/sqt/ - Stupid Questions Thread: Contracting Homotopies Edition

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Post all your stupid questions that don't deserve their own thread here.

What's the motivation behind this definition of [math] t_n [/math] in Rotman's algebraic topology textbook?

Other urls found in this thread:

en.wikipedia.org/wiki/Diagonalizable_matrix#An_application
en.wikipedia.org/wiki/Rule_of_inference
desmos.com/calculator/v9vuw6mhlk
lmgtfy.com/?q=statistics in excel
en.wikipedia.org/wiki/Bayes'_theorem#Statement_of_theorem
ncbi.nlm.nih.gov/pmc/articles/PMC4706048/
twitter.com/SFWRedditGifs

I'm trying to quantify how much amperage a capacitor could push out, compared to a regular DC voltage source.

Say you charge a 100uf capacitor to 200 volts. We can get the energy in joules by: 0.5 * F * V^2 = 2J. Since 1J = 1W, does that mean that the maximum current the capacitor can dish out is W/V = 10mA?

Could some of you /lab/ fellows answer the following questions:
>what are you majoring in?
>how many hours do study a week?
>best part of being in a lab?
>worst part?
>any regrets?

What exactly are you asking? If the complex is acyclic then t_n, so defined, is a contracting homotopy. The motivation is that it proves the theorem.

>What exactly are you asking?
Obviously the definition proves the theorem, I'm asking how would one come up with such a definition of the [math] t_n [/math]?

a capacitor can dish out as much current as ohms law allows, but it will only be instantaneous as a capacitors voltage will drop with time

Vc is a function of time, and W has a dimension of time, so the equation W/Vc = 10mA doesn't really make any sense to me, there might be some use for it but I have no idea what the 10mA even signifies

I guess I was looking for a way to figure out how big of a capacitor I would need for it to be able to dish out as much current if you connected it to something for 1 second, as a regular power source.

Assume a reliable 10v power source connected to a 100ohm resistor for 1 second. That would be 100mA of power flowing.

Replace the power source with a capacitor charged to 10v. How many farads of charge would it need to be in that capacitor to be able to dish out the same current?

is earth rhombus?
will gw fags ever admit defeat?
when will atheists be able to define atheism?
is string theory really the most noble field of study?

>is earth rhombus?
probably not
>will gw fags ever admit defeat?
maybe
>when will atheists be able to define atheism?
eventually
>is string theory really the most noble field of study?
no

How the fuck do magnets work?

how do we solve the poo-in-loo problem? do we install subcutaneous mind control microchips that push the need for "self respect"?

does jet fuel soften steel beams to the point of structural weakness to below it's design and ultimate F.O.S.?

It's fascinating that in the Stupid Questions Thread average IQ is about 20 points higher than the rest of the Veeky Forums

how do i get A^2014?

A=[5 1 9, 0 5 1, 0 0 5]
>A -> matrix
what term should i search for to find solution for problems like this

en.wikipedia.org/wiki/Diagonalizable_matrix#An_application

The following are equivalent, right?
[eqn] \forall \epsilon > 0 ~ : ~ \exists \delta > 0 ~ : ~ \forall h \in \mathbb {R} : 0 < |h| < \delta \implies \frac { | f(x+h) - f(x) - Th |} { |h| } < \epsilon [/eqn]
And
[eqn] \lim _{ h \to 0 } \frac { | f(x+h) - f(x) - Th |} { |h| } = 0 [/eqn]

The first is clearly just the definition of a limit, with [math] c = 0 [/math]. But I don't see where the =0 part comes from.

Dunning–Kruger effect

Yes

any capacitor with an initial voltage of 10V will only produce 100mA of current for an infinitesimally small amount of time

the capacitor with an initial voltage of 200V would need to be 3.34 milliF to keep at least 100mA of current for an entire second or 500microF to keep an average current of 100mA

both of these would probably just burn the shit out of the resistor anyways

equation I used for this was
[math]I=\frac{V_0}{R}e^{\frac{-t}{RC}}[/math]
[math]C=-\frac{t}{Rln\frac{IR}{V_0}}[/math]

When do I start using series/sequences from calculus in future math classes?

how the shit do I proof by induction pic related

Base case [math] n=2 [/math], [math] 1 + 4 < 8 [/math]. Well that checks out. Now we want to prove that [math] 1+ 2^2 + \cdots + (n+1)^2 < n+1)^3 [/math]. So we ASSUME that to be true and go from there. All you're really doing is a series of algebraic manipulations, so in your case: [eqn] 1+2^2+3^2 + \cdots + (n+1)^2 \\ = 1+2^2+3^2 + \cdots + n^2 +2n + 1 < n^3 + 2n + 1 ~\text { by the inductive hypothesis } \\ < n^3 +3n^2 + 3n + 1 \\ = (n+1)^3 [/eqn] The second line might trip you up, all that we've done is expand [math] (n+1)^2 [/math] and noticed that it gave us our original series, but with [math] 2n+1 [/math] added on the end. Since we assumed that [math] 1+2^2 + \cdots + n ^2 < n^3 [/math] it follows then that [math] 1+2^2 + \cdots + n ^2 +2n+1 < n^3 + 2n+1 [/math]. The chain of inequalities follows from the fact that [math] n>1 [/math]

>So we ASSUME that to be true and go from there

Sorry, that should be:
>We ASSUME [math] \sum k^2 < n^3 [/math] to be true.

I have a series of points that are uniformly distributed in a certain slice of the unit disk (y>=x>=0).
How do I calculate the covariance of x and y?

I was following the example in the pic related (the white notes are from the video, the rest ugly written are my notes, sorry about that), from a youtube channel I found, so I proceeded likewise

but when I reached p^2 as you can see, I did p^2 + (p+1)^2

how wrong is that?

I can't do the fancy writing here, sorry, math is alien to me, but I'm trying to solve every exercise I'm given

I'm supposed to solve this by Picard iteration, but what exactly am I supposed to use as my starting point? Using 0 will just continue giving me 0 for all terms in the series .. Or is that supposed to be the case? Can the other solution only be obtained via separation?

You could do it like that, but (imo) it's more cumbersome. The way I was thinking about it is:
>You don't care about the nth term anymore, just the (n+1)th term.

What they did in that video was to show that the [math] 1/(c+1)^2 [/math] term was just the original series with an added term. That's exactly what I deduced as well, except only by looking at the (n+1)th term.

If you wanted to to it the way you're doing it, then what you'd do is:
>Notice that [math] 1 + 2^2 + \cdots + n^2 + (n+1)^2 [/math] is the our original series with [math] (n+1)^2 [/math] added on.
>So we use our induction hypothesis: [eqn] 1 + 2^2 + \cdots + n^2 < n^3 \\ \implies 1 + 2^2 + \cdots + n^2 + (n+1)^2 < n^3 + (n+1)^2 \\ = n^3 + n^2 + 2n + 1 \\ < n^3 + 3n^2 + 3n + 1 \\ = (n+1)^3 [/eqn]
>Notice that in the second to last line we ended up in the same place as before.

And you're done. Does that make sense?

>And you're done. Does that make sense?

it totally does, beautiful, thank you user

Good to hear. Induction can be a touch tricky when you first learn it because some of the ideas seem to come from nowhere (for example how did I know to massage [math] n^3 +2n+1 ~~ \text { into } ~~ n^3 + 3n^2 + 3n + 1 [/math]? Well the answer is I cheated, I looked at what I wanted [math] (n+1)^3 = n^3 + 3n^2 + 3n + 1 [/math] and then added the required terms. If you end up studying [math] \epsilon - \delta [/math] proofs, a similar "trick" is used then.

Also the "fancy writing" is scalled latex, it's not too hard to learn and is helpful when trying to communicate your ideas, especially over the internet. You can write inline by using [ math ] [ /math ] only without the spaces and block using [ eqn ] [ /eqn ] again without the spaces. There's a bit of an issue with how Veeky Forums parses your commands though so it's advisable to throw in whitespace everywhere, for example a fraction would be written as \frac { } { } instead of \frac{}{}.

you saved me, when I hit an exercise I can't solve, I cannot progress until I get it right

I've been meaning to learn a LaTeX, kinda feel like an idiot when typing "x^2"

oh well, thanks again, you've made my sunday

Given that I know [math]Pr(A)[/math], [math]Pr(B)[/math] and [math]Pr(A|B)[/math], how do I work out [math]Pr(A|B^C)[/math]?

In logic, or propositional calculus, what is the difference between a transformation rule and a rule of inference?

en.wikipedia.org/wiki/Rule_of_inference

This page seems to list Rules of Inference as a subset of Transformation Rules (in the image on the right), but then in the first sentence implies they're synonyms.


Pls, satisfy my autism

A[1,2,2] and B[2,3,0] lie on p
C[4,0,5] and D[5,1,2] lie on q
p and q are skew lines and (1,2,3) is the direction vector of their transversal r
R[?,8,?] lies on r.

how do I find the distance |C,R|

I can't get this going at all

answer's supposedly sqrt20386

Anyone?

Having a small physics problem (reposted from yesterday's sqt)
Okay, I'm having trouble witha simple physics problem:

The problem asks "What's the acceleration between the two blocks (which are connected by a pulley system)?" When I found the net force, the system moves in the direction of the 100kg block.

But here's where my problem lies:shouldn't the acceleration of the two blocks with different masses be equal? Intuitively, it seems difficult to see how F_net = ma applies here when the net force in the system will give different accelerations...

What am I doing wrong?

>the net force is applied to the combined masses, not the individual masses

=======
Anonymous 01/29/17(Sun)08:19:29 No.
Okay... Then to find the acceleration, would I do:

Mass 1 Net Force = (Net Force / Mass1+Mass2) * mass1
and
Mass 2 Net Force = (Net Force / Mass1+Mass2) * Mass2?

I'm kind of confused about something.

How come the graph of sqrt(4-x) moves 4 units to the right instead of to the left? I thought anything under the radical or within parenthesis with an X moves the opposite direction of its sign.

We've not went over anything like this specific problem and I really don't understand why it would move like that.

The parent function would be sqrt X, I believe. I could be wrong. Don't recall if making the X negative counts as a transformation or not.

Yes, it's the definition of f'(x) converging to T.

Unless you're into a math major, epsilon-delta proofs are rather annoying and don't see much use. Just learn limit arithmetic and go from here.

The easiest way to find out why is working out the points on the graph yourself

Because [math] y=0 ~ \text { when } ~ x=4 [/math] I don't know how else to explain it.

I'm having trouble understanding part of a proof of the Lyapunov function theorem (for non-strict Lyapunov functions). Pic related is a statement of the full theorem. Here is the proof I have:

By continuity of V, we can find [math]\delta > 0[/math] such that [math]|x| < \delta[/math] implies [math]V(x) < \epsilon[/math]. Then if [math]|x(0)| < \delta[/math], we have
[eqn]
\frac{d}{dt}(V(x(t))) \leq 0 \implies V(x(t)) \leq V(x(0)) < \epsilon \quad \forall t \geq 0.
[/eqn]
So we may conclude [math]x(t)[/math] is contained in the set of [math]\{x \in U \mid V(x) < \epsilon\}[/math].

We need to show [math]|x(t)| < \epsilon[/math] for all [math]t \geq 0[/math], but I don't see how that follows from what we've shown.

>I thought anything under the radical or within parenthesis with an X moves the opposite direction of its sign.
General advice: Don't think in such absolute terms. These "rules" work for certain given reasons - dig in and find out those reasons.

So if the x is negative it kind of reverses things? It seems kind of obvious now that I look at it when actually finding pairs. I had just assumed the "opposite whatever it's under" applied no matter what.

Does that mean sqrt-x actually was the parent function or did I have it right when assuming it was just sqrt(x).

It's been a while since I went over this stuff in detail, and right now we're at the stage of zooming pas everything to get to the new stuff, so a lot of examples are very brief.

Is it possible to live without consuming anything that was once part of another living thing?

Since you can't eat rocks, no.

I find it's helpful to try to think of these things more generally and then try to apply this to particular functions.

Suppose I have a function f(x). There are four simple ways to transform the function:
1) af(x). This "stretches" the function vertically by a factor of c. This occurs simply because you're multiplying each output of f by a.
2) f(bx). This "squishes" the function horizontally by a factor of b (relative to zero). This is because you're multiplying the functions input by b, the function will take on values b times as fast.
3) f(x + c). This will shift the function to the left by c. One easy way to see this is to realize that f will take on the value f(0) at x = -c in the new function. Realize then that this will happen with every point. If you want f(x+c) to take on the value f(t), you need x = t - c.
4) f(x) + d. This simply shifts the function up by d. This simply occurs because you're adding d to each output.

Here's a demo I made. I strongly recommend playing around with this until it makes sense to you and feels intuitive: desmos.com/calculator/v9vuw6mhlk

What's the actual definition of direct sum? My textbook says that
[math]
U_1 \bigoplus U_2=\{u_1+u_2 : u_1\in U_1,u_2\in U_2\}.[/math]
But looking up wikipedia, it mentions that [math]
\mathbb{R} \bigoplus \mathbb{R}=\mathbb{R^2}[/math]
but [math]\mathbb{R}\bigoplus \mathbb{R}=\{r_1+r_2:r_1,r_2\in \mathbb{R}\}=\mathbb{R}[/math] according to my textbook's definition. So what's the actual definition?

you actually take the disjoint union, the elements of the sets "don't mix". if they have the same elements you just force them not to be
it's as if you were actually adding Rx{0} and Rx{1} with your book definition

u1 + u2 should be taken as just a symbol. + should not be interpreted as the addition on the underlying group.

i.e. just think u1+u2 = (u1,u2)

So I'm really interested in sound (digital, analog, and such since I'm an EE) but I'm also interested in acoustics and how sound propagates in reality, how timbres changes depending on the surface, so on so forth.

So my question is does anyone know where I find a good acoustics book? Math preferred but not necessary

is there a nice guide on the internet out there to learn about doing statistics based shit in Excel?

Given that the measure for how acidic something is is H+ concentration, why are proteins that have more NH3+ groups basic?

Also, the dissociation constant for acids says your product is H3O+ and a corresponding A- base, but in protein the COO- deprotonated group usually signifies and acid (glutamate and aspartate).

I had a shit teacher in high school and I don't have a problem understanding most of biochemistry but this shouldn't be 'not-right', right?

lmgtfy.com/?q=statistics in excel

I wish people asked and others answered questions that can't be solved by google

Am I retarded?

This answer is apparently wrong. But... the rank of the matrix is 2.

I believe your answer is correct.

Can somebody please tell me where I'm misunderstanding this question before I punch a wall.

> probability that a dog is affected by a certain rare disease is 0.002
> probability of a test returning positive, given that the dog has the disease, is 0.99
> probability of a test returning negative, given that the dog does not have the disease, is 0.95
> find the probability that the test returns positive given that the dog does not have the disease

So we're working under the assumption the dog doesn't have the disease. Either the test returns negative or positive, right? So Pr(positive test, given that dog doesn't have disease) + Pr(negative test, given that dog doesn't have disease) = 1. Therefore the answer is 1 - 0.95 = 0.05. Only this is far too easy for the number of marks and the info given in the question, plus we're supposed to use Bayesian probability formulas. But surely those two probabilities *have to* add up to 1?

>Pr(positive test, given that dog doesn't have disease) + Pr(negative test, given that dog doesn't have disease) = 1
wrong

they just need to add up to Pr(dog doesn't have disease)

which is why you use
en.wikipedia.org/wiki/Bayes'_theorem#Statement_of_theorem

btw i got 0.00051983967 doing it quickly

ncbi.nlm.nih.gov/pmc/articles/PMC4706048/

Does this mean precog abilities really exist?

>>Pr(positive test, given that dog doesn't have disease) + Pr(negative test, given that dog doesn't have disease) = 1
>wrong
>they just need to add up to Pr(dog doesn't have disease)

So [math]Pr(positive test | healthy dog) + Pr(negative test | healthy dog) = Pr(healthy dog)[/math]? Because I have the last two probabilities and the first one is what the question's still asking for. Which is obviously not right.

sorry i meant Pr(positive test & healthy dog) + Pr ( negative test + healthy dog) = Pr (healthy dog)

you cant add up givens like this since you move to a new probability space

You are right, A is the correct answer.

what the hell is [math]\dot V[/math]?

its 0.05

Did you misread the question? A more logical question would be:
> find the probability that the dog does not have the disease given a positive test.

Maybe I'm misreading, but I don't think so.

Newton's dot notation, it means dV/dx.

Dot notation is really always used for a derivative with respect to t. To avoid this notation, the hypothesis is saying that [math]\frac{d}{dt} (V(x(t)) \leq 0[/math], where [math]x[/math] is a solution to the differential equation [math]\frac{d}{dt} (x(t)) = f(x(t))[/math].

Seems you haven't misread, it's 0.05.

You shouldn't overthink this,

Sample group: dogs without disease:
Given the test results either negative or positive.
P(negative)+P(positive)=1

It's the teachers own fault if he accidentally puts in an easy question like this.

Just solved it as a simultaneous equation, you're right. Fucking hell, I just spent 3 hours wondering why I was such a retard. Turns out I'm a retard in a completely different way.

Ok, but then what does [math]{\dot V}(x)\le 0[/math] for all [math] x \in D[/math] mean? How is [math] \dot V[/math] defined off the curve?

[math]\le 0[/math] for all [math]x\in D[/math]?

Is time travel (into the future) possible?

That's correct. Also, you want \langle and \rangle.

should be replying to .

probably not

As you read this sentence you have been traveling into the future.

inb4>How to make it faster?
idk

If some dude has a 40% chance to have object A and a 40% to have object B, what's the probability he has neither?

I was thinking that it'd be 20% but that sounds wrong

Not necessarily instantaneously, but if you go fast enough (approach c), you could experience time "slower" than say people on earth.

Source: 'I F*cking Love Science'.

t. Average newspaper idiot

What the absolute fuck

>Mastering Physics

I'm triggered

Have another

You're looking for probability of not A and not B. You multiply when you want to know the probability of one event and another, so its:
[math] 0.6 \cdot 0.6 = 0.36[/math].
That is, there's a 36% chance of neither.

jesus fucking christ that word soup

Could someone help me figure out what I'm doing wrong?

The question asks for the total charge of the rod, I plug in the numbers and it seems to give me a wrong answer

Pls respond

So I think I need to revise how absolute values work.

With |a+b| is it not |0.9+ (-0.4), but then converted to 0.9+0.4 = 1.3 on the number line? Their answer looks approximate 0.5.
What is it that makes |a| + |b| = 1.3, and how do I get to the answer of 0.5 for |a + b|?

if a= 0.9 and b=-0.4 then
|a+b|=|0.9+(-0.4)|=|0.5|=0.5
and |a|+|b|=|0.9|+|-0.4|=0.9+0.4=1.3

I understand now. So you only convert the answer to positive after what was put in the bracket's expression is finished. Thank you.

[math]P(A|B^c)=P(A\cap B^c)/P(B^c)=(P(A)-P(A\cap B))/(1-P(B))=(P(A)-P(B)P(A| B))/(1-P(B))[/math]

Determine if the given function is a linear transformation.
T(x1, x2) = (5x1 + x2, −4x1 + 6x2)

what's the trick

In Physics 3 right now doing a homework problem and have absolutely no idea what I am doing wrong.
The question goes:

What is the momentum uncertainty of a single photon in the pulse?

Given that the pulse has a duration of 8.60 fs and produces light with a wavelength of 496 nm.

The only equation in the book related to this section is in pic related and has not worked from my understanding of the equation.

just kidding I figured out what I had to do

>look at definition of linear transformation
>proceed

Brainlet here

How does the definite integral make your life easier in physics? I get calculating pi with a definite integral, but how it would be useful in a function of r, v or a over time doesn't click for me.

Nevermind, took 10 minutes to get it.

>>Dot notation is really always used for a derivative with respect to t.
source = undergraduate

now THAT was a stupid question

What is continuous map in topology and how maps work in topology space

preimage of open sets are open

We can define a number i such that i^2=-1.
What would it mean if we tried to define a number j such that j=1/0? Would it even make sense to do so?

assuming 0 is the number 0 in the reals.

division by zero is not defined in a field (the real numbers). So, no, it wouldn't make sense to do so.