/sqt/ - Stupid Questions Thread

>in the definition of an ideal I of a ring R is there any difference in requiring that I is a subgroup of R under addition and requiring that I is a subring of R?
Yes, An ideal is a subring with the additional property that any element OUTSIDE of the ideal multiplied by any element of the ideal is INSIDE the ideal.
That property is there so that the quotient can be made into a ring by defining this multiplication (a+I)(b+I):=ab+I.
For it to be well defined, it has to be independent of the representatives, and for this to happen you need the additional property.

fuck off

thanks.
so the definitions in pic related arent equivalent?

The second definition is a bad one.

They are equivalent.
The first one at (ii) acounts that multiplication in I is closed (thus subring), and that for x outside I and y in I you have xy in I and yx in I (ideal subring).

The second one is a retarded definition. It's correct, but redundant.
Change textbook. This one seems bad.

>They are equivalent.
They're not. Since I is a subring in the second definition, it contains 1, and so R itself would be the only ideal because of (I2).

Did 0! = 1 first come from definition or from the Gamma Function? I'm assuming the former but heard someone imply it was the latter. Curious.

>The first one at (ii) acounts that multiplication in I is closed (thus subring)
Wrong,

First let us look at the symmetries of [math]\mathcal{L}[/math]. Suppose [math]T_\vec{a}[/math] and [math]T_\beta[/math] are representations of the space and time translation operators such that [math](T_\vec{a}f)(\vec{x},t) = f(\vec{x} - \vec{a},t)[/math] and [math](T_\beta f)(\vec{x},t) = f(\vec{x},t-\beta)[/math]. If [math][T_\vec{a},\mathcal{L}] = [T_\beta,\mathcal{L}] = 0[/math] then it follows that [math]G[/math] is also translationally invariant, and therefore [math]G(\vec{x},\vec{\xi},t,\tau) = G(\vec{x}-\vec{\xi},t-\tau)
[/math]. So you can WLOG solve the PDE [math]\mathcal{L}G(\vec{x},t) = \delta(\vec{x},t)[/math] to get the Green function, namely the Green function at the origin and [math]\tau=0[/math] determines the full Green function.
If the above is satisfied then you can perform a Fourier transformation. Given [math]G \in \mathcal{S}(\mathbb{R}^n)[/math] is a Riemann square-integrable distribution in space (i.e. [math]G\rightarrow 0[/math] as [math]\vec{x} \rightarrow \pm \infty[/math]), you can Fourier transform in the [math]\vec{x}[/math] coordinates and obtain an ODE in [math]t[/math] which you can solve depending on initial conditions, then inverse Fourier transform back into real space. If [math]G\in \mathcal{S}(\mathbb{M})[/math] is a square-integrable distribution in both the space and time coordinates then you can let [math]x = (t,\vec{x})[/math] and Fourier transform in [math]x[/math]. This gives you an algebraic equation that you can just inverse Fourier transform back directly.

Subrings don't necessarily have a unit. A ring might not necessarily have a unit. And even if the ring and the subring have units, they might not even be equal.

Are you retarded or what? I is a subset of R.

I meant "unity", not "unit".

>Are you retarded or what? I is a subset of R.
Not enough to guarantee being a subring.

>Subrings don't necessarily have a unit.
They do for any useful applications.

>A ring might not necessarily have a unit
Wrong.

Those are called rngs.

Wrong.
1) It is a subset of R.
2) It is a subgroup from the hypothesis.
2) Multiplication can be restricted there since I is closed under it.
3) Associative and distributive laws for * trivially follow since + and * on S are the same ones as on R, just restricted to S.

>if the ring and the subring have units, they might not even be equal.
Also wrong.

>They do for any useful applications.

>1) It is a subset of R.
>2) It is a subgroup from the hypothesis.
>2) Multiplication can be restricted there since I is closed under it.
>3) Associative and distributive laws for * trivially follow since + and * on S are the same ones as on R, just restricted to S.
Still not a subring, existence of a multiplicative identity is not implied by any of these statements.

Next?

[math] \mathbb{Z} \times \mathbb{Z} [/math] has unity [math] (1,1) [/math] .
[math] \mathbb{Z} \times \{0\} \unlhd \mathbb{Z} \times \mathbb{Z} [/math] has unity [math] (1,0) [/math] .

proofwiki.org/wiki/Definition:Subring#Definition
proofwiki.org/wiki/Definition:Ring_(Abstract_Algebra)#Definition

>wrong
>wrong
>wrong
>everything turns out to be right
you're just a retard

>Z×{0}⊴Z×Z
Wrong.

Not a subring, doesn't contain the ring's multiplicative identity.

>you're just a retard
Nothing I claimed was wrong has turned out to be right.

Next?

>hurr I'm right even when I'm wrong

Next?

>proofwiki.org/wiki/Definition:Subring#Definition
>proofwiki.org/wiki/Definition:Ring_(Abstract_Algebra)#Definition
Your personal blog is not a legitimate source.

Next?

>Next?
Unless you finally point out something I claimed incorrectly (which you can't), there is no "next".

I bet you are the same retard who spams Wildberger memes.

>I bet you are the same retard who spams Wildberger memes.
You lost that bet.

Plus that doesn't even make any sense, you're the one using unconventional naming and just generally being confused about mathematical standards.

>unconventional naming
It's not unconventional at all. It's what most texts use.
If you define a ring to have unity, then you'd get shit like "the kernel of a homomorphism is not necessarily a subring" which is plain fucking retarded.
It's just bad terminology. There is no reason to restrict the definition.

>It's not unconventional at all.
Wrong.

>It's what most texts use.
Wrong.

>[blah blah] which is plain fucking retarded.
How so?

whatever you say, friend

Feel free to attempt to lend credence to any of your inane statements.

>lend credence
>inane
You seem very smart, since you are using such words.
I concede.

>You seem very smart
I'm not, just smarter than you.

true

Meh, there are some relatively natural examples of rings that don't have units (for example L^1 with convolution)

>natural examples of rings that don't have units (for example L^1 with convolution)
That isn't a ring, it's a rng.

Can someone tell me why this regular expression is failing to accept?

regex: [0-9]{5}
input: 12345

Has no one ever heard of tutoring before? Or is Veeky Forums too socially retarded that the aspect of getting help in person deters them?

The latter, and that you usually have to pay for tutors.

Why does gas cause feelings of depression and anxiety? It's a pretty immediate effect in most people but I can't find out why.

Thanks user.

Because it looks like space itself is expanding at a rate so fast that the effects of gravity will be to weak and slow to pull all the mass back together. It's looking like a big rip or heat death.

Not exactly a science question but more of a person question.

How do I find purpose in life when I'm an atheist?

Your uni probably has tutors and shit yo.

As a fellow athiest I ran into this as well. Your purpose is whatever you want it to be. You just need to focus on doing whatever you focus on well, and being happy.

What if I focused on becoming a serial killer and started murdering people at random and did it because I wanted to? People like you make atheists look retarded. Really smart right there.

>make atheists look retarded
It's not hard.

Pic is shopped?

>Taking something to the most extreme, unlikely conclusion because you didn't like my answer
Ok buddy. Just be sad and depressed then.
>What is my purpose
To kill yourself

>tfw i get legitimately blindingly enraged when I get stuck on a problem for too long

Why isn't the earth perfectly flat?

Shouldn't the north pole sag down to make it flat? Like with tectonic plates

No.

>Shouldn't the north pole sag down to make it flat?
Why would it? Gravity pulls toward the center of the earth.

Is EE really as bad as its famed to be? I find the topic incredibly fascinating but I question whether I'm intelligent enough to make it. I was thinking of going to college this next semester, but I'm worried about being overwhelmed. I have a very poor math education and a lot of catching up to do.

Does anyone have any textbooks or resources you'd recommend so I can get an idea of what I'm in for?

Wait.... so big head ed is not a meme?

So gravity pulling the sides is why it's pushed up to make the dome on top?

Like a carpet?

No. I attended one of his conferences on paracompactification of the moduli space of connections for [math]N = 2[/math] superconformalsymmetric string theory and his head was so big that I wasn't able to take down any notes at all.

bumping this. using C# btw

Hi,

youtube.com/watch?v=ufU6b7OHb8M

Can someone quickly derive this formula in this video at 26:05 where he goes from the halves to the 2 minus the exponentials? I know that he's trying to get the real parts of the exponential, and to do so he has to add another exponential of opposite sign. I don't understand why both exponential terms are negative (one must be rotating one way, and the other in the opposite direction)..

Besides that, how does he get from the halves to the next part? It's basic integration, I get it, but based on the rules I know so far I can't get it.

How come sometimes you have to pee really bad, but when you finally do there's a lot less than you expected?

On Thursday I'm going to take the Mercedes 4Matic exam, what should I expect? Have any of you taken it before?

Fucking autocorrect, I mean the AMATYC exam

How do i calculate the volume of a unit cell with a two atomic basis ?

Reposting since I posted in the dead thread.
I'm supposed to prove [math]\int \int \int_{E}f(x,y)dxdy[/math] exists and calculate its value. What I thought I'd do was calculate the integral for the [math]x^2+y^2\leq z^2+1[/math] side and substract the integral for the [math]2z^2\leq x^2+y^2[/math] side, but since I get [math]\sqrt{x^2+y^2-1}[/math] I'm stuck.
Does [math]\int \int \int_{E}f(x,y)dxdy[/math] actually exist and if so, how should I solve?

Alright, hoping some cunt will help me.

Don't know much about chemistry but am tackling a predictive problem which involves finding the amount of aromatic compounds found in diesel fuels.

Why is this useful to be predicting this? In the context of diesel fuels of course.

I've done a bit of research and aromatic compounds are apparently especially stable; so maybe you want less of them in your diesel fuels because less aromaticity means less stability; more reactivity - therefore a more energetic combustion?

Am I close? Completely wrong? Does it have no real useful effect on diesel fuels and I'm just predicting the aromaticity for the sake of it?

How do I prove that [math]( f \circ g \circ f)[/math] bijective is equivalent to [math]f[/math] bijective?
Would [math]g[/math] then also have to be bijective, or can it be anything?

>this level of reddit spacing

I thought it would be a bit more readable this way; feel free to copy it all and remove the line breaks though

Are MIT calc lectures good enough for a first course in calculus?
Should I complement it with Stewart calculus textbook?

Let [math]E\subset \mathbb{R}^n[/math]. Prove that for every [math]\epsilon >0[/math] we can find a succession of closed [math]R_{k}\subset \mathbb{R}^n[/math] such that [math]E\subset \bigcup_{1}^{\infty}R_{k}, \sum_{1}^{\infty}R_{k}0[/math] we can find a succession of open [math]A_{k}\subset \mathbb{R}^n[/math] such that [math]E\subset \bigcup_{1}^{\infty}A_{k}, \sum_{1}^{\infty}v(A_{k})

take g = 0 for example, then f(g(f(x)) = f(0) for all x, which isn't bijective unless f is only defined on one element

No lecture is ever better than a textbook.

how do I get rid of ADD, I can't focus longer than 10min at a time studying something

I did not used to be like this

What is that dual-way arrow thing in mechanics, I always see it when I'm working with restitution and collisions but never know what it actually is. You know the , what is it called and what does it do?

but that is true. That's why most people study ideals as modules. This is by far the approach which is generalized the most (sheaf of ideals, etc.). Things get nasty when you are interested in rings with unity and start considering homs which don't preserve them (e.g. direct limit of rings with unity won't even have to have unity).

>A separator N is minimal if N\{i} is not a (k, x)-separator
What does N\{i} means in mathspeak? N is a subset.

be warned that throughout wikipedia, the incorrect definition of a ring is used (although to its credit it does specify that there is one other (the correct) definition of rings, which it does not use).

Alright sci
Help me with this exam problem
"Find the volume by rotating the region bounded by [math]y = cos x[/math] and [math] y = x [/math] around the x-axis."

No calculators, no shit.
How can I solve this?

N excluding i. The subset of N containing all elements of N but i.

>No lecture is ever better than a textbook.
Which college for brainlets do you go to?

In probability, if a question asks something like:
"What is the probability of x happening *at least once*?"
does this include it happening 0 times?

So for instance A = a man his a target at least once.
P(0 hits) = 0.2963)
P(1 hit) = 0.4444
Would P(A) = 0.2963 + 0.4444?

>In probability, if a question asks something like:
>"What is the probability of x happening *at least once*?"
>does this include it happening 0 times?
No, that would be "at most once" (=1)

At most once is what I meant
shit
So 0.2963 + 0.4444 is at most once right?

>So 0.2963 + 0.4444 is at most once right?
Yes.

Was just offered a job In Oklahoma $65k base pay once I graduate this coming December. Ill have to leave all my friends and family though. Is the money worth it.

how many golf balls to equal the mass of the sun in kilograms?

1.989e30 kg/0.04593 kg

All universities are filled with brainlets (the only difference is their parents' money) and professors have to deliver to them.

>All universities are filled with brainlets (the only difference is their parents' money) and professors have to deliver to them.
Which college for brainlets do you go to?