x=4

Watch this entire series.

youtube.com/watch?v=kjBOesZCoqc&list=PLZHQObOWTQDPD3MizzM2xVFitgF8hE_ab

Thanks, this helped

What about something like this?
"The points (3, −1, −5), (1, 4, 14), and (5, 3, 3) lie on a unique plane. Where does this plane cross the z-axis?"

I got the answer as z = 4 but I had to use vectors and cross products (I'm supposed to use matrices in linear alg or something else, not cross product).

I tried setting up a matrix in the form

ax + by + cz + d = 0

1 4 14 1 0
3 -1 -5 1 0
5 3 3 1 0

But I think I did it wrong.

I then tried again without the zeroes at the end (ax + by +cz = d) and I got nice looking answers (a = 1/2, b = -3/4, c = 1/4, but I'm not sure what to do with those answers)

>(3, −1, −5), (1, 4, 14), and (5, 3, 3)
you can write
(0,0,z)=(3,-1,5)+t[(3,-1,5)-(1,4,14)]+u[(3,-1,-5)-(5,3,3)]

use the first two equations to solve for t and u, then substitute it in to get z=4

just looking for a hint, not a solution

given a continuous function f from the unit sphere embedded in R^3 to R, show there exists an orthonormal basis u1,u2,u3 of R^3 with f(u1)=f(u2)=f(u3)

i can do it when its a function f(theta):[0,2pi] to R from the unit circle in R^2 instead of the sphere in R^3 but i don't know if the proof is adaptable.

an orthonormal basis u1, u2 in R^2 has a pi/2 angle between them so we can consider the function f(theta)-f(theta+pi/2)

since the circle is compact f has a maximum u and a minimum v

these satisfy f(u)-f(u+pi/2)>0 and f(v)-f(v+pi/2)

Use the inverse of the CDF (inverse transform sampling).