SQT Thread - Stupid Questions Thread

Though the answer being looked for is (show that an equivalent expression converges to zero) a somewhat intuitive explanation is that the a spike with no width has no area under it. What you are looking at is a form of the Kronecker delta function, if you want to look it up.

For every [math] \varepsilon>0 [/math] consider the function
[math]f_\varepsilon[/math] which is equal to [math] 1 [/math] for [math] x \in [1- \varepsilon, 1][/math] and [math]0 [/math] else. Then

[math] 0 \leq \int_{-1}^1 f(x) dx \leq \int_{-1}^1 f_\varepsilon(x) dx = \min(\varepsilon,2) \leq \varepsilon [/math]
Since this is true for every [math] \varepsilon>0 [/math] we must have
[eqn] \int_{-1}^1 f(x) dx = 0 [/eqn]

Do humans really affect climate change?

youtube.com/watch?v=ztninkgZ0ws

he explains a lot about what influences climate

>is an ice age coming
we're still in one

what university should you check if you're interested into body implants/nanomachines and all that kind of stuff?

he means in 12000 years

>body implants/nanomachines
no one is interested in a micropenis transplant, trust me.

How do you go from step 1 to 2? I don't see how you get that right side of the numerator to reduce down the way it does. I keep getting something different.

Is there an intuitive explanation for why the sum of all pos numbers is -1/12? I saw the numerphile's proof of it, but it is counter to all intuition.

s goes into a how many times?

it sure is. I didn't understand the numberphile explanation either.

It's not in the traditional sense. We have a thread on this every day. Try lurking or reading one of the hundreds of internet articles on this.

It makes no sense to me. The one I watched they showed what a few sums converge to and then used those facts to manipulate the fact that infinite summation of the positive numbers converges to -1/12. It's almost as if they just did a proof by using trickery, picking certain sums that add to things they needed to show the fact they wanted to present. It's like a magic trick and you're left wondering what the trick was.

Care to point me to a few? I don't see these threads everyday and tried googling it but keep getting the numberphile's explanation.

4gravitons.wordpress.com/2014/01/24/how-not-to-sum-the-natural-numbers-zeta-function-regularization/

We should just sticky a post about this.

they factored out (1+x^2)^(1/2)

sorry, they factored out (1+x^2)^(-1/2)

>4gravitons.wordpress.com/2014/01/24/how-not-to-sum-the-natural-numbers-zeta-function-regularization/

Thanks.

hope this helps senpai. they factored out [math] (1 + x^2)^{-\frac{1}{2}} [/math] in the numerator.

Thanks based user

That's exactly how I felt when I saw it. LIke it was some smoke and mirrors bullshit.

M

what are the steps involved simplifying this:

(1/15((2x+1)^5/2)) - (1/15((2x+1)^3/2)) + c

into this

1/15((2x+1)^3/2)(3x-1) + c

how the fuck do I do this?
don't I need to know the force applied?
I certainly need to know how fast it goes
wtf

I am taking a community college professor who had a PhD. Does this mean this guy is an asshole who doesn't know how to teach?

Mumble something about Riemann integral doesn't care about single points and write 2

math meme man himself

(mg)(y)

it's horizontal

Thanks!
You're probably gone by now, but in case anyone else can help:
I'd just integrate with respect to y if that was an option, but the assignment says to integrate with respect to both; and I honestly don't know how to do it for x because I'm bad at math.

How do I solve using these formulas? No L'hopital's

Taylor expand, you fucknut.

Ezpz

>find the area between the curves x^2+y^2=R^2 and x+y=R
>when trying to find the intercept keep getting results like x=R and y=R which of course doesn't make sense
>for some reason I can't find an example of this question no matter where I search
why

How do I force myself to study?
Drugs, punishment, rewards, etc. What works best?

lighting your computer on fire.

The intercepts are (x,y)=(R,0) and (x,y)=(0,R). The area is just pi/4 R^2 - 1/2 R^2

That doesn't make sense though, shouldn't it be 0.707R?

hey guys my Real Analysis exam is worth 70% and insemester work 30%(I gotted 12.74/30=42%). I need to get 41/70 (58%) to pass. Will I make it :/?

My exam is in 3 days; will i pass? I've finished two practices exams and redone four problem sets and 7 more to go >.

what if i theoretically need a computer to code even though i don't ever code

for those who do not hypothetically code, this is good advice, water damage also works

What do Software engineers use calculus for?

> 50% is passing

Nigga, what kind of grade inflation bullshit is this? Where do you go to school? We had 10 point systems (60 is passing, 70 is C- (or C), 80 is B- (or B), 90 is A- (or A)) which seemed generous, but what is this? Also, do they curve? I had a class where I got ~40/100 points and got a B-, lol.

Suppose a single particle is broken into an infinite number of equally sized, infinitely small pieces. If a particle equally massive to the original particle and the infinite number of particle fragments are propelled at equally sized objects in the same exact manner, would there be any difference in how much the targets are displaced? Or does having an infinite supply of infinitely small fragments result in an infinitely high output?

They rarely use it for anything.

What is your answer to the Fermi paradox?

Fucking Monash. All the math units/subjects weighted percentages are 70% exam and 30% assignments/tests.

Normally, students that get 20+/30 have a better chance of passing...

But honestly do you think a three hour exam thats worth 70% of your grade, sucks? I mean they can pull any cuntish questions in the exam. *sigh* everyone; please just call me a brainlet.

Why is it that for quarks the mass eigenstates are identical to the qcd eigenstates?

Just draw a big breasted woman

In the real world this isn't possible.
In the abstract mathematical world, you should take a look at banach-tarski. But, yeah - it would be infinite.

Having trouble solving this problem. According to the solution, the acceleration of aA=.5aB. But wouldn't they have opposite signs since they are accelerating in opposite directions? i.e: aA= -.5aB?

[eqn] (x2-2x+3)^1/2 - (x2-2x+3)^3/2 [/eqn]

What are the steps in simplifying the above

into this:

[eqn] (-2x+2x-x2)(x2-2x+3)^1/2 [/eqn]

Is psychology considered a science?

Random question that popped up while studying classical fields.

When you define the field equations to be isotropic, does that induce a spherical symmetry on the equations? It would explain where the factor 4\pi comes from.

If not, where does the spherical symmetry then come from? Is the factor 4\pi only for 3D?

Probably not. My Real Analysis final was murderous.

Are they accelerating in opposite directions?

I'm just kidding, that's one of those teacher questions people use when they don't know.

You're right.

What are some good prereqs with regard to math that would be useful when self studying classical mechs and electromagnetism?

Kind of a game theoretic / stochastic question
Imagine 2 players shooting at each other in an alternating way (player 1 shoots first, then player 2, then player 1 again and so on) until someone dies.
They don't have perfect aim, so they will only hit with a probability of p_1 and p_2.

How do I calculate the probability of for example player 1 surviving?
I already did it numerically, but it would be nice to have a closed form solution.

How am I meant to remember all of these for my exam.

They take forever to derive from fp and are only a small part of the exam, but any of them could come up

hardest / most complex fields of math?

Use Markov chains to represent the state vector for (p1hp, p2hp) and the changes as a transition matrix. Then just keep applying such a matrix.

never worked with markov chains so far.
would you be so kind to tell me what the transition matrix should look like?
I should be able to do the repeated application with eigenvalues/vectors

how much do you know

I'm having trouble getting an intuitive feel for the motivation behind constructing a normal subgroup from a group.

Also, does being cyclic have anything to do with normal subgroups? The process of constructing residue classes eerily seems like it is. I understand that given a group G and h in G we can make a subgroup H = = {h^n : n an integer}. We then make the left (or right) cosets by multiplying everything H by x. If x is in H then we get H since of course H is closed to be a group. If x is not in H (not in the cycle ) we get the coset Hx.

Is the fact that that xH may be different from Hx lead us to the importance of normal groups? Sorry if this isnt a very well formed question.

high level algebraic geometry / arithmetic geometry

i would include IUTT but i've never done any IUTT so i don't know how hard it is

I got the solution now for anyone interested.
The transition matrix is
[math]
A =
\begin{pmatrix}
(1-p_1)(1-p_2) & p_2(1-p_1) & p_1\\
0&1 &0 \\
0&0 & 1
\end{pmatrix}
[/math]
where the first column contains the probabilities that
-nobody dies
-player 1 dies
-player 2 dies
in one round.
the second and third column just describe, that once a player is dead, they stay dead.
With some eigenvalue trickery, we get
[math]
\lim _{n\to \infty} A^n =
\begin{pmatrix}
0 & \frac{ p_2(1-p_1)}{p_1+p_2-p_1p_2} & \frac{p_1}{p_1+p_2-p_1p_2}\\
0&1 &0 \\
0&0 & 1
\end{pmatrix}
[/math]
which leads us to a probability of [math] \frac{ p_2(1-p_1)}{p_1+p_2-p_1p_2} [/math],that player 1 dies

if numberphile gives me 1$ + 2$ +..... then i will give them -1/11$s just to be nice

anyone think the proof of fermats last theorem is not legitimate in the sense of fermat not being involved with that branch of maths?

that would make a lot of proofs illegitimate and is pretty arbitrary.
Would you think the proof would be more legit, if wiles was the first one making the conjecture?

i guess so yea.

I can't for the life of me remembers how a certain type of diagram is called.

It's something in electronics when you're talking about basic transistors and NP juncties etc. They draw like valleys and hills with electrons on wone side and wholes on the other site. I think. It has something do with visualizing the voltages as gravity or something.

I don't know. I just took a sleepingpill, so I'm feeling pretty stoned.

I didn't know those diagrams had a name.

"energy band diagram" is apparently how they're called, but aster 3 years of seeing them everywhere, I still don't have the slightest idea what they mean

they just represent the potential energy of particles with a certain charge as a function of position.

This allows you to easily visualize it and you can superimpose the density of said particles to see how a certain potential shape results in a certain distribution of particles

>Do humans really affect climate change?

Everything effects climate change.

Even the dim starlight in the night sky effects climate change.

Your question is too vague to have an answer of any significance.

Solar cycles play the primary part in earth climate, as would be expected, as the primary energy input in this non closed thermodynamic system.

>what university should you check if you're interested into body implants/nanomachines and all that kind of stuff?

Hardware backdoor exploits.

>Suppose a single particle is broken into an infinite number of equally sized, infinitely small pieces.

It wouldn't matter as their mass would be infinitesimal.

>What is your answer to the Fermi paradox?

Optical cable.

What is this continuously divisible to infinity bullshit? The answer is "fuck you, it doesn't work that way, there are fundamental particles". Math is dope as shit but not all is equivalent to the real world.

Prove that if f: A->B and k: B->C are isomorphisms, k o f: A->C is also an isomorphism.

Definition I am using: A maps f: A->B is called an isomorphism, or invertible map, if there is a map g:B->A for which g o f = 1_A and f o g = 1_B. A map g related f by satisfying these equations is called an inverse for f. Two objects A and B are isomorphic if there is at least one isomorphism f:A->B.

My attempted Proof:

Let f: A->B be an isomorphism with inverse g: B->A. This means g o f = 1_A and f o g = 1_B. Let k: B->C be an isomorphism with an inverse h: C->B, this means h o k = 1_B and k o h = 1_C.
Then g o h o (k o f) = 1_A and (k o f) o g o h = 1_C thus we see that k o f: A->C is isomorphic.

Is this correct?

...

The intuition is that you have to require a subgroup to be normal for quotienting to give a well defined group.

sorry bout that, couldn't posttextitfor sum reason.

That's not what isomorphism means though. Just show bijectivity and multiplicativity, which is very easy.

It is what isomorphism means in Set.

he clearly means set isomorphism, which is bijectivity

there are many kinds of isomorphisms. "set isomorphisms" are bijections and are what you're looking for

This user is correct: I am using the set theoretic definition of an isomorphism. Is my proof not correct?

Yes, set isomorphisms are bijections.

Is my proof correct?

If not, how would you prove it using set isomorphisms?

Fucking category theorists

What if the objects are topological spaces? Even loosely interpreting multiplicative as continuous, your post still won't prove isomorphism.