SQT

>>9133498
a is trivial
b is trivial by contradiction
c looks easy
d is easy trial and error

I've heard that as an object accelerates to the speed of light, it gains mass from increasing kinetic energy. To accelerate it to 100% of the of light, it would take infinite energy. So would the object then have infinite mass? If so, would it then collapse into a black hole that would have an ever expanding event horizon due to its infinite mass?

>>9133519
It never gets to 100% due to the energy requirement, you said it yourself.

is westworld the most /sci/ show

or is it vice principals

>>9133500
care to elaborate on a

>>9133564
Start with [math]S_0=\{x_1^{e_1}\}[/math], then iteratively let [math]S_{n+1}=\{xy|x,y\in S_n\}[/math]. Clearly [math]S_n=\{x_1^{e_1}...x_k^{e_k}|k\leq 2^n\}[/math]. Then [math]S_\infty[/math] has closure (verify), inverses (verify) and identity.
Also, I think any coprime of 45 suffices for d.

>>9133615
Ahhh I get it now. And I was thinking the same thing for d. Any little pointers for c?

>>9133625
Not familiar with the notation of M used there.
By the notation, I would guess that the group itself is finite.

>>9133639
M1000(Z1000) is the ring of 1000x1000 matrices with entries from Z1000

>>9133526
I meant hypothetically, or do we just not have an idea of what would happen because it can't happen in the first place.

>>9133644
That's finite, though very large, so its group of units is finite. Then the group is generated by a finite set, namely itself.

Would it be feasible to create a miniature dyson sphere-esque dome over a particular area (village, city) to capture all heat inside it for repurposing? Barring concerns such as livable atmospherics ofc

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What is the "E^E" set mentioned here ?

>>9134464
Y^X={f:X→Y | f is a function}

Is this equation non-linear?

d^2R/dt^2 = -k/R^2

What I did was:
d^2R/dt^2 + k/R^2 =0

This is non-linear because R is being squared for k/R^2, right?

>>9134716
Yes. But it's also nonlinear because the second derivative is squared as well.

>>9134737
>second derivative is squared
No it's not

>>9133498
>>9133500
The asterisk by the rationals and by the integers is meant to signify "non-zero," correct? Also, I'm not familiar with the "unit group" M(S), if someone would care to elaborate on that?

Btw, I've been thinking about studying cryptography, which I think, beyond number theory, is mostly group theory, correct?

>>9134737
>>9134753
Yeah, you're right. It's hard to see in that form.

>>9134759
>The asterisk by the rationals and by the integers is meant to signify "non-zero," correct?
Yes

>Also, I'm not familiar with the "unit group" M(S), if someone would care to elaborate on that?
M(S) is not the unit group, its matrices with entries in S

the unit group of a ring is the group of ring elements that have multiplicative inverses

>>9134759
The asterisk means that multiplication (denoted *) is the group operation. Essentially it does mean nonzero, yes, since there is no multiplicative inverse for zero.
Cryptography is more about finite fields than plain groups, I think. I've only ever taken coding theory but it's probably not too far off.

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>>9134766
>>9134774
Thanks senpai.

I'm required to get a graphing calculator for my math courses, instructor recommends a TI-84. Are there any other alternatives to it (I heard Casio and HP are cheap) or should I just drop the money on one?

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How do i answer this

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>>9134863

>>9134863
>>9134932
actually just disregard that, this is sufficient:
>T1 sin(50) + T2 sin(30) = whatever force 100 lbs creates
>T1 cos(50) = T2 cos(30)

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how do i get a whole number distance from these vectors? i dont think it wants a distance vector because when i try typing one in it gives me an error

>>9135216
It's asking how far, not where it is. You have to find the distance by subtracting the two vectors and find the magniTunes of the third.

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Anyone know a good resource on where to grind input problems for postfix/RPN notation?

It's one of the only calculators allowed in the program I'm going into in less than a week (mech eng) and the calculator has algebraic but also an RPN mode. The consensus seems to be that RPN is a lot faster for putting in numbers and no parentheses needed. Is it worth learning anyway? The calculator in question is an HP 35 S

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I'm pretty retarded when It comes to dealing with arrays
I'm new to c++

>>9134863
Fx: T1cos(50) = T2cos(30)
Fy: 100lb = T1sin(50) + T2sin(30)
Find one of the tensions and plug it it into the other equitation find the next one

>>9135262
i got it. thanks dude

Is the order of operations intrinsic to math-as-such in non-superficial ways or is it a purely arbitrary human convention?

>>9135368
>Is the order of operations intrinsic to math-as-such in non-superficial ways
Why do you think this can possibly be true?

>>9135368
Math as a whole is a purely arbitrary human invention

When you drink water, most of it, I assume, is turned into urine, sweat, tears, and so on. But I assume some of it is also converted into energy or other matter through the body's biological functions, to power cells and so on.

It's not just humans that convert water into energy. All animals, plants, and even single-cell life does this. And it's estimated that the first signs of life showed up on Earth 3.8 billion years ago.

After 3.8 billion years of an uncountable amount of organisms removing water from the water cycle to turn it into energy, shouldn't we have run out of water a long time ago?

>>9135423
wat

So I worked for this place for a year and a half, 3 months as a research scientist intern and the rest as an independent employee. It was a small company so there wasn't much documentation of titles and whatnot. A recruiter advised me to drop "intern" from my title and just go with research scientist since most of my time there was working independently. The contract I had with them specifies an intern position for 3 months, everything after that was just on an at will basis and there was no paperwork.

Now I've learned that title is typically reserved for people with a PhD (did not know that before). I'm trying to get a research associate position right now, just had the final interview. I'm paranoid as fuck that if they do a background check my title will come up as "intern" and they'll think I was lying about my background and I'll lose the job because of that.

How fucked am I?

>>9135423
>But I assume some of it is also converted into energy or other matter through the body's biological functions, to power cells and so on.
No, it is not. Only nuclear fusion reactors can do that.

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Is there a way to find all zeros for this without graphing?

[math]y = x^3 - 3x^2 + 2[/math]

>>9135653
So there are no chemical reactions happening in cells that convert water into some other kind of matter?

>>9135654
guess one root, factor it out, use quadratic formula for the other two roots

>>9135465
>How fucked am I?
Not at all. Companies give employees derptarded titles all the time, and nobody thinks anything of it. Your formal titles like PhD are mentioned in your resume, making it very clear that you don't actually hold one. Your previous boss could have called you Highlord of the Universe and recruiter wouldn't blink an eye.

>>9135660
Chemical reactions, certainly. But there are also plenty of chemical reactions that convert it back.

>>9135465
Background checks normally verify job title. If the person doing the check sees "research scientist" on your resume and gets "intern" from your old boss, that might be a problem. Maybe call your old boss and see if he/she can cover for you?

>>9135671
What's the net result, though? Surely there's ultimately at least SOME water left in a non-water state upon death where, even if it's an infinitesimally small amount, would add up over such a huge span of time and with how many organisms are alive.

It means we would eventually run out of water, right?

>>9135767
Sure, there's lots of water that's used in photosynthesis, after which the biological matter dies and sinks into the sediments. Some minerals also absorb notable amounts of water AFAIK.
However, the lithosphere is a closed system, so you get equally much rock coming back to surface. The dead plants (coal, oil, natural gas, etc.) are often turned back into water through combustion.
The only way you'd have water disappearing is if it goes outside the planet (either as vapor or as other chemical compounds), which does happen but in such miniscule amounts that the sun will probably blow up before it runs out.

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path 0 > 1 > 2a of the famous "meme list" in pic related will be enough for statistics?

>>9135423
Water isn't converted to energy. In fact, it's one of the end products of the primary energy-producing reaction: carbohydrates + O2 -> CO2 + H2O.

>>9135465

No and yes to some extent or interpretation.

you do not extract energy from water, if anything your body generates water as a subproduct of producing energy(think about it like a fire; when you burn an organic compound you always get CO2 and H2O)

But there is someone that actually "extracts" energy from water: oxigenic photosynthetic organisms, in fact the reaction involved is suposedly the most oxidative reaction you can find(that is, you take electrons from the water) but this reaction requires energy from the sun, so what you actually do is store that energy and the water only provides the electrons to generate intermediate compounds that are like the gears in this machine.

That stored energy is transformed into sugars, that later you eat. To process sugars you do the exact oposite process, you generate the same intermediaries out of sugar to extract the electrons from them that you can use to move the biological metabolism, and those electrons end reducing oxigen(adding electrons to the oxygen atom which gives you O2 with a charge of -2 so you add 2 +1 protons to compensate=H2O)

Think about it like a lever; on one side you have oxidation and the other side reduction, to get energy, one has to be high and the other low and the difference of energy is transmitted through biochemical reactions.

What raises the lever in the first place? The sun.

So, no you do not extract energy from the water but the whole process starts and end with water.

Is there any equivalent of autism in the field of biology to atomicrockets, atomic-skies or braeunig?

What areas of math do I need to know to study formal methods and verification?

>>9135296
http://www.cplusplus.com/reference/list/list/push_front/

>>9135465
>2017
>Lying on your resume

Any good books for learning differential equations?
I'm taking my first semester on it and need something other than my textbook to understand it more.

I had my first lecture on Stochastic calculus today and I do not understand the definition of a variation of a function. I don't understand how this limits work: [eqn] V_g([a,b])=\lim_{\delta_n \rightarrow 0} \sum_{i=1}^n |g(t_i) - g(t_{i-1})|, \delta_n = \max_{1\leq i \leq n}(t_i - t_{i-1}) [/eqn]

I conceptually understand that the variation measures how much a function vary on a interval but I do not understand how to reason about this limit. Can anyone explain it to me?

>>9136667
https://en.wikipedia.org/wiki/Total_variation

>>9136685
Thank you anon

I am trying to figure out how to prove with induction that if gcd(a, b)=1 then gcd(a, b^n)=1 for all n>=1 WITHOUT prime factorization and was leaning towards doing a proof by contradiction but am not sure. Any hints and tricks will be appreciated

Very silly question here.

In certain equations I don't understand why components are squared. Take e=mc2 for example. Why is the c squared?

>>9136708
Yeah it's a silly question and very broad. In general mathematical models which aim to represent the world simply involve squares because that's how the world works. There's no deep answer here.

>>9136739
In other words you don't know why the c is squared?

>>9136746
You don't understand what "In other words [...]" mean.

>>9136748
You don't understand math.

>>9136758
Define math you prick

>>9135296
Either :
Add each new element to the beginning of the list. Print the array with a loop.

Or (not what is being asked for) :
Add them all to an array and start printing the end first, remove the element at the end, repeat.

gb2 >>>/g/ faggit

Has someone ever worked for tutor.com?

I'm about to do one of the exams to enter but I'm kind of afraid. Of course that I already know the subjects, but I'm afraid because maybe I don't remember everything and they could put some rare exercise.

Someone knows how are they?

I'm a sophomore in Physics and I want to do Calculus BC that it should be super easy I guess. But maybe not???????????

I know that I'm a pussy.

I’m trying to find the velocity in a position function [math]f(x)=x^3[/math] at time 0. According to what I know,
[math]\lim_{x \to 0} \frac{f(x+1)-f(1)}{x}[/math]
is the traditional equation for converting position to velocity, but when I factor and get rid of the denominator to take the limit, I end up with an answer of 3. Wolfram Alpha seems to agree, though I know for a fact the answer is 0 because of the power rule. So what gives? Does that equation not work here for some reason?

What's that word that describes something that has been thoroughly explained with evidence? It starts with an 'e'. Usually with evidence that is beyond sufficient: more than enough.

>>9137182
evident?
irrefutable?

>>9137182
Are you sure it doesn't start with "i"? Irrefutable?

I was gonna make a joke and say "evident", but I didn't. You're welcome.

I am working through "Beginning and Intermediate Algebra" by Tyler Wallace. It is a free pdf. I have 2 questions that I absolutely cannot arrive at the same conclusion as the answer key. I need to know if I am just retarded, or if the book is wrong. If I am wrong please show me how.

-17/9 · -3/5
My answer: 51/45 or 1 2/15
Book answer: -19/20

13+(-3)^2+4(-3)+1-(-10-(-6))
--------------------------------------------
((4+5)÷(4^2-3^2(4-3)-8))+12

My answer: 5
Book answer: 3

>>9137178
>According to what I know,
>limx→0f(x+1)−f(1)x
>is the traditional equation for converting position to velocity
You mean [math]\lim_{x \,\to\, 0}\frac{f\left(x\right)\,-\,f\left(0\right)}x[/math]?

>>9137194
>>9137199
I think it starts with an "ex". I used to use if before and can't remember what it was.
"My research ___ implies that..." Or there is ___evidence that this suggests that

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>>9137206
Not in this case. This works on other equations, too, but not [math]x^3[/math], for some reason.

>>9137218
Extensive!

>>9137223
>the instantaneous velocity of that object at time t = 1

>>9137234
Aww, son of a bitch. I thought it was saying 1 could be used as a representation of an instantaneous action. I don't know how I came to that conclusion. I'm retarded. Thanks!

>>9133519
>>9133645
Only photons can move at the speed of light. For what you're thinking of to be possible, the particle would have to be massless. And remember, [math]E=mc^2[/math]. When a particle (with mass) speeds up, its energy increases and, at a certain point, it becomes prudent to describe it with "m" and not "E". This is where the "infinite energy gives infinite mass" part comes from. The density is totally irrelevant here, so no black holes.

Also, even though photons are massless, their energy can still be represented in terms of momentum. When a photon hits an object, that object will move; hence, it imparts some momentum despite having no mass.

>>9134759
re: crypto
yes,
>>9134774
is correct, but honestly, assuming you're in undergrad right now, knowing very basic number theory, group theory, algebra, and linear algebra is enough to get started in a graduate program and just pick up what you need to know. I started only knowing one course worth of number theory and a bunch of linear algebra and was able to pick up the group theory and algebra I was missing along the way. The best thing to do is to get a decent crypto textbook (I recommend An Introduction to Mathematical Cryptography by Hoffstein et al., though make sure you pay attention to the errata online), work through however many sections in the book you need to to get through elliptic curve crypto, then start reading papers from the latest top-tier crypto conferences/journals you find interesting (protip: crypto, security, and privacy are kind of weird in that conferences are often more prestigious than journals, though honestly the difference between the two is becoming smaller every year), then study the parts of the paper you don't understand. The crypto stack exchange and freenode channels can help.

Does anyone know of any interesting visual representations of block designs other than the fano plane and (9,3,1)-BIBD? I'm running a puzzle D&D campaign for my lab and I need something to toss the combinatorics people, and that shit looks like summoning sigils but those two are too obvious.

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I've been interested in things that predate science that have since been experimented with to see whether they're actually effective or not.

i.e.:

https://en.wikipedia.org/wiki/Tai_chi#Health
>There was no conclusive evidence of benefit for any of the other conditions researched, including Parkinson's disease, diabetes, cancer and arthritis.[27]
> the Australian Government's Department of Health published the results of a review of alternative therapies that sought to determine if any were suitable for being covered by health insurance; t‘ai-chi was one of 17 therapies evaluated for which no clear evidence of effectiveness was found.[28]

https://en.wikipedia.org/wiki/Research_on_meditation
> there is moderate evidence that meditation reduces anxiety, depression, and pain, but there is no evidence that meditation is more effective than active treatment
>Meditation has been shown to change grey matter concentrations and the precuneus

Is there anything similar that's been reviewed and found actual benefit?

>>9133498
I have a strict and somewhat limited set of time to spend working on classes. I currently am taking chemistry, Calculus, and working 30 hours a week.
Should I spend the extra time it takes to take notes from the book a day or two before lecture ? or spend that time solely practicing material that has been covered? What do you think if the most effective when working with time constraints?

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>>9137580
taking more notes seems like a bad idea to me
I would practice and read the textbook straight up - no summary notes

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>>9137587
You're probably right. It takes up too much time

>>9137580
>Should I spend the extra time
With time constraints? No. Also, there's no point. For chemistry the most important thing is paying attention in class - and asking questions, if you're that sort of person. For calculus it's mostly practice; take notes only while you're in class and write the highlighted theorems/definitions at the top of your homework sheet so you don't need to keep flipping back and forth through your book.

>>9137587
>>9137614

Thanks. you've reinforced that I've been going about this all wrong from the beginning.

Why are there 13 IQ threads?
Why is IQ mentioned so much?
Why do people even want to know their IQ? Wouldn't they know by now whether or not they're an idiot?
>inb4
even idiots know they're idiots. I'd know, I'm an idiot.

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>>9137484
Insightful and valuable answer, Anon. Thanks dawg.
And yeah, you were right to assume I am a foolish mortal undergrad.

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>>9136860
That spacing...

>>9137218
The word you are looking for is "empirically"

>>9137856
It's complicated. A subject can only consider itself as a subject, and all other stimuli are objects. Thus, a subject cannot know what it is objectively like to be a subject, they only have their own intuition. Combine that with the strange hero culture of intelligence and the dunning-kruger effect making people double guess themselves and it's not hard to believe that some people would just want a somewhat standardized view of their own mind.

How would I show that the functions [math] f_n(x)=e^{nx}, n=1,2,...[/math], are linearly independent? I arrive at the conclusion that they're not linearly independent, reasoning like this:

Assuming that said functions are linearly independent, then so are [math]f_1[/math] and [math]f_2[/math]. So we expect that [math]a_1 f_1(x) + a_2 f_2(x) = 0 [/math] implies that [math]a_1 = a_2 = 0[/math]. Now, [math]a_1 f_1(x) + a_2 f_2(x) = a_1 e^x + a_2 e^{2x} = e^x (a_1 + a_2 e^x) = 0 \text{ iff } a_1 + a_2 e^x = 0 \Leftrightarrow e^x = - \frac{a_1}{a_2} [/math]. Hence [math]a_1 f_1(x) + a_2 f_2(x) = 0 \text{ iff } e^x = - \frac{a_1}{a_2} \lor a_1=a_2=0[/math]. So it doesn't imply that [math]a_1 = a_2 = 0 [/math]. I have clearly done something stupid here but I cannot figure it out. Anyone knows what I did wrong?

>>9138092
>Anyone knows what I did wrong?
You have e^x(a_1+a_2 e^x)=0.

e^x is never zero so a_1+a_2 e^x=0, and this has to be true for all x.

If a_1 = 0 then 0 = a_1 + a_2e^x = a_2e^x implies a_2=0.

If a_2 = 0 then 0 = a_1 + a_2e^x = a_1.

If a_1 != 0 and a_2 !=0 then when x= log( a_1/a_2) we get 0 = a_1+a_2 e^x = a_1+a_1 = 2a_1, a contradiction to a_1 != 0.

>>9136693
Not proof by contradiction but you could consider this: If gcd(a , b) = 1, xb = ya + 1 for some integers x and y. Now raise both sides to the n-th power and proceed.

why isnt there a symbol for "differentiate both sides with respect to x" like how we have f'(x) of d/dx for differentiating

Starting Calc2 and I think I understand the concepts but I'm not sure what I'm supposed to do to solve actual problems

"Evaluate the integral by interpreting it in terms of areas."

In the interval (-3,0) ( 1+ sqrt(9-x^2) ) dx

Not sure what I'm trying to find as my final answer and I can't find it online or in the book. Is my final answer a number or an equation? I found the area to be 2.25 under the specified interval, but I can't check my answer anywhere.

>>9136148
BS Stats?

What protein complexes regulate the cell cycle?

Is m-cyclin the same as cyclin B?

>>9138419
that's a circunference with radius 3 shifted by 1 unit above the x-axis, so you calculate the value of the integral is a quarter of the area of the circle plus the rectangle from y=0 to y=1, if you're having trouble visualizing just use some plotter, but you can recognize the circunference eq with radius 3 inside the sqrt

>>9138311
What's the point?

>>9138733
So with problems like these I am trying to recognize the shape the equation is making and use the information I know to find the area?

Also what if the interval doesn't start or end at the center/midpoint of the circle and I don't know the radius or center. Do problems like that exist?

>>9138791
the moment they tell you to evaluate the integral in terms of areas, they're pretty much telling you that the integral could be calculated in an easy way through known area formulas (circle,rectangle,triangle...), so all these problems are pretty much just figuring out the figure the function defines, so i really doubt they would give you a weird interval

>>9136330
>braeunig
still interested

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I feel dumb for not knowing this.
Would it be e^(-3t)/3t?

>>9138941
No. It's a special function. This particular one is the Ei(-3x)-Ei(1). Ei is the exponential integral.

How do I do the mathjax thing?
$$\mathcal"Like this?" xd =3$$
$$69/420 -2^2$$

>>9139309
$d/dx(1337x^2)$

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fugg

Someone show me how to use MathJax before I end up shitting up an innocent thread with dozens of failed attempts

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I know what I have to do, it's just:

[math]\ddot{x} = \frac{q}{m}E_0\cos(kz-\omega t)[/math]

And find [math]\dot{x}[/math], pretty easy. But should I take [math]z[/math] constant in time, zero or linear?

The other differential equation from Newton's Second Law is: [math]\ddot{z} = 0[/math], which implies that [math] z = At +B [/math]. But since it is free to move only in the xy plane, should [math] z = 0 [/math]. Which one is it?

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So uh, how the hell do I go about proving this?

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>>9139368
spherical geometry for reference

>electrical engineer major
Will I use math in my career?
Do any engineering majors use math at all?

>>9137202
Can I please get an answer on this? I know it is a stupid question, but this is the place for that.

$${{x^2+ 1)}}$$
\[x^2+ 1\]

>>9133529
Westworld is shit. Hopkins was one of like three actors who gave an above medicore performance. Thw blonde man jaw lady and the black uber genius whore were some of thw worst actors I have ever seen. Also, the black ladies story was the most annoying and mind numbingly stupid thing Ive seen since Sharknado.

I know the answer..

>>9139427

No, electrical engineers never use math at all, not even adding small numbers together.

>>9139343
My guess is that the particle is stuck in the xy plane. So its z postion is 0 at all times. Might be wrong.

>>9139427
no and no

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>>9139374
>>9139368
See image. I will let you do the last question. See here if you are confused about lower case "r" threw me off a little would be better if they called ir "l" or something. https://en.m.wikipedia.org/wiki/Spherical_cap

Sorry about the shitty photo, lamp bulb popped and camera flash throws off the exposure.

>>9139445
I agree with ur first answer, 51/45. But sorry I'm too lazy to do the second, try symbolab for a step by step solution?

>>9137202
51/45 reducez to 17/15 not 12/15. May have just been a mistype on your part. The book is obviously wrong because you are multiplying two negatives so the result should be positive.

Not typing the second try wolfram or symbollab like the other guy suggested.

>>9139661
>>9139634
Thank you. This helps. I was trying to type 1 & 2/15 btw. I might need to switch books.

Is it possible for an infinite group to have an element of finite order other than the identity? I could swear it's not, but I can't find it anywhere in my book.

>>9139685
Yes, consider [math] GL_n(\mathbb{C})[/math] which has infinitely many elements of finite order of the form
[math] \zeta * Id [/math] where [math] \zeta [/math] is an m-th root of unity i.e. [math] (\zeta * Id)^m = \zeta^m * Id^m = Id [/math]

>>9139685
Also by the fundamental theorem of finite generated abelian groups you can any finitely generated abelian group is isomorphic to some direct sum of primary cyclic groups and infinite cyclic groups. Any element purely in the primary cyclic part of the group will have finite order.

>>9139690
sheeeit

>>9139685
Consider [math]\mathbb{Q}/\mathbb{Z}[/math] Every element in this group is of the form [math] \frac{m}{n}[/math] so [math] \frac{m}{n} + ... +
\frac{m}{n} \text{n times is } m = 0[/math] in [math]\mathbb{Q}/\mathbb{Z}[/math] i.e. finite order

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are peano axioms covered in bourbaki books?

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What the fuck?
Is WebAssign messed up or what am I misunderstanding?

>>9139732
The text above the question is wrong and so your answer which follows that text is also wrong.

>>9139736
What should the text be then?
This is Physics I and my first exposure to vectors, we didn't do them in Calc I or II.

>>9139753
>What should the text be then?
Look at the definition of magnitude of a vector and you should be able to figure it out

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>start reading book about concentration
>find this on page 10
This is where I delete the pdf right?

>>9139756
Ok it's the square root of each coordinate summed, so it can be zero.

I hope this whole textbook isn't shitty like this.

>>9139763
*square of each coordinate

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Let's say I have an intuition some mosquito gives cancer to cats after years of observation and reviewing biology articles. Whom do I convince to make a scientific study if I am not a scientist? Do universites or students make standalone research?

>>9139761
>This is where I delete the pdf right?
>book about concentration
No. You delete the pdf on page 1.

https://en.m.wikipedia.org/wiki/Small-angle_approximation

where does theta^2 /2 come from in this article? why can't they just say cos(theta)=~1 for small angles? because the former is just a bit more accurate I guess?

>Whom do I convince to make a scientific study if I am not a scientist?
Nobody. Scientists generally have FAR more things they really want to research than time or budget to do it. Very few are going to be interested in your idea. Your only real hope is to write up your reasoning convincingly enough that some scientist thinks "holy shit he might have a point there", by which point you are like 50% done with research.

>Do universites or students make standalone research?
Students do research projects all the time. Most graduate programs have it as a required component of the curriculum, to greater or lesser degree.

>>9140422
It comes from the Taylor series expansion of cos. Which approximation you use depends on what you're trying to compute. If you need the limit of something like (1 - cos(x))/x^n as x approaches 0, the higher order terms in the approximation come into picture.

Is it 50/50 whether your offspring is male or female?

>>9140659

if I remeber correctly males were suposed to be a bit more probable, like 10% or so.

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im confused by d) lads, I feel like im not understanding what the question is actually asking
it seems to me its asking me to prove a general case using an example, which seems bizarre

Why does being gassy cause anxiety?

Whenever I eat a slice of pizza or burger I get bloated and start contemplating what comes after but once I take a gasex I'm chipper as can be after belching

I mean it's been great for weight loss but kind of annoying when you're at the bar

>>9141305
d is trivial, just assume you have some set lambda 1,..., lambda n and construct a matrix with those eigenvalues

the proof will hold for general lambda, so it proves the general case

>>9141313
thanks friend im retarded

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Wolfram is telling me everything in the denominator should be multiplied by 2, did I fuck something up or is Wolfram just trying to make the solution look nicer?

Sorry for this.


But fuck, i started doing meth again, it's been only about a day ( a full 24 in about an hour ), and i always have this question pertaining to masturbation but i never ask it because i dont think anybody will answer, but also because i dont think we have an answer yet.

Anyway, the following happens when i do meth, with VERY fast diminishing returns over repeated dose cycles. Basically, if i start to masturbate on a first generation meth ""relapse"", I will very very very likely masturbate for HOURS. (meth yesterday at 10pm, masturbate 2am-7am, food, tv, masturbate 2pm-9pm (or something wtf)
The details of this masturbatory-catatonia are interesting to me.
I completely lose track of time and the motivation to keep it, to the point where when i am finished, it suddenly feels like only a few moments have passed, and the realization of how much time has passed is shocking.
Normally, I have premature ejaculation, or at least, the amount of orgasm control i have on meth makes it look that way.
I dont move (much) , unless it's hot, or i need water. The first time this event happened to me i didnt move anything but my fingers and hands for five hours, and when i started moving again it was like strong ataxia that quickly became less severe, but lingered for hours.
My eyesight, something is fucky here, if i dont take breaks from staring the screen, when i do pull my gaze, perception is super warped in a very hard way to describe, its like your eyes are behind a bad pair of glasses. It goes away after a few minutes (i try to ease my eyes out).

Well i guess my comment is too long, but my question is WHY does this happen. Im curious about the systems affected by this because it is profound and measurable(to me) in an empirical way. Doubtful anyone with actual neuro* education would touch this with a 10 foot poll, but im on meth so FUCK IT.

>>9141529
For fucks sake anon even if you're just trolling go get some fucking help.

>>9141555
i hope you realize the only reason you made this post was to pat yourself on the back

and the only thing you've accomplished is coming off as sheltered

So ill ask the stupid question, why do you come here? To pat yourself on the back?

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I'm going to start use LaTeX, never written in it before.

Which version should I use and why?

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How do we observe antimatter without annihilating it with our measuring tools?

Is it possible to mass produce it and contain it in the future with more efficient accelerators and magnetic traps so that it can be put on display for macroscopic behaviors?

>>9141712
When matter and antimatter interact they give off a very specific signal:
e+ e- -> 2 gamma
The photons come off back to back and thus provide a very characteristic signal

They used this signal to first detect neutrinos at the Savannah river reactor:
https://en.wikipedia.org/wiki/Cowan%E2%80%93Reines_neutrino_experiment

>>9141712
>How do we observe antimatter without annihilating it with our measuring tools?
We observe the gravitational fields they produce.

>Is it possible to mass produce it and contain it in the future with more efficient accelerators and magnetic traps so that it can be put on display for macroscopic behaviors?
I think it's possible, but that's a pretty far ways away.

Is it acceptable to use a certain value (that is not actually the probability) to express the chance of occurrence of some event as long as it is just about as accurate? Also how does it happen that a seemingly arbitrary value correlates closely with the estimated probability?

>>9141726
How would you go about measuring those tiny gravitational fields and even if you could, how would you distinguish them seeing as matter is universal?
>>9141712
An other way of doing it is just sticking them in a magnetic field B and looking at the way they curve, different signs give opposite curvatures.
This also gives you a way of containment but they'd constantly lose energy due to brehmsstrahlung.

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>>9141354
You need to multiply the rest of the denominator by 2 to be able to pull up that factor 1/2

>>9133615
Wait, why are you doing this iteratively? You can just show that the RHS is a subgroup of G that contains X and that would show left inclusion, is your iteration giving the right inclusion?

>>9141773
The proof is constructive, so it's easy to follow.
I think by inclusion you mean what he called closure, which follows trivially either way.

>>9141809
Well, you want to show that two sets are the same no? Which I would do by proving double inclusion, if you could prove that the RHS is a subgroup of G that contains X then it's one of the groups being intersected over in the definition of <X> so that inclusion is done, what about proving that the RHS is a subset of <X>?

>>9141821
Ah, I see.
I guess the idea is that there cannot be a subgroup that is a proper subset of S_infinity that still contains X, since all S are directly constructed from X.
Not sure about formal proof, but it seems intuitive at least.

>>9141830
Oh, I guess there are different approaches by the different branches, I've just learned not to trust my intuition.

>>9141834
Well, here goes.
For any subgroup [math]H\leq G[/math], for which [math]X\subset H[/math], it must hold that [math]S_0 \subset H[/math]. If [math]S_n\subset H[/math], then by closure [math]S_{n+1}\subset H[/math]. Then, [math]S_\infty[/math] must be a subset of all subgroups of G that contain X. On the other hand, [math]S_\infty[/math] is a subgroup, so the definition simplifies to just [math]<X>=S_\infty\cap( \cap_{H\leq G,\\S_\infty\subset H}H)=S_\infty[/math].

>>9141842
Ok, so the induction gives S_{n+1} in H for finite n, I don't feel like this immediately gives a result for S_inf.
PS. Note that I'm not OP nor have I done any serious group theory in a while.

>>9141857
Yeah, I'm not really familiar with infinite groups either, so can't say anything further about that. The definition in >>9133615 also has the problem that S_inf contains non-terminating products of x'es, not sure if it's a problem.

>>9141871
No, there just is no bound on the amount of products, that doesn't mean they're infinite.

How do I prove that the vector space [math]C(\Omega)[/math] has infinite dimension?

I assume there is a basis [math]B[/math] for [math]C(\Omega)[/math], then [math]C(\Omega)[/math] has finite dimension.

I try to find a element [math]x[/math] which is a linear combination only for one candidate basis [math]B[/math] and then show that there is another element [math]y \in C(\Omega)[/math] that is not a linear combination of basis-vectors of [math]B[/math]. Then I conclude that there does not exist a basis [math]B[/math] and hence [math]C(\Omega)[/math] has infinite dimension.

But I struggle with the details. What element [math]x[/math] should I choose? What is [math]B[/math]? What is [math]y[/math]? Or is there a much simpler way to approach this problem? Any hints are appreciated!

>>9141878
It says k<=2^n, but it's actually equality (at least for finite n) unless the products are simplified.

>>9141885
You're right, I think that's just a typo, I don't think they mean to have infinite products.

>>9133498
These kinds of questions are not stupid questions.

>>9141884
I chose another approach and I think this is solid but I'd like some feedback:

All polynomials are continous hence [math]P[\mathbb{R}] \subset C(\Omega)[/math]. Assume [math]P[\mathbb{R}][/math] has a basis [math]B[/math]. Then all polynomials can be expressed as a finite linear combination of monomials. But we can always chose a polynomial of higher degree and hence [math]B[/math] would have to have another monomial in it. This argument can be repeated infinitely many times and hence [math]B[/math] must be an infinite set and as such not a basis. Hence [math]P[\mathbb{R}][/math] has no basis and as such is of infinite dimension and so is the set of continous functions.

>>9136746
it's a unit thing

[math] kg \cdot \frac{m^2}{s^2} = J =[/math] energy

it works out like that when you look into special relativity

>>9136746
The c squared in special relativity falls out of simple geometry. Drawing world lines where the angle of reflection of light is always 45 degrees is the main trick.

>>9141884
>>9141913
A basis can be infinite: (1, x, x^2, ...) is a basis for the set of polynomials in x. Your proof seems correct but I think it could use more precision and justification ("this argument can be repeated infinitely many times"; and you assume infinite dimensional to mean "not finite dimensional" as opposed to the more proper "an infinite basis" (although they are equivalent by Zorn's lemma), etc.).

>>9133500
>trivial by contradiction
>by contradiction
You don't need double negation elimination to prove a negation.

>>9134863
Triangle of forces ftw.
i.e. tensions + weight must form a triangle since their vector sum is 0
Solve with sine rule

Is it a legal move to exchange a definite integral and antiderivative of different variables ? I'm trying to solve [math] \int_{0}^{\infty}te^{-st}\ dt=g(s) [/math] by doing [math]\int \int_{0}^{\infty}te^{-st}\ dt \ ds=G(s)+C=\int_0^\infty \int te^{-st}\ ds\ dt=\int_0^{\infty}-e^{-st}\ dt=-\frac{1}{s}[/math] then taking the derivative w.r.t. s [math]g(s)=\frac{1}{s^2}[/math]

>>9137417
Is this why some spacecraft use solar sails? If so that's incredibly fucking cool.

Having never worked beyond classical physics, would it still be possible to describe the transfer of momentum from light to matter? Or is this strictly the field of General Relativity/Quantum Mechanics?

>>9142434
I think you need to verify a domination condition to do that.

>>9142448
Sorry, a what? looking that up gets me https://en.wikipedia.org/wiki/Dominated_convergence_theorem which doesn't seem relevant

>>9142538
I think you want Fubini's theorem.

>>9142544
That works. Thank you!

how do I explain Riemann series theorem to normies who only know calc 2?

I just need a good example to work with.

>>9142625
>I just need a good example to work with.
The standard example for rearranging series is the alternating harmonic series. You can get it to sum to several different things easily just by rearranging and grouping terms.

Given the function

[eqn]f(x) = \frac{sin^3(x)}{3+cos(x^3-3x)}[/eqn]

how can I prove that f(x) is odd?
I tried pluggin -x but I couldn't find the answer

>>9142783
>I tried pluggin -x but I couldn't find the answer
It's trivial, what went wrong?

>>9142788
I did 3+cos[(-x)^3-3(-x)]
but I'm stuck at sin^3 (-x)

can I just write - sin^3(x)? why?

>>9142792
You could look at it like the product of three sine functions, seeing as sin(x) is odd you'd get (odd*odd)*odd = even * odd = odd
dropping the minus sign in the cosine is because it's even

>>9142812
I see. Thank you, anon

>>9137951
Constructing the reals from the rationals is a neat read. I don't suggest you try it yourself as its very dull (to do) but the ideas are interesting.

>>9142876
>I don't suggest you try it yourself
You should if you are a non-brainlet.

>>9142917
theres better math to spend your time on.

>>9142938
Only a brainlet would need much time to do such trivial tasks.

did the mass race mixing between the Spaniards and the indigenous effect anything in terms of science

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Can someone explain the relative charges of protons and electrons?

If the total charge of quarks within particles determine charge, then why do electrons and protons have that -/+ 1.6*10 to the -19th charge?

I am guessing that the actual measured electrical charge?

i still dont know what +1 and -1 particle charges mean

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Why the fuck won't this submit? All of the online calculators say it is all real numbers, so what the hell am I doing wrong?

>>9143494
>online calculators say it is all real numbers
but that's wrong

>>9143494
can be negative you fucking retard

>>9143497
can't*

shit i need to go to bed

>>9143494
>Domain
There are an infinite number of possibilities. This question is not well defined

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>>9143497
>>9143500
>>9143502
[0, infinity) did the trick.

>>9143511
but do you understand why you were wrong? for negative x, g(x) is undefined, and f(undefined) is also undefined, even if it reduces to something like x^1.

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why do things turn shades of cyan or celeste even when it is dark during the winter months in relatively northern places (like some of the rooftops here)?

Is it frost or something else?

How the fuck do I stop being depressed and focus in mathematics?

All I think about is loneliness and lack of purpose...

>>9143516
> for negative x, g(x) is undefined
Irrelevant, as f(x) is always positive.

The issue is that g isn't the inverse of f. Consider negative x.

>>9143589
>Irrelevant
Wrong.

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This is probably a really stupid question and I'm probably a big, dummy, baka, idiot for asking but let me try to lay it out.

Q. To put it simply, do numbers have infinite roots, one real and the rest non-real?

Lets say you want to find the [math]\sqrt[5]{2}[/math] . That means there will be one real (but irrational) root, and 4 non-real 5th roots of 2, right? Assuming that's true, then is it also true that [math]\sqrt[100]{2}[/math] will have one real root, and 99 non-real 100th roots of 2? Assuming that's true, then is it also true that [math]\sqrt[100,000]{2}[/math] would have one real root and 99,999 non-real 100,000th roots of 2? Basically, does this pattern continue on to infinity or am I totally wrong about everything and should start looking for a job flipping burgers right now?

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>>9143637
The roots usually form a nice geometric shape in the complex plane

Whenever x is real and positive then z^(2n)=x has two real solutions, one positive and one negative

For example z^4 = 1 has real solutions z = 1 and z = -1

How exact is the measured time we're commonly given for the heat death of the universe? (5 bn years)
Is it possible that it's massively wrong or inaccurate and could be closer to double or even off by an order of magnitude?

What commonly available flour or starch product has the smallest particle size?

>>9143779
literally trivial, what have you tried?

>>9143779

Counterexample: Circle, rotation.

>>9143801

I'm sorry, I assumed strict f(x) =/= x. My bad.

I am very bad at math.

I want to know how to determine the approximate floor space of a hypothetical tetrahedron shaped building. Given it is 1200 meters on eac side of its base and 1600 meters tall with 190 floors.

Is it simply the area of the base times the number of floors divided by 3?

Is there a method to find the roots of an equation such as [math] 3^{x} - 3x^{2} - 6x +5 =0[/math]

>>9143489
The relative just means that they are scaled in a nicer way, specifically relative to the elementary charge.
It's much cleaner and easier to work with the simple units +1 and -1, rather than the actual charges.
After you have computed the total relative charge, which is just protons minus electrons or something similar, just multiply the result by the elementary charge to get the actual charge.
Similarly, quarks' charge is scaled relative to the elementary charge.

>>9143921
As far as I know there's no analytic methods that will work in all cases. Your best bet is numerical root finding. Since the derivatives are easy, I'd suggest plain old Newton-Raphson

>>9143921
no, mixing exponentials and polynomials makes root-finding much harder

>>9143779
>Prove that there exists a nonempty set
Already impossible.

>>9143941
This example in particular is trivial though. It has no solutions.

>>9143936
>>9143941
Thanks that's what i assumed

What's the mathematics behind cycling? Say the back wheel is fixed, and the front wheel is under an angle a with respect to the back wheel's path. Call the distance between the two wheels d. What's the radius of the circle the bicycle is travelling in? Obviously for an angle of 0 degrees the circle has an infinite radius, and for 90° the circle is 2pi*d (the path of the front wheel, that is).

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>>9143948
>what

>>9143952
>pi
>"infinite radius"
"pi" can't really be shown to exist.

>>9143955
>[math]\approx[/math]
>.
I see.

>>9143944
>>9143948
>>9143956
>>9143961
Please put on a trip so I can filter you.

>>9143965
And what if I don't?

>>9143956
then how you describe the ratio of a circle's circumference to its diameter?

>>9143952
Bicycle fags count teeth on the sprockets and do math from there.

>>9143956
>goes to infinity for a -> 0
Happy now?

>>9144010
You can also think of a car but it's effectively the same; a bicycle is just more intuitive since the path-tangent is imposed on the wheel itself instead of the middle of the bar.

How do I show that:
[eqn]|z_1 + ... + z_n|\geq |z_1|-|z_2|-...-|z_n| [/eqn]
Given that all z are complex numbers?
I know how to prove the "normal" version of the triangle inequality, but I have no idea how to get to these "-" signs and the inverted inequality.
Halp.

>>9143916
Mathfags plz halp. I don't want to ask again and the internet can't tell me.

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>>9143952
Consider the attached diagram, where inner circle is the back wheel and outer is the front wheel. Draw triangles as in the picture and notice that:
[math]r_2 \sin\theta =d, r_2 \cos \theta = r_1[/math],
where r2 is the outer radius and r1 inner. Then:
[math]r_2=\frac{d}{\sin\theta},r_1=\frac{d}{\tan\theta}[/math]
This matches your predictions.

>>9144085
[math]|z_1|=|z_1+z_2-z_2|\leq |z_1+z_2|+|z_2| [/math] Therefore [math]|z_1+z_2|\geq|z_1|-|z_2|[/math]

Then just use induction for n numbers

>>9133498
how come when i mention tesla's work here i am met with "fuck off with your pseudoscience, retard"

>>9144127
Thank you very much, anon!

>>9144144
1. He was an engineer, not a scientist, which /sci/ hates
2. He's popular with normies who exaggerate his importance

>>9144011
>goes to infinity
No such thing.

>>9144097
>two circles
That makes perfect sense, I feel a little ashamed for not figuring that out myself but then again this is the SQT. So thanks.

>>9144144
Because "Tesla's work" = pseudoscience.

>>9143916
>>9144088
>Is it simply the area of the base times the number of floors divided by 3?
Yes, I think you got it right! That is a good approximation.(Assuming that the rooms are same height.).

I'll try to prove/explain this in another post.

>>9143983
Why are you assuming this can even be done in general?

>>9144196
because they're both measurable quantities?

okay, let's start simpler. if you have square with side lengths of 1, how do you describe the length of the diagonal?

>>9143916
>>9144192
Yeah I believe that's right.
You just divide the volume of the tetrahedron by the height of each floor.
[math]floor\;space=\frac{V}{h}=\frac{1}{3}\cdot A \cdot\frac{H}{h} =\frac{1}{3}\cdot A\cdot number\; of\; floors[/math]

>>9144222
>measurable quantities
I don't understand what you're saying. It doesn't sound rigorous, whatever it is.
>how do you describe the length of the diagonal?
Why are you assuming it can be described?

>>9144192
Proofs I can't figure out since a 4 sided pyramid vs a 3 sided tetrahedron seem to have the same 'divide by the cube' solution when it comes to floor space, albeit the tetrahedron is something less than a 4-sided pyramid, so I think I have something wrong.

>>9143916
Index the floors from the top, such that the topmost (smallest) floor is indexed 1 and bottom-most is indexed n.
Let [math]A_k[/math] be the area of the kth floor. Since areas scale distance squared, you have [math]A_k=A_1k^2[/math].
Then the total area is [math]\sum_{k=1}^n A_k=A_1\sum_{k=1}^n k^2=A_1(n^3/3+n^2/2+n/6)[/math], see https://en.wikipedia.org/wiki/Square_pyramidal_number
Plug in [math]A_1=A_n/n^2[/math] to get the area [math]A_n(n/3+1/2+1/6n)[/math].
For sufficiently large n your approximation is applicable.

If we have some injective(surjective) function [math]f: A \rightarrow A[/math] can we say it is also surjective(injective) if [math]A[/math] is an infinite set? My guess/intuition is that we can't

>>9144252
finitists should be gassed.

>>9144280
no, you only get 2-for-1 if the domain and codomain are finite sets

>>9144192
>>9143916
>>9144088
Intuitive proof:
The height of the building doesn't change the area.(imagine changing the stretching or squashing it: the floors get closer or farther apart but their area remains the same). So assume the height of the building to be 190meters. Floors are 1 meter apart from each other, so each 1m x 1m floor tile corresponds to 1m x 1m x 1m cube of volume inside the building, except for edge tiles where part of the cube would be outside. The number of edge tiles is very small compared to the inside tiles. So total floor area is approximately the same number as the volume of this squashed building. Volume of tetrahedron is given by base area times height divided by three, which results in the approximation you gave.

So the approximation isn't exactly right, but it's pretty close. My math skills are too rusty to do this mathematically precisely. And >>9144256 seems to have done it.

Example with your numbers and assuming regular tetrahedron:
Base area of equilateral triangle is [math]\frac{\sqrt{3}}{4}[/math] times the side length squared.The approximate total floor space would be
[eqn]\frac{190 \times \frac{ \sqrt{3}}{4} \times 1200m \times 1200m}{3} \approx 39500000 m^2 [/eqn]
So nearly 40 square kilometers.

>>9144283
>finitists
I don't understand what you're saying. It doesn't sound rigorous, whatever it is.

>>9143931
so the +1 or -1 is just a meme?

what about formal charges for atoms in molecules?
are they also relative?

>>9144280
No. Consider the injective but not surjective function n -> 2n on the natural numbers, or the surjective but not injective function n -> 0.5n rounded down.

>>9144306
>[math]\frac{\sqrt{3}}{4}[/math]
It is not clear that this number can be shown to exist.

>>9144328
please kill yourself

>>9144280
Every function [math]f: A \rightarrow A[/math] where [math]A[/math] is an ``infinite set'' is obviously an isomorphism, so yes.

>>9144331
Why would I want to do that?

>>9144334
>obviously
That doesn't sound very rigorous.

>>9144334
you're not funny

>>9144318
In a sense, yes. On the other hand, they are as much a social convention as the definition of a Coulomb, and you could view relative charges as simply another unit.
Formal charges are indeed relative, and a good example for using relative charges. Instead of having to think about the charge of an electron, you can instead just count the number of electrons, and the relative charge is equal to the number of electrons times -1.

>>9144328
>>9144334
It's hard not to bite. Even now I'm giving you (you)s. sorry

>>9133498
OK anybody knows how to solve this

find the domain of

f(x)=log(x^2 -x-3) +sqrt(x^2 -3x) + sqrt(x^2-x)

>>9144342
Indeed, I should have added that the principle of explosion has to hold as well.
>>9144353
This isn't supposed to be funny.

How do I prove that [math]\mathbb{N}[/math] is a proper class?

>>9144363
Logs and roots never can never go below 0 so find the roots of the polynomials in those functions. Look at which intervals are positive.

>>9144285
>if the domain and codomain are finite sets
So if the domain and codomain are sets?

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I did the good old ping for manuscript status. Does this look good or bad lads?

>>9144306
Thanks, that was an expert explaination. I figured my divide by 3 solution wasn't actually how to do it.

how come f(x)= sqrt(x^2+2x-1)

ends up x≤−1−√2

x≥−1+√2

>>9144498
>√2
It can't be shown to exist.

>>9136148
> No Rudin in sight
Yeah, /sci/ turned into shit.

>>9144556
Don't meme his homework, anon.
I didn't even check it but it this is the case his teacher is surely from here.

What are the simple techniques used to put a transfer function in standard form? I need to put
[eqn]\frac{1\,-\,\mathrm i\,\omega\,\tau\,\mp\,\mathrm i\,\frac{\sigma_0\,H}{n\,e\,c}}{\left(1\,-\,\mathrm i\,\omega\,\tau\right)^2\,+\,\left(\frac{\sigma_0\,H}{n\,e\,c}\right)^2}[/eqn]
in the form
[eqn]\frac1{1\,-\,\mathrm i\,\left(\omega\,\mp\,\omega_c\right)\,\tau}.[/eqn]

How vulnerable is the pulling out method
pls help

>>9133498
What methodology could be used to strongly suggest a given event is caused by climate change and wouldn't have happened otherwise?

>>9144793
Ask your dad.

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>>9144797

>>9144794
Strong belief in fairy tales is a pretty good one.

How do I become gay? (Not joking)
I'm trying to desensitize myself to gay porn and trying to get more touchy to a guy that's into me.
Will I succeed? I still feel kinda repulsive sometimes and it's been really hard getting an erection.
I prefer having relationships with men, so I want to become gay so I can make them deeper and have not to deal with women emotionally, since doing it doesn't really make me happy (I'm not misogynistic or anything, I just don't feel happy anymore around them).

Thanks in advance.

Why does y^2 result in a positive or minus value for x but y^3 doesn't?

x^2+y^2=16 is not a function but
x+y^3=8 is

Someone pls explain to a brainlet

>>9145153
A function can't assume two values at a certain variable value.
For example: f(x) = x, if x = 1, then f(x) = 1 and can't be any other value but this, like f(1) = 1 AND f(1) = 2.

>x^2+y^2=16
Can have to values for a given x or y value. It's a circle, so you can see it easily.

>x+y^3=8
Same idea goes for this, but in this case each value for the variable, no matter which one you pick as your variable, will not return two values for the function (plot it and see it).

>Why does y^2 result in a positive or minus value for x but y^3
y^2 can be a negative or positive y, since (-a)*(-a) = a^2 and (a)*(a)=a^2
but y^3 means that: (-a)*(-a)*(-a) = -a and a*a*a = a, that is, the sign doesn't change.
Hope it helps.

>>9145153
Negative times negative is positive for algebraic reasons (to keep distributivity while still having [math]0\,x \,=\, 0[/math] for all [math]x[/math]).
[eqn]\left(-1\right)^2 \,=\, \left(-1\right)\,\times\,\left(-1\right) \,=\, 1[/eqn]
[eqn]\left(-1\right)^3 \,=\, \left[\left(-1\right)\,\times\,\left(-1\right)\right]\,\times\,\left(-1\right) \,=\, 1\,\times\,\left(-1\right) \,=\,-1[/eqn]

And neither of your formulas is a function (they're equations).

>>9145175
>>9145185
I understand now. Thanks for the help!

>>9145084
>>>/r9k/ek

What are gradient fields actually used for?

So I had to find [math]\int \arctan (x) dx[/math] which, according to what I did, equals to [math]x\tan^{-1}(x) + \int x\csc^{2}(x)dx[/math].

When I try to find [math]\int x\csc^{2}(x)dx[/math], I get to [math]\ln \left | \sin(x) \right | - x\cot(x)[/math].

Therefore, my calculation ends up being:

[math]\int \arctan (x) dx = x\tan^{-1}(x) + \ln \left | \sin(x) \right | - x\cot(x) + {C}[/math]

BUT! Wolfram Alpha says it should be:

[math]\int \arctan (x) dx = x\tan^{-1}(x) - \frac{1}{2}\ln (x^2+1) + {C}[/math]

Are these equal? Did I fuck up? I seriously can't find an answer to these two questions. Please help ;_;

>>9140659
It's 50/50.

>>9145442
Is [math]\tan^{-1}[/math] supposed to be [math]\arctan[/math] or [math]\cot[/math]?

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>>9145472
Holy shit, for some reason I messed up thinking [math]\arctan[/math] was equal to [math]\tan^{-1}[/math], didn't even think about it (and I even had to use a [math]\cot[/math]!). Thanks for answering, I'll do it again.

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>how do microwaves work?
>why do some people fear they are unsafe for household purposes?
>how reasonable are these fears?

>>>9143931
>so the +1 or -1 is just a meme?
>what about formal charges for atoms in mole

No, +1 -1 is not a meme, I'm sure the diagram in your post has 1.6*10^(-19) c = 1.

In literature, if there's ever a mention to a charge in a molecule to be X e, then to obtain the charge in coulombs you just multiply by 1.6*10^(-19) c. This is done a lot in physics to simplify things. We set a lot of constants equal to 1.

>>9145492
microwaves work by accelerating electrons in a certain container at a certain speed

they're using broken microwaves

not reasonable. the metal grate you see on the window is there so the microwaves can't escape
unless you remove that you're fine

>>9145492
Water molecules are unbalanced electrically speaking (due to the shape of the molecule and the polarization of the H-O bounds). It has a + and - electrical (not magnetic) poles which react to electric fields. Light is an electromagnetic wave and therefore causes variations in the electric field. Microwaves happen to be at the resonance frequency of water molecules, so they agitate a lot, resulting in fast-increasing temperature. It doesn't cause cancer directly, but it can kill cells. Unless you spend half of your life in telephonic conversations and mostly eat microwaved garbage (and some people do that), you're mostly safe.

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>>9145492
Microwaves work via a very small nuclear reactor that produces heat, which it transfers into the food. This is where the term "nuking" your leftovers derives.
The microwave radiation from the radioactive isotope has been shown in many studies and anecdotes to be a direct cause of numerous kinds cancer. Radiated food, or being exposed to the waves themselves, can be fatal on a long enough timeline.

>>9145417
morse theory

there's the number i representing the number whose square is -1.

are there special numbers or functions for concepts like...
something to represent division by 0?
something to represent conversion from irrational to rational, or a number's irrational part as a generalized concept? perhaps something like some factor times the square root of 2 suffices, as the square root of 2 is the first irrational number produced by a function of whole integer values(if i'm not mistaken)?

>>9142441
https://en.wikipedia.org/wiki/Energy%E2%80%93momentum_relation

>>9144498
https://www.google.com/search?q=y%3Dsqrt%28x%5E2%2B2x-1%29%2C+y%3Dx%5E2%2B2x-1&oq=y%3Dsqrt%28x%5E2%2B2x-1%29%2C+y%3Dx%5E2%2B2x-1&gs_l=psy-ab.3..33i160k1l3.25861.38489.0.40586.5.5.0.0.0.0.420.1241.0j2j2j0j1.5.0....0...1.1.64.psy-ab..0.5.1238...0i8i30k1j0i22i30k1.4TmwHi7TIHM

>>9145560
There's nothing for division by zero (unless otherwise defined, which is rare and slightly dangerous), since then your set won't form a field. Complex numbers are a field, and that already makes them rather useful.
For the irrational question, I think you are looking for algebraic numbers. I don't think all of them are expressible in closed form using radicals, but they are represented by a rational-coefficient polynomial by definition. In addition, they are countable, similarly to rational numbers.
Also, [math]\{a_n+\sqrt{b_n}\mid a_n,b_n\in\mathbb Q\}[/math], what you somewhat described, is a field and a subset of algebraic numbers. It's too limited for most purposes, but sometimes useful.

>>9145610
That should be [math]a+b\sqrt2[/math].

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Are [math]\mathbb{Z}[/math] and [math]\mathbb{Z} \oplus \mathbb{Z}/2\mathbb{Z}[/math] isomorphic as groups?

>>9145622
No. See the fundamental theorem of finitely generated abelian groups.

>>9143683
Bump

>>9133519
If you sped up a fairly massive object to close to the speed of light, I think it would become a black hole. It would have huge values for momentum flux in the stress-energy tensor. It would be more something like a "black ellipsoid" though.

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>>9144556
>X+(X^2-1)
It's fucking algebra, MITnigger.

>>9145492
> why do some people fear they are unsafe for household purposes?
> how reasonable are these fears?
A correctly-functioning microwave oven is perfectly safe. One which leaks microwaves can cause cataracts or (rarely) other injuries. The main thing is to check that the seal around the door is tight. Even a fairly narrow gap can leak enough power to be harmful (the total amount of power for a domestic microwave oven is 500W-1000W; a leak of a few watts is significant).

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Is there a non-brainlet way to show 3 is a primitive root mod 257 besides just showing that 3^128=/=1 mod257?

>>9145848
>>9145492

it doesnt do shit

i know a person who bypassed the safety system so you can put it on while door is open just to put his head into the oven and turn it on

result: minor headaches

sooooo denbunked i guess

>>9145860
[math]0\neq 3^{128}-1=(3^{64}+1)(3^{64}-1)=(3^{32}+16)(3^{32}-16)(3^{32}+1)(3^{32}-1).[/math]
Then show that 3^32 is none of 16, -16, 1 and -1.
I don't see a way to split 3^32+16 further, except for solving other difficult equations.

>>9145953
Ahh clever, cheers for that

>>9145926
Can I see the scientific paper on his experiment? If not, take your spacing back to where it belongs.

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The fuck are these?

I have been self studying modern algebra from a basic undergrad introductory text. I thought everything was making sense, but I am worried I'm not seeing the big picture. I realize the number systems we use of course have all of this built in structure, but what exactly does all of this have to do with the elementary algebra we learned in highschool?

>>9146168
>what exactly does all of this have to do with the elementary algebra we learned in highschool?
Not much.
At least around here, high school teaches the calculation techniques necessary for many fields, such as economics, engineering and some statistical fields.
Modern algebra has higher abstractions that are very useful for higher level mathematics and its applications, but would be a nightmare to teach at high school.
>I thought everything was making sense, but I am worried I'm not seeing the big picture.
That sounds about right. The point is that the constructions are as minimal as possible, so you can apply them in many areas.
For example, group theory can be applied not only on numbers, but also on invertible operations on various structures. Typical examples include the operations on a Rubik's cube and permutations.

In the same way that physical laws might be different in a parallel universe, is there any reason to believe that the laws of mathematics and logic might be different there as well?

>>9145560
>something to represent division by 0?
https://en.wikipedia.org/wiki/Wheel_theory

>tfw brainlet that constantly fail at circuit because my teacher is autistic and only test us with some weird circuits full of shorts and dependant sources
just kill me please

>>9146211
Most appreciated anon

I wanna memorize the periodic table like a champ, the more details the better. Anyone here already do it? Mind sharing some tips?

>>9145926
One unverified (read: invented) anecdote on a Mongolian basket-weaving forum doesn't debunk shit.

Pumping several hundred watts into any part of your body can give you serious burns rather quickly.

Putting even a tiny fraction of that into your corneas will cause damage, because there's no blood flow to remove the heat.