/sci/ - Science & Math

qm superposition

>>15899159
>adding things is le spooooky
This board became sich a letdown.

I learned this lesson over years of management.
Most of the actions you take are a net negative to reaching whatever goal you are trying to obtain. A high percentage of the time the best course of action is to take no action at all.
The number of times I've reached my hand into something just to realize it would have sorted itself out are countless. I've seen people die because they wanted to get involved in a process that ultimately has no consequences to their or the companies functioning, and in fact would have been better if they had just stood 100 feet back and took pictures.
I guess what I'm trying to say is "look before you leap". Even the most simple looking processes can be confounded by myriad of damnable variables.

>>15899099
Logic.

>>15899271
based
I'm gonna stay locked inside my suicide box and wait for a blue eyed cutie pie gf to knock on my door and ask me to breed her

>>15899271
The punitive war in Mexico is a classic example of this

>>15899307
Staying inside is also an action.

>>15899184
>*such le letdown

>>15899099
The elimination of suffering is evil.

>>15899099
Time dilation from velocity. Time dilation from mass make sense. From velocity make no sense

>>15899493
Why not?

that "scientists" don't get time does not exist. there is only a recording of the past and a prediction of the future. but they have the delusion "time travel" can exist like literal retards doing astrology lol..

>>15899658
Because with gravitational time dilation something is actually happening to space. Space is getting squished the more gravity there is which in turn causes time to go slower. With time dilation from velocity nothing is happening to space, apparently if you got in a spaceship and went really fast around the earth a few times the people on earth would have aged faster than you did, so the faster you go the slower time goes. And I initially thought that well we know that when we go faster our mass increases so maybe it's that increase in mass that's affecting the local gravity around us causing space to squish a bit and slowing time down. But apparently that's not the case, mass isn't involved, only velocity is. So somehow the universe knows how fast you're going relative to everything else and adjusts the speed of time where you are accordingly
https://en.wikipedia.org/wiki/Time_dilation#Time_dilation_caused_by_a_relative_velocity

>>15899666
Time is moving at different speeds all over the universe. Time travel in the scientific sense just means say starting at earth, then travelling to somewhere with high gravity like a black hole, then waiting for a bit, then travelling back to earth. The gravity near the black hole is much grater which causes time to go slower. And because you were there in the slow time spot for a while things were progressing faster on earth. You're still on the same timeline though, there's no jumping timelines or anything like in the movies. Time is kind of like temperature, where it's different in different areas. Obviously its function is totally different though

>>15899184
if you think 'adding things' covers it, you're retarded

>>15899755
Saying time is moving at different speeds sounds wrong. I think anon means time is just recorded events relative to other events. So, time is more like a pattern and measure we're looking at rather than a real thing. Time would be a conceptual system of effects all over the universe and never really a cause of anything. Time happens after the facts as an abstract thing; like a metronome, it's more of a tool to help cope and create systems to further cope and make music out of chaos. Like a longitude and latitude grid, you can worship its precision all you want, but thinking it's real is like thinking the tail wags the dog. Which is fine ofc, but it's more of a convenient truth to get us from a to b than something that's actually in our faces.

>>15899745
The four velocity of every object (massless or not) is c at all times. Something that's not moving relative to you moves through time with c. An object that's moving relative to you has velocity components in the space direction. Its four velocity vector got rotated into the space direction. That automatically means that it's moving slower through time

>>15899099
"Serverless" is a retroactive term for Google AppEngine, and it's not actually severless (more like serverful).

Exact sequences and projective and injective modules.
I have no idea why any of this exists.

>>15899837
Time dilation definitely exists. GPS has to account for it in its transmissions for example. It is kind of unintuitive though

>>15900298
time does not dilate, the recording you had of the past has distortions. it's all recordings and predictions and the present.

>>15899745
>Space is getting squished the more gravity there is which in turn causes time to go slower
But how is that intuitive or logical?
>if you got in a spaceship and went really fast around the earth a few times the people on earth would have aged faster than you did
That's not what's happening. From your perspective, people on earth are moving at some speed relative to you, too. That's the point here; the situation is perfectly symmetric. Hence, they will not have aged faster when you land or something like that. The point of that experiment is to show you that the age difference comes from the fact that the spaceship must have had to accelerate and decelerate at some point, so the situations is not symmetric anymore. In GRT, acceleration and gravity are the same thing, so in that thought experiment it's ultimately gravity causing the age difference.

>>15900427
>time does not dilate
It does. That's not up for debate. It's a measurable and demonstrable fact about reality.

>>15899766
Wrong.
>The superposition principle,[1] also known as superposition property, states that, for all linear systems, the net response caused by two or more stimuli is the sum of the responses that would have been caused by each stimulus individually.
You read too much pop sci. Superposition is this:
[math]z = ax +by[/math]
I.e., z is the superposition of x and y. So spooky.

>>15900525
It's comical how so many posters on this board has solved quantum strangness yet none of you have submitted your results to the Nobel laureate committees for you prize in physics

>>15900531
Are you actually dumb or just pretending?

>>15899099
mass x light (((squared)))
Like, what? My retard son is using it in his paper and thinking he’s going to get a job with this.

>>15900531
It's comical how many posters (including(you)) in this shithole don't understand a single thing about what they shitpost.

>>15899099
Clopen sets.

>>15900524
>measurable
By the fingers on my hands?
>demonstratable
independent from my fingers?

>>15899311
Rush is gay and so are you

>>15900524
the recording you made dilated. the fact is the recording is a solid unchangeable fact. what we call "future" is only probability.

>>15899099
quadratic reciprocity

>>15900525
>full-blown dunning-kruger
lol

>>15900829
Sure thing, bud. Let's hear your definition defying all actual experts then. I'll get some popcorn.

>>15900982
Question, oh wise one: a large mass is in a superposition of two locations, spatially separated by many times the size of the mass, what does the gravitational potential around this mass look like?

>>15901010
>Can't define superposition
Thought so.

>>15901037
Oh wise one, please define superposition using your big brain and use your definition to answer my question with your large wisdom

>>15901041
Already did post the official definition here: >>15900525
It's your turn. Surprise me, come on.

>>15901055
That's not quantum mechanics. The original poster said qm.

Protein and DNA assembly is an entropy driven process.

>>15901158
superposition is literally the same concept regardless if were talking sound, water, or spacetime

go read a fucking book nigga

>>15900519
the time comes out the same his watch will by synchronized with everyone on earth after land

however if we watch him with a telescope and radio him asking for the time, he will "appear" to be moving ahead of his reported time, until he returns back to earth at which point he appears to suddenly accelerate faster than light before landing at exactly the right time.

time dilation does not literally accelerate or slow down temporal quantities, its only a relative distortion that goes away the moment you sync reference frames

the only theory that has any evidence for time dilation is muon tomography and its based entirely off the idea that known cosmic rays are too slow to penetrate all the way though the atmosphere by the time a muon should interact and be destroyed, so somehow a muon wont react with air while its compressing space. or it's equally likely there are just more and faster muons than we expect and perhaps special high mass cosmic rays manage to decay into a muon right before hitting the surface

>>15901217
He didn't say he was confused about the superposition principle in general, just qm superposition. You're still pretending he said something he didn't. Are you illiterate?

>>15900563
I sure as hell don't, who wants to put a bunch of time into studying in order to shit post?

I learned that we exist in a tilted universe that's not a normal atomic universe. It's a special kind. It has other aliases such as Error Atomic, which implies it can go all the way and then into a end zone without breaking the simulation. Such as the Sun having a spasm and attacking the planet - what would actually happen is there would be a consequential change of circumstance and life would miss the event or it would be distorted enough to make it painless.

Tilted Atomic is atomic on a scale of beginning and end and they're mixed.

>>15901293
Its literally the same in qm, its in the post you replyed to, you're illiterate lmfao

Imagine getting filtered by adding a dimension

>>15901354
>Imagine getting filtered by adding a dimension
Yes, imagine what the guy is actually talking about instead of shitting up threads with your beyond braindead shit.
He explicitly said it's in this specific context that he's confused. He's not confused about the idea of combining rotation and translation for example.

>>15901158
What a copout, lol. You don't know shit about both QM and linear algebra is what your posts reeks of. So you're not acting but actually retarded.

>>15901241
>he will "appear" to be moving ahead of his reported time
Time intervals dilate. You're not talking to someone in the future. From the spaceship's perspective, the same thing happens to earth people. So how would that work?
>he appears to suddenly accelerate faster than light before landing
No.
>the only theory that has any evidence for time dilation is muon tomography
You mean experiment and no, that's not the only one. I did the experiment when studying btw.

>>15899099
Prime factorization

>>15899099
Tychonoff's theorem, specifically for non-finite products.

>>15901401
PID implies UFD is the one line proof of unique prime factorization in integers.

>>15901309
Kinda ruins the immersion, you know? I want high-quality shitposts on ma /"sci"/.

>>15901420
Okay, now factorize my post number in polynomial time. My point is the elusive nature of factorization does not connect with the ease at which we can state the fundamental theorem of arithmetic.

>>15901401
What's unintuitive about that?

>>15901429
>Every single number has a unique prime factorization
>Okay what's this number's?
>Uhh well it's practically impossible to tell heheh
Would you rather I said conductors of elliptic curves? Because that's what I'm talking about.

>>15901438
No, I just don't get what's unintuitive about it. It's a difficult problem to solve, but I don't see how it is unintuitive to understand. I was thinking about number sieves and I don't think they're I intuitive. That's why I was asking.

>>15899099
when i try to move a wall i sweat and spend energy but do zero work because wall isn't moving

>>15901451
Suppose you knew that a+b=c (for example 42 + 28 = 70) and you know the prime factorization of c (for example 2*5*7). For -c≤n≤c and n is an integer, what is the prime factorization of (a+n)(a-n)(c)?

>>15901465
Entropy is very unintuitive :(

Black holes aren't really that complicated and public speakers like to try and mystify them for no reason. It's just a bunch of shit crammed together.
If you could actually observe it without the gravity field it would just be a mass of everything that's ever been trapped in there.

>>15901381
Nothing you say relates to anything anyone else says. You're completely incoherent. Do you understand what any words mean? Where's the "copout" retard?
I'm not presenting myself as knowing anything about either. I am literate, capable of extracting meaning from text, which you refuse to do for some reason. If you have some understanding about the subject that's lost on us lower mortals you could try to present some information or hints but all you've done is repeat over and over a definition from wiki and declaring that the original poster doesn't understand that definition. You should never post again about anything. It will not help you or anyone.

>>15901476
Are you >>15901158? Because you're as illiterate as he is. Get some basic reading comprehension.

>>15901505
lol, doubling down on your retardation. This board has gone to total shit.
So what's superposition then? Still waiting for your expert-defying definition.

The Time Travel Interpretation of the Bible
>https://vixra.org/abs/2304.0073
We describe the Biblical work of ages as a time travel program for saving humanity from extinction. God's existence is proven as a consequence of the existence of time travel, which is supposed. We present the case that Abraham's grandson Jacob, also called Israel, is Satan. We make the case that the Israelites are described as God's chosen people in the Bible despite their identity as the children of Satan because God's Messiah is descended from Abraham through Satan. They are chosen as the ancestors of the Messiah rather than as Satan's children. We propose an interpretation in which God commanded Abraham to kill his son Isaac to prevent Isaac from becoming the father of Satan. We suggest that God stayed Abraham's hand above Isaac because preventing the existence of Satan would also prevent the existence of Satan's descendant the Messiah. The history of the Israelites is summarized through Jesus and Paul. This book is written so that the number of believers in the world will increase.

>>15901536
The fuck are you doing, Tooker? Post the pdf. Better yet, convert to epub. I wanna read your schizo ramblings on my E-Ink reader

>>15901543

>>15899875
it's almost as if c is the computational speed of our universe, oh wait

>>15901465

>>15901511
Part of reading comprehension is not making wild leaps to support your deranged fantasies like this. Making up these stories based on nothing doesn't help you understand anything.
>>15901518
>So what's superposition then?
Again your post doesn't make any sense. It's like you completely ignore everything said to you. You already posted the definition of the principle of superposition, a principle the original guy didn't express any opinion about. He is confused about quantum mechanics and you didn't help him at all.

Inflammable means flammable. Seems like that would cause some problems. Bad design decision.

>>15901629
>not making wild leaps
I was asking a simple thing in each case. You did not answer. Instead, you wanted me to solve a difficult problem. Why? Three options:
1. You're a schizo
2. You're trolling
3. You're genuinely dumb
Most likely choices are 1. and 3., wanna help me determine the correct one?
>superposition, a principle the original guy didn't express any opinion
Superposition is also superposition in QM. Nothing changes. It's literally adding things. You very likely don't even know that QM is linear and deterministic up to measurement. You don't know anything about anything.

>>15901669
fucking Latinists

>>15901751
>I was asking
You were making incoherent, irrelevant garbage posts that don't fucking say anything about anything. You have no clue how to make any kind of point. You should never post or pretend you're capable of the simplest tasks.
>It's literally adding things.
You're literally braindead. Your posts are like if I said I find modelling simple physics with vector math unintuitive and you would completely ignore any intended meaning behind that statement and spam about how vector math is just math and my confusion about what adding two vectors means is equivalent to not understanding 2+2. You can't elaborate on anything you say because there's no thought behind any of it. You have no clue how to think about any subject.

>>15901779
Wrong. Original post was about superposition specifically. Your incoherent ramblings and ignoring any point does not change that. You're not sounding smart through your irrelevant "gotchas", you're just showcasing your blatant illiteracy as >>15901354 pointed out.
As you demonstrate here >>15901041, you are a disingenuous fuckwad. Define qm superposition then, if you're so keen on irrelevant modifiers. Still waiting. Popcorn is ready.

>>15901792
>Wrong
So you keep saying, based on nothing, while not explaining anything or helping anyone intuit anything. You spend all your time building up this deranged fantasy world where for example everyone who points out your braindead shit is the same person.
You didn't even make any sort of attempt to answer his question or hint at how to answer it, you just repeated the definition of the superposition principle. Like posting the definition of addition, not elaborating or relating it to anything while smugly declaring this means any confusion the guy might have had is now resolved.
Your posts are way, way beyond simply being stupid. There is no mind there.

>>15901802
Define qm superposition, bro. Popcorn is hot 'n' ready.

>>15900531
what he fuck's the source of your picture

>>15901805
Again, completely incoherent. Nothing in my posts rests on this definition and anyone can look it up. The original post is saying the guy does NOT intuitively understand qm superposition and I didn't claim I do. You claim you do, that it's as easy and intutive as understanding how to add rotation and translation but you refuse to share these great insights about quantum mechanics with us poor plebs. All you've done is post the definition of the superposition principle, something anyone can look up.
>>15901792
>You're not sounding smart
That's not my goal retard but it is what every post you make is actually about, on a fucking anonymous forum. There is not even the slightest hint of interest in finding things out or really challenging anyone, just jerking off in your fantasy world. Everything you say just reveals what a pathetic and unaware piece of shit you are which I wouldn't even mind if you were capable of adding something to any discussion about any subject.

>>15901817
But that's wrong. Two Anons gave you the definition of superposition, with citation. Now, where's yours? How is qm superposition different from superposition?

>>15899745
>https://en.wikipedia.org/wiki/Time_dilation#Time_dilation_caused_by_a_relative_velocity
What fucks me, is that the blue clock that is at rest is going faster, but if you switch the reference so the red clock is at rest then the blue one is the slower one with no actual change in the system. Thats kind of a brainfuck since its both faster and slower at the same time and I cannot picture it in my head.

>>15901818
>But that's wrong.
Use your fucking words retard. What is wrong? The post you're replying to says you gave the definition and your reply is "ackshually I gave the definition". There's no communication happening and you're working very hard to keep it that way. Use your words.
>How is qm superposition different
The point is not that it's fundamentally different. You would have gotten this already if you had read even one of the posts you've replied to.
>the net response caused by two or more stimuli is the sum of the responses that would have been caused by each stimulus individually
The definition of the superposition principle on its own doesn't help intuit anything about the peculiarities of QM. The actual question raised by some naive kid that thought retards like you would help him instead of being the irredeemable cancer you are.
The original poster talking about unintuitive quantum mechanism probably only heard the word superposition in relation to a particle supposedly having multiple positions at the same time when you calculate using Schrödinger. It's from pop-science but at least he's apparently capable of thinking unlike you who go around parroting basic definitions at posts you refuse to read.

>>15901861
>What is wrong?
Use your alleged reading comprehension to get it from context by reading the sentence afterwards.
>There's no communication happening
Yeah, from your side. You've claimed that somehow QM superposition is something magically different from what Anons have posted. Go ahead, "use your fucking words" and tell us. Still waiting. And no, you shifting from "QM superposition" to "QM peculiarities" is no answer.
> it's fundamentally different
Explain "us[ing] your own fucking words".
>peculiarities of QM.
That's not what was asked or mentioned. This is also not what you criticized. You're being a really disingenuous fuckwad.

>>15901933
stop replying to obvious trolls idiot

>>15901933
>Use your alleged reading comprehension to get it from context by reading the sentence afterwards.
The sentence is
>Two Anons gave you the definition of superposition
The post this is replying to does not claim anything that contradicts this statement. So what's wrong in the post retard?
>You've claimed that somehow QM superposition is something magically different from what Anons have posted.
You're replying to a post that explicitly says the opposite. Again nothing you say relates to anything I actually say. I am using very simple language but you still pretend I'm saying something completely different. Why can't you just engage sincerely like I'm doing with you?
>it's fundamentally different
Again, the exact opposite the actual words in the post say in context.
>That's not what was asked or mentioned.
Yes it is retard. The original faggot mentioned QM superposition specifically.
Understanding how to add rotation and translation is very easy and intuitive, the Schrödinger equation, the concept you'll find if you look up "qm superposition" is not as easy and intuitive but you keep pretending it is for some reason. Why? What the fuck is wrong with your brain?
>>15901938
You're not funny or interesting. You're just cancer.

>>15901977
lmfao I was really thinking you're trolling but with such a wall of text you're actually for real. Look. QM superposition implies that you think superposition is weird. Otherwise your have just said QM or something else more specific. You're just backpedaling after you noticed that you fucked up differentiating between QM and QM superposition after multiple people pointed it out, and now you're just plain disingenuous about it. See all your post in the beginning containing nothing but insults. Go fuck yourself, acquire some basic reading comprehension, then come back.
>the concept you'll find if you look up "qm superposition" is not as easy and intuitive
lol yes it is. Adding things is easy. Linear algebra is easy. What makes QM weird is the measurement process, but you have no single clue about any of that.
t. actual physicist who also worked on Newton-Schrödinger states in the past which you were probably implying with your pathetic goalpost-shifting "gotcha" earlier.
>>15901938
True, true... No more (you)s from me.

>>15899099
If you are mean to a girl she will like you

>>15901388
radio is two way, we have to wait for a response, it seems out of sync because of his relativistic speed and the distance between us and him
>no
well you can be certain that the clock on his wrist will say the exact same time as the clocks on earth when he gets back
>You mean experiment
that's literally just an observation of muons, google translate is failing you (or youre a bot)

>>15899383
>The elimination of suffering is evil.
>Up is down
>Square is round
Conservatives are truly fucked in the head lmao

>>15902094
Utilitarianism is one of the most water brained ethical systems ever conceived

>>15902142
Utilitarianism is always objectively correct.

Dot and cross multiplication aren't the same thing and for literally no fucking reason people are taught one and then switched to the other before having the difference explained to them.

It was finding out there were secretly 2 ways to walk and you actually switched from one to other at some point but never knew because it's only apparent on certain surfaces.

Why for the love of all that is holy don't math teachers just fucking start with dot multiplication?

>>15902142
I'm a virtue ethicist

>>15901996
>Look. QM superposition implies that you think superposition is weird.
No it doesn't you mindless fuck. Trouble with Schrödinger does not imply trouble with combining translation and rotation for example.
>You're just backpedaling
What is wrong with your brain retard? Backpedalling from what?
>See all your post in the beginning containing nothing but insults.
You're still dishonestly misrepresenting everything I say. Every post you make is mindless noise. What do you expect other than getting called out as the mindless subhuman retard you are?
>Adding things is easy.
Which is why nobody finds it unintuitive or is confused about it. Someone expressed confusion about qm and you're still ranting about the dumbest shit imaginable. Pure noise and dishonest horseshit. Almost every sentence you wrote in the last few posts is misrepresents something I said as the exact opposite to what was very clearly meant. I went over multiple examples of this dishonesty but you just keep going with the irrelevant noise. Seriously, what is wrong with your brain?
>actual physicist
You're an incompetent idiot. You have never done anything in your life except parrot. If anyone pays you for anything they're being scammed. If you were literate you would understand my posts aren't about physics but the fact that you're mind is mush. You don't have the slightest clue how to begin thinking or contributing to any discussion about anything. Sincerely look at the examples of your shit I gave you. Seriously consider what you actually said in the posts you made in this thread. If you're actually serious about any of these posts there are toddlers with more rigor and honesty in their thinking than you. You're the retard destroying all public forums with incoherent noise. That you've moved on to undermine the project of physics is not something you should be proud of.

>>15902244
Teachers believe young students might confuse the dot operator with a decimal place.

>>15899099
a gas that expands against a vacuum is doing expansion work on the vacuum

Computers don't do math, they approximate it

>>15902526
Utter fool.
The only worthwhile definition of "Math" is "the thing that computers do". All else is schizo garbage.

>>15902538
math isn't real unless you can make rock full of lightening imitate it

>>15901465
Unironically a great analogy to explain entropy

>>15902063
>well you can be certain that the clock on his wrist will say the exact same time as the clocks on earth when he gets back
No, you can't. The spaceship must have accelerated and decelerated, that's where the delay ultimately comes from. It does not come from velocity. Only acceleration does that.
Observing something is called an experiment, not a theory. Try not being dumb, it helps.

>Spin
Electrons despite being point masses they can somehow rotate around themselves and that in exactly 2 directions despite existing in 3 dimensions while the laws of physics are rotational invariant.

All this thread shows is that this board is >90% pop-sci. Shame what happened. No wonder all the Anons from pre 2012 left.

>>15899099
That we are programmed to die.

>>15904314
Only lifelets like you.

>>15901807

Your bosses will like you more if you sometimes fuck things up and then fix them rather than do everything consistently correct, even if you have to pretend you didn't know how to do it right the first time.

>>15899159
its just oscillating between states really fast, nothing special

>>15899271
corporate mind control tuned to being as risk adverse as possible to maximize shareholder profits

>>15899099
https://ep00.epimg.net/descargables/2018/09/25/b133e2bf9a3e7bb55f5fae26dcf9b8c0.pdf

This was from a famous mathematician's attempt at a proof of the Riemann Hypothesis. Let's just say it didn't pass peer review.

Beginner algebra word problems. I don't know why I got filtered so hard during self-study but I did and it fills my heart with such shame. I feel like such a failure but I still won't give up.

>>15905084
We all believe you can do it, Anon. Awareness of these issues is the first step to betterment.

>>15905116
Thanks for the support, anon. You don't know how much it means to me to read those words. I won't forget them. God bless you and merry Christmas.

>>15905018
don't use that one, it's too obviously impossible

>>15905084
How can you get filtered during self study? You get infinite retries.

>>15901828
The key information you are overlooking is that only the blue clock is an inertia reference frame. The red clock isn't, it's accelerating (it's orbiting the blue clock). Time dilation becomes much easier to comprehend when you realize that all you need to do is consider who is actually accelerates or decelerates.

>>15899099
Multiple pulleys making a object "lighter"

>>15899099
Schotten-Baumann makes no sense. But it works, somehow.

>>15900531
It's the only worthwhile interpretation of quantum mechanics, "shut up and calculate".

>>15905290
Agree. Everything else is esoterics.

bef

The Scientific Method's rulings. Who needs an experiment to start the expedition 'what if?' and then have it eliminated with the answer.

Technically, asking 'what if?' is forward momentum in light of discovery, with a bit more effort from mind, it is science. No experimentation involved. But experiments are good for science and so is the process of elimination. However, it's quite a big jump to suggest only experiments count. I can do either an expedition, elimination, elipse or experiment.

>>15904907
Retarded faggot.

>>15899159
>|s> = a|x> + b|y>
What's so weird about this?

>>15905183
I gave up too quickly because I got discouraged.

Delta functions are some bullshit
[eqn]\delta(x) := \begin{cases} 0 & \text{ for } x\neq 0 \\ \infty & \text{ for } x= 0 \end{cases}[/eqn]
[math]2 \cdot \infty = \infty[/math] so
[eqn] 2 \delta(x) = \begin{cases} 0 & \text{ for } x\neq 0 \\ \infty & \text{ for } x= 0 \end{cases}[/eqn]
Yet [math]\delta(x) \neq 2 \delta(x)[/math] since
[eqn] \int_{-\infty}^\infty \delta(x) dx = 1 \\
\int_{-\infty}^\infty 2\delta(x) dx = 2 \int_{-\infty}^\infty \delta(x) dx = 2[/eqn]

>>15905018
Best robbery sar

>>15905084
Based. Keep goin', fren

>>15905018
Name one (uno) time this would be relevant

>>15905018
Nice try, Rajesh l