STUPID QUESTIONS THREAD: I'll start because I am stupid.

>>7779489
http://www.rcsb.org/pdb/ligand/ligandsummary.do?hetId=NC6

>>7779495
>http://www.rcsb.org/pdb/ligand/ligandsummary.do?hetId=NC6

thanks but the article says acidS

I'm assuming it's a type of acid.

What does the 6 mean?

>>7779489
http://pubchem.ncbi.nlm.nih.gov/compound/6420120#section=Top

>>7779489
if you give us the name of the article it'd be faster

>>7779578
Clostridial constipation’s broad
pathology

Are you too stupid to use the catalogue?

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>>7779584
OP, it says "butyric and NC6 acids"

so it's plural because it's talking about 2 acids, not because there are many types of NC6.

what the fuck you mongol.

you made me waste 5 mins of my precious time

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>>7779602
>so it's plural because it's talking about 2 acids, not because there are many types of NC6.
Okay forgive my idiocy.

NC6 and butyratic okay.

Also another thing I'm confused about is that on the first page of the article it says medium chain fatty acids are produced by clostridia and cause water absorption in the intestines and short chain fatty acids reverse this and cause water retention instead

But a few paragraphs into the article it says clostridia produces butryric acid(which is a short chain fatty acid) and that this short chain fatty acid causes water ABSORPTION and constipation.

Did he not just contradict himself severely?

The fuck?

Also is butyric acid and butyrate the same thing? Why do they have two different wiki articles and yet are used interchangeably in these articles?

Please thank you I'm really sick and need to research....

>>7779625
>Also is butyric acid and butyrate the same thing? Why do they have two different wiki articles and yet are used interchangeably in these articles?

butyrate is just the deprotonated form of butyric acid so yes, the same exact molecule. This sort of nomenclature is used very often, just think about the Krebs cyclus, all those names end in -ate because they are deprotonated whereas the dehydrated molecules are called acids.

also, i don't know about the fatty acids and i'm not going to read the entire article for you, so here's a bump. for all it's worth.

>>7779638
>also, i don't know about the fatty acids and i'm not going to read the entire article for you, so here's a bump. for all it's worth.
thanks friend

bumping for help

>>7779648
i'm not your friend, mate.

How do i stop being lazy piece of shit.
I literally can not motivate myself to do anything productive.

>>7779714
kay well whatever then

>>7779730
meth

or figure out what's wrong with your body's biochemistry
thats what im doing

>>7779741
>figure out what's wrong with your body's biochemistry

but how does one do that?

>>7779750
Fall into insane craziness over the past 6 years trying to figure out what the fuck is wrong with you, do like a million test from doctors and 3rd party labs, take a billion different supplements and drugs and find out only 4% of them were even beneficial.

I'm actually doing a fecal transplant this summer. Sounds great.

Medical science is in the stone age and innovation has stagnated, I blame the FDA and AMA.

Is there such a think as jerking off too much?

I'm talking like 3 to 5 times a day.

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I'm having too much trouble finding a suitable function for this: Let [math]G[/math] be the set of the nonzero real numbers with operation [math]x*y=xy/2[/math]. Find an isomorphism from [math]\mathbb{R^*}[/math] (the multiplcation group of [math]\mathbb{R}[/math]) to [math]G[/math].

>>7777777

>>7779839
yes there is.

I'd say, once a day is a-ok!
Twice a day is already damaging to your productivity.
Thrice and you will 90% stay a NEET with no gf

>>7779489
My problem is the following:
Given two isosceles triangle the first one has an incircle touching the two equal sides at the further third the second one touches the closer third. In which triangle occupies the circle more space?
Sorry i couldn't translate it better.

Where can I find an actually legible .pdf of Vol 1 of Apostol's calculus?

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Hoop of radius r, mass m, velocity = 0, and angular velocity wo is placed on flat surface. What time does it begin to roll without slide? mu is coefficient of friction.

>>7780878
http://4chan-science.wikia.com/wiki/Obtaining_textbooks

Books about hard determinism?

When do you use RBF networks instead of MLP?
I understand that RBF usually has 1 hidden layer, and they differ from MLP via their activation and combination functions among others, but how do I decide when a data set is suited better by RBF instead of MLP? Do I have to try both and compare the results every time?

>>7779867
First, note that the identity element of [math]G[/math] is 2. So [math]1 \mapsto 2[/math].

So [math]f(x) = 2x [/math] seems like a possible candidate for the isomorphism; at least, it would be my first guess. And you can check that it is indeed an isomorphism.

Need something for Calculus 1.
I am thinking about some already solved exercises I can work on aside the homework I solved.
I feel very uneasy and stuck on the simplest exercises and it is because I am not really sure of myself yet.
Especially proofs and limits.

In trying to find functors from the category of groups to itself which fix all objects (so they just have to take each homomorphism to another homomorphism in a way which respects identities and composition), I was only able to come up with the identity functor and the functor which takes all maps to the trivial map. Are there any other obvious ones?

>>7781301
Do you want it to strictly fix groups or just up to unique isomorphism?

>>7781316
I want it to strictly fix groups.

I'm going to take a math class over the summer, but since it's an accelerated semester I only get 10 weeks instead of 14. Because of this I do not know if I should take Linear Algebra or Integral Calculus.
Generally speaking which one is easier, so the lack of 4 weeks won't kill me?

Does the order of addition of the ingredients (sugar, lemon, water) in the making of lemonade changes the flavor?

That is
>water-sugar-lemon
>water-lemon-sugar
>sugar-lemon-water

I was asked this in class and I thought that it doesn't matter the order, but seems like a tricky question.

>>7781319
Stop being such a fag

What are the values for x when tan2x+sec2x=0.5
I've gotten to 2sin^2x + 4sinxcosx + 1=0

>Wat do
>Inb4 homework
>there are no solutions to this online

>>7781341
I think this depends on what you are more familiar with. I would take Integral Calculus because I've had calculus courses for the past 2 years. And linear algebra (I have never taken it) would be new content for me so perhaps would take me a little bit more to understand the problems.

>>7781354
>I would take integral calculus because I already know it
What?

>>7781354
That's what I initially thought which made me want to take Calc, but I then realized that although you get 4 extra weeks you also are taking another 9 or so hours in addition that can create conflict when over the summer I can devote all my time to one subject.

>>7780891

bump for this

>>7781364
you know that there are more than one integral calculus course?

>>7781348
We have [math]\frac{\sin(2x) + 1}{\cos(2x}} = \frac{1}{2}[/math]

Thus if [math]\sin(2x) + 1= a[/math], [math]\cos(2x} = 2a[/math]

We solve this system of equations for x and a. We have

[math]2x = \sin^{-1}(a-1) = \cos^{-1}(2a)[/math]. Solve for a:

[math]a-1 = \sin (\cos^{-1} (2a)) = \sqrt{1-(2a)^2} [/math]

[math] a^2 -2a + 1 = 1-4a^2[/math]

Solve for [math]a[/math] using the quadratic formula and substitute back in to solve for [math]x[/math].

>>7781375
Basic integral calculus? No measure theory, not multivariate functions (which is still just calc 3), etc? No, there's not.

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What kind of maths is this?

What is trying to be proved/solved here? What is this technique of expanding/recompressing a tree of variables?

It's not homework, I just came across this picture and it intrigued me.

"w --> x"? "w = x"?

>>7782231
My first thought is that it could be a lattice of subgroups, where the symbols indicate generators for the subgroup. But these all would have one generator (and form a strange group), so I'm skeptical.

Assuming g(x) is the Gaussian density function. What does g(x) even represent?
I know that to calculate the probability that a <= x <= b, I just have to integrate g(x) over [a,b].
However, it just bugs me that g(x) does not represent anything. Is g(x) really just a value of a function? Does it not represent anything by itself?

How to prove that 1+1 = 2? Given that the triangle inequality is true?

>>7782405
The real numbers are an ordered field. One of the operations defined on this field is addition. That means 1 exists in the field and 1 + 1 = 2. That's how.

>>7782322
Someone help me on this.

>>7782322
>>7782422
The probability of the random variable X taking on any specific value is 0, but g tells us the "relative chance" of X taking on a specific value, in the following sense:

The probability that X = x is g(x)/g(y) more likely than X=y.

So if g(0) = 3 and g(1) = 2, the random variable is 3/2 more likely to be 0 than it is to be 1.

>>7782428
Thanks for this.

>>7782241
Lattice theory deals with many things that aren't groups as well.

So, guys, how hard is it to TA at a good uni ?
I'm a grad student and I'd like to study abroad for a while (a semester or a year) in a year and I heard that you could support yourself as a visiting grad student by TA-ing.
Have any of you guys done it and if so, how was it and how did you get the job ?

Can someone explain me the dB scale?

They say dB only measures a ratio. Good.
Then they say it's measured by `10 * log10 of (ratio)`. Good
But then they say that +3dB doubles the initial number. I say okay, it's not very intuitive, but I guess that's what the log base says?

But then I try it with a calculator and take ratio = 5

10 log10 of 5 = 6.98970004336 ~ 7
5 + 3 = 8
10 log10 of 8 = 9.03089986992 ~ 9

9/7 =/= 2

So how does it work?

>>7783064
Oh wait I'm stupid, I'm not supposed to add 3 to the ratio, I'm supposed to add 3 to 7 (the dB result) and calculate the ratio from it. Will this give me the right result?

On the topic of dB... how is the formula in pic related calculating dB? The number of the log is not a ratio, it's a square root of the product of 2 values. I thought the denominator should be "the reference" in decibels..

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Forgot pic as always

Hey Guys, I was doing problems on limits, namely L'Hopital's rule problems.
I came across a set of indeterminate forms in my text book that I'm not really sure about
[math]1^{\infty}[/math] and [math]\infty^0[/math]
Clearly both should equate to 1 right (at least the first one should)?

>>7783322
For the first one, consider [math] \displaystyle \lim_{x \rightarrow \infty} (1+\frac{1}{x})^x [/math]. This is of the form [math]1^\infty[/math], yet is equal not to 1 but to [math]e[/math].

For the second one, let's try to think of a sequence of the form [math]\infty^0[/math] that diverges to [math]\infty[/math]. Consider [math]\displaystyle \lim_{x \rightarrow \infty} x [/math], which diverges to [math]\infty[/math]. This can be written as [math]\displaystyle \lim_{x \rightarrow \infty} (x^x)^{\frac{1}{x}} [/math], which is of the form [math]\infty^0[/math].

You can modify the above examples to get limits of either form that converge to any non-negative number.

>>7783337
Wow, Thank you my friend. That is a really good explanation !

In multivariable calculus, there are ways to prove that a limit exists for a certain point in the domain, and there are also ways to prove that a limit does not exist for a certain point in the domain. However, is there a way to get a definitive yes/no answer as to whether a limit exists at that point?'

I've been trying to restrict the domain of the function to a circle with radius r around the point and see what happens as r approaches 0, but no luck.

>>7779625

I can only assume that the author is referring to the small intestine as the intestines and the large intestine as the colon. He refers to the intestines in one instance and the colon in the other.

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>>7779489
is pic related supposed to be a pun or is it just le random nerd XD nonsense
>implying the latter excludes the former

sorry for ruining the thread with senseless pop-sci in advance

>>7779489

Fatty acids with something with the 6th carbon

>>7783529

ΣF=0
mg=-kx

I don't get it, birthday?

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I need some help related to angles in vector's components.
In example A, how do I know I'm supposed to add/subtract from the angle the vector gives me? The angle always goes from x-positive to y-positive like the unit circle(or reverse if negative)?
That's why, in example B, even if is not exactly like the normal Cartesian coordinates(y+ to up, x+ to right), it still subtract from the given angle because it goes from +x to +y?

Can someone tell me how do you get from
k*k!+k!
to
(k+1)!

Thank you.

>>7780957
David Bohm Wholeness and the Implicate Order

>>7783720
k*k!+k!=(k+1)*k!=(k+1)!

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>>7783716
In example A, the author just associates y+ axis with north and x+ axis with east (With this he also implicity associates -y axis with south and -x axis with west), and locates the vectors accordingly. Like "32º east of north" means you stand in the north (90º in the book's example) and walk 32º to the east (to the right, in the book's example). Which is exactly what it's done after: "(90º - 32º) = 58º".

In example B I got confused to at first, but it's just because it's not only flipped, but mirrored as well. Check pic related and you'll agree the calculations makes sense

given two points there's only one n-dimensional rectangle that has the segment determined by those two points as its diagonal?

>>7779730
Try meditate

>>7783740
I understand, so in the B vector from the A example, how it turns to be 216º? It's because he was standing to the west(180º) and turned to south(36º) so it becomes [180º + 36º] 216º? But that is because he decided that west = 0º, north = 90º, east = 180º and south = 270°? Also, it follows the unit circle that turning left is positive and right is negative(add and subtract)? Thanks, btw.

>>7783748
No? I could be wrong, on top of my head, if you have two points horizontally lined up in a plane, any diamond with its vertex in each point would have the segment that joins them both as a diagonal.

>>7783529
where you born in the spring?

>>7783748
Nah, if you get one, then you can rotate it (at least for n > 2)

>>7783758
It doesn't follow any unit circle thingie, you add to 180º simply because south is defined as 270º, which happens to be on the "left" of the 180º. If south were 90º, you'd have to subtract.

>>7783774
I see, thanks.

>>7779489
Why is benzene carcinogenic?

Also, do esters confuse anyone else?

Who absolutely has to masturbate before studying here?

Can somebody give me a quick breakdown of what the telecommunications field encompasses, and what sort of projects one might expect to work on with a background in communications networks.

I wound up in a grad level computer communications networks class, but have no clue what i'm getting myself into. Just looking at the title of the course makes me think it'll be boring as hell, but the professor teaching it reached out and asked if i'd like to take it, and the previous class I took with him was one of my favorites so far, so i'm kinda taking a chance on this class.

>>7779489
A speeding car has a velocity of 25m/s and passes a police car which starts at rest then begins chasing after the speeder with an acceleration of 5m/s^2. The police car catches up to the speeder after 10 seconds and is going 50m/s when he catches up. My stupid question is how fast is the police car going when he is 25 meters behind the speeder? I cannot figure this out for the life of me.

position of speeder = (25m/s)(t)
position of police car = (5m/s^2)(t)(1/2)

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>put a bunch of women's lingerie in a duvet cover
>tie up the duvet cover
>wash it with detergent and fabric softener (30 degrees Celsius)
>wash it again without detergent/softener to rinse it (30 degrees Celsius)
>tumble dry on low heat
>duvet cover has a fairly large pink stain from one of the panties
What should I do to try to get rid of the stain? Wash the duvet cover obviously, but are there any particular detergents I should be using and what about the temperature? Should the temperature be low so that the dye doesn't "set" or should it be high to help oxidation or whatever? Any other tips of what I can do to get rid of the stain?

The panties are 79% polyamide and 21% elastane. The duvet cover is made of cotton.

>>7783799
>Why is benzene carcinogenic?

Because it has been demonstrated to cause cancer

>>7783069
>>7783068
>>7783066
>>7783064
bump

Is MSE automatically lower if you normalize all the values between [0, 1] before calculating whatever you're calculating? It feels like it should be but can't ifnd anything on the internet to discuss it.. cause it would make MSE by itself meaningless

>>7783069
>doubling the photons or the exposure time doubles the SNR

well that's cool, guess i know now why bright areas and long exposures are less noisy

>>7784853
>more photons captured on the sensor means less noise caused by low amount of photons
genius discovery m8

>>7783064
>>7784825

10 log10 of 5 is ~7

if you double 5, you get 10 log10 of 10, which is 10 = 7+3dB


same if you start with... 35 for example

10 log10 35 = 15.44

10 log10 70 = 18.45


this is easily provable.

if you have a ratio R, and take its value in decibels D, then you have:
D = 10 log10(R)

now if you consider 2R and its value in decibels D', you have
D' = 10log10(2R) = 10log10(2) + 10log10(R) = 10log10(2) + D ~ 3+D

this is where the 3dB comes from (10log10(2) ~3dB)

>>7783069
>>7783068
when only "log" is written, it's assumed to be logarithm in base 10
when "ln" or "Log" is written, it's the natural logarithm.

>>7784861
you don't know how dumb you sound now, but one day you will

>>7784863
I see.. many thanks mate it makes sense, especially the proof
>>7784864
Thanks, but I guess I'm more wondering about the number of the log rather than the base... How is sqrt(a*b) a ratio?

>>7784865
do explain

>>7784866

[math]SNR = 10 log_10 (\mu / \sigma) = 10 log_10 ( \beta t / \sqrt{ \beta t} ) [/math]
I swear if the latex doesn't work I'm not trying again, this shit is cancer.

>>7784869
the more you listen to a woman, the lower the signal to noise ratio.

>>7783529
perhaps using Hooke's Law to reference getting birthday hookers? It's a stretch, to say the least

>>7783529
reverse image search
you find a website where they sell this

the inside text reads
"Just
wishing you
some
good vibes."

>>7784875
Oh damn I see it now thanks a lot

So, I don't know a whole lot of maths, but I want to know if I can make this into a function of some kind. How to explain this stupid shit?

I have 1/10 * x, where x is a series of fractions multiplied by each other, each reducing by 1/10. So, if x is 1, it would be 1/10 * 9/10. If x is 2, it would be 1/10 * 9/10 * 8/10. If it's 3, I would have 1/10 * 9/10 * 8/10 * 7/10, and so on. The values of x would be 1<=x<=9.

>>7784895
(1/10)^(x+1) * (9!/(9-x)!)

! stands for factorial.

>>7784902

Greatly appreciated, off to do some reading now.

I injected acetonitrile into a GC-MS.
The MS showed a molecule with a mass of 54, but acetonitrile has a mass of 41,05. How the fuck could the MS have found a molecule with a higher molecular mass ?

>>7783799
Benzene has been found to be carniogenic, because it can break the DNA strands and cells in general.

http://www.maneyonline.com/doi/abs/10.1179/oeh.2007.13.2.213

>>7784904
np, enjoy your reading!

>>7783799
Why would esters confuse anyone?

>>7784190
>>7784190
>90km/h
>speeding
wew

Integrating twice for the police car, we get its position as 2.5*t^2 after t seconds, so all you have to do is solve for (2.5*t^2 + 25) = 25t, or t^2 - 10t + 10.

>>7784190
>>7784930
Whoops, meant t^2 - 10t + 10 = 0.

My textbook says the Doppler effect is only noticeable if the difference in speed is not negligible, and the sound source and the observer's speed are lower than the speed of sound.
What happens if the sound source is moving faster than the speed of sound?

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How do I simplify this further? I can see that terms in the numerator and denominator cancel but how do I write this?

>>7784949

Then you can't hear it coming. And then you get a sonic boom.

Hey Sci, need some advice:

I have fucked up and am now gonna prepare for Calculus 1 with a crashcourse script and supplementary exercises and tests for about a month and hope for a D.
How many hours should I study for that a day, if I have 12 weeks of knowledge to fill?
10 hours?

If I manage to pass, I want to learn it properly in the hopeful 2 months of winterbreak to prepare myself for calculus 2 along with organic chemistry and Java.
you think it is possible?
I really do not want to fail anymore and want to become someone who invests in himself.

>>7784966
cancel out the 5s, 7s, etc. You will be left with (3i + 2)/2 because both (3i + 2) and 2 appear only once.

>>7784966
I'd break those up into a product of fractions and then show how the first few products in the series cancel out. I would probably also write it out using the product version of Sigma notation (because as it's currently written it's not entirely clear that the number of terms on the top and bottom of the fraction are equal.

This technique has a name, but I don't know it (I've been mistakenly calling it the telescoping product argument). If you find out what it's called then probably just saying it together with some brief exposition will be enough for the reader to know (or be able to figure out) what you're talking about.

Where do /sci/entists get articles from that aren't blocked by pay walls?

>>7784988
>>7785018

Much appreciated. Thank you.

I felt a tingling and my hair started sticking up on my right arm (Might have been all my hair,) in the shower, I jumped the fuck out as soon as I saw the hair sticking up as I know it's a sign of lightning and static electricity and my hair instantly went down, however I'm in my house and it isn't storming. Can anyone explain what the fuck just happened? I tried googling but found nothing

Can someone post Non-Euclidean Definition on 5th postulate about parallel lines. Can't fucking find it anywhere

>>7784930
>>7784931
Thanks anon,, the book didn't give a clear explanation of the solution. also the speeder was in a school zone and ran over several children.

>>7785321
>yfw the police car runs over more children in the process of catching up with the speeder

Is there a reason for the electric dipole moment and the magnetic moment to have the same symbol?

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Why can't you divide by zero?
If you have a number, and dividing it by a number that approaches zero causes that number to approach infinity, then why wouldn't dividing it by zero just equal infinity (or negative infinity) itself?

yo hol up

you know that galaxy that has a ton of gas that moves at thousands of miles per hour

how come its temperature is like, 1 degree F over absolute zero if it has so much kinetic energy?

in fact, why does wind lower temperature if it is movement. Isn't movement energy and therefore heat?

yes I never took science classes outside of highschool

>>7785567
If you identify [math]-\infty[/math] and [math]+\infty[/math] together, they any nonzero number divided by 0 would equal [math]\infty[/math], sure. But 0/0 would still be indeterminate.

>>7785591
>But 0/0 would still be indeterminate
Oh shit yeah
That's interesting
Thanks anon

>>7785608
>>7785591

my abstract algebra prof. once said

>you can totally divide by zero. you just can't ask what the result it

he meant that you can determine whether a number is or isn't divisible by zero. it's kinda interesting how the same problem is approached by various fields (algebra vs. analysis)

>>7781343
Depends on what you're making. Generally, it DOES make a difference. Chemical pathways often have more than one results.

But for something as simple as lemonade? The only thing different is the rate of homogeneity, i.e. the rate at which it all mixes evenly. Optimally, water should come last, since it's typically the thing with highest mass in the mixture, so energy used in mixing it up will mostly come from the huge mass of water sploshing the mixture.

So if we go with the assumption of ONLY adding it in, without any extra energy in mixing it and shit, most efficient path would be sugar-lemon-water.

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Given this drawing of two topological spaces X, Y I am asked to show that -
• X and Y are not homeomorphic;
• The one point compactifications X* and Y* of X and Y resp. are not homeomorphic.
I have no clue what I could use. Does someone else see it?

>>7786092
For showing the spaces aren't homeomorphic: remove a point and count connected components. This is a standard trick.

>>7786243
What points would you remove? I know of this trick but say I remove a point from either of the circles, the result is still connected. If I remove any other points Im left with two connected components in both cases. Right?

>>7786248
if the line in Y is tangent, then removing the intersection point will result in 4 connected components. there's no such point in X.

>>7786291
Fuck, ofcourse. Thank you!

>>7786294
yeah, but at the first sight, I was so fucking sure that Y stays connected even after removing the point

>>7786092
>>7786243
Also, do you at least see intuitively what the one point compactifications are? From there, you should have no problem finishing the second part.

>>7786354
isn't the one point compactification basically just gluing the "open" points together ? not sure, I have yet to take a course in topology

>>7786392
The one point compactification of X is a compact (Hausdorff) is compact space Y such that Y-X is a single point. It turns out it's unique, so if you find something that fits the bill (which you did) you know you're right.

>>7786480
How would you go about proving such a thing (uniqueness)?

>>7786487
You suppose you have two compactifications and find a homeomorphism between them. In this case, it's even the first thing you'd think: each space only has one point that's different, so map those points to each other.

I spent my christmas holiday studying for optional scholarship exams. I tanked the last one (of 3). I feel like this is the thread for me...

What is the difference between a number and an integer?

>>7786623
Number = a super general term for numerals. Can be classified into integers, primes, etc. This is a pretty shallow list of examples though.

Integer = specifically, numbers not in decimal form. Just a straight ass digit value, no dot/point.

if i multiply two rotated matrices is the result the same as performing the rotation to a 3d cartesian plane twice.

so if i rotate a plane about the z-axis 60 degrees and then rotated it about its' x-axis 30 degrees, would that end result be equal to A'*B' where the primed matrices are of course their rotated form.

>>7779714
faggot

>>7781348
>highschool junior

>>7786623
>>7786658
Natural number: 0,1,2,3,4,5,...
Integer: ...-3,-2,-1,0,1,2,3...
Rational: any number described by p/q where p and q are integers and q is not equal to zero. 1/1, -1/4, 245/2111, etc
Irrational: any number that cannot be described as the quotient of two integers. square root of 2, pi, etc.
Real: any natural, integer, rational, or irrational.

>>7785591
-1

not stupid but not sure it deserves it's own thread:
I've learnt Linear Algebra on Lang's book, which very beautiful and algebraics but completely void of applications. What good book could I use next to learn more about topics that aren't covered, such as matrix decompositions?

(Original poster of the question here)

>>7786313
Yeah so was I, til I realised that the line was in fact tangent. That pretty much cleared everything up.

>>7786354
Yep, X* looks like θ and Y* looks like an 8.

>>7786392
Definetely go on and follow the course, I need some real practice on proving spaces are homeomorphic (if anyone has some tips, theyre welcome!) but I love learning about it so far. Its the interesting side of analysis.

>>7786487
Unique up to homeomorphism mind you, its possible there exist two one-point compactifications which are not identical but are homeomorphic, so for topological purposes they are practically the same. That is why a general point "at infinity" is added instead of of an explicit point. If you dont have a good grasp of homeomorphisms, read the wikipedia page and puzzle it out for a bit if youre interested.

>>7786494
On what grounds could you say this is a homeomorphism? If you consider the one point compactification as a pair (X*, i) wherein i is an embedding and |X*-X| = 1 with X* compact Hausdorff, the embedding i ensures that X and i(X) are homeomorphic, but how can I be so sure that adding an extra point to this map does not affect it being a homeomorphism still?

I need a General chemstry site to solidify my mushy knowledge for The 2nd exam in gen chem I have amassed from the workbook on gen chem for dummies.
Wasn't enough. :(
I feel dumb for being unable to do more than the half of all the questions I thought I would ace.

What is a good source if I am willing to spend 20h a Week?
I can not spend more and the math test is in almost a month.
I need help.

https://infotomb.com/4gq25.jpg

Where do I need Crammer's rule? I mean, there is a way faster and simpler way to solve systems of equations so why bother?

>>7780852
Post original language statement.

>>7780891
>>7781371
coefficient of friction does not mean a thing. it can be static or dynamic. not to mention all the other kind of friction but I'm assuming you're talking about 'standard' friction.

>>7781301
Do you actually call it 'the category of groups'? I usually call it Grps which is funny and autistic especially since my prof is German and he pronounces it something like 'gehrpss'

>>7781341
Don't take linear algebra if you know you're not going to study it well. Especially since if it's condensed it's probably going to miss essential stuff.

If [math]\frac{dy}{dx} = \frac{\frac{dy}{dt}}{\frac{dx}{dt}}[/math] then is it true that [math]\frac{d^2y}{dx^2} = \frac{\frac{d^2y}{dt^2}}{\frac{d^2x}{dt^2}}[/math] for 2nd (and higher) derivatives?

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>>7787659
>>7787660
...I give up.

>>7787660
no, it doesn't even work for y = x

>>7787676
Well shit, have my teachers been lying to me all this while?

>>7779489
Was the Evolution observed?
I mean, a changing from one species to another?

>>7787682
why?
You're drawing a bad conclusion on your own anon

d2y/dx^2 = d(dy/dx)/dx = d((dy/dt)/(dx/dt))/dx.
now apply this again but with z= (dy/dt)/(dx/dt):

>>7787718
Oh, I thought you were talking about the first part.

>>7787667
No, it isnt, you know the product rule right? Apply that to the chain rule to find the higher derivatives, you'll actually find it follows a nice binomial pattern

>>7787724
I see. I think I got a bit of it now.

>>7787729
Good boy

>>7787729
>>7787734
Also, stop writing it as a fraction over a fraction, just write it as the product of 2 fractions, much more useful

>>7787735
Product rule applies if y is a function of t and t is a function of x. However I kept getting cases where x is a function of t but not the other way round.

>>7787741
I dont understand what problem you're having, you can just find dx/dt and reciprocate it to find dt/dx

>>7787766
Of course it works for the first derivative. Does it work for higher order derivatives?

>>7779489
im gay

>>7787575
>On what grounds could you say this is a homeomorphism?
This is what you need to prove; all I've stated is that the first map you'd think of is indeed correct.

You know the map is invertible, so you just need to show it's continuous both ways. This can be accomplished by showing the map takes open sets to open sets.

>>7787639
In context I'll just call it "Group" or write "Grp" or something. But in a one off post in a thread full of random shit, I prefer to be a little explicit.

>>7779828
Yes, the FDA and the AMA suck pretty hard.

Cases to prove my point:
FDA - the say cannabis has no medicinal properties. Hahahaha, good one.

AMA - they once conspired (and got caught and charged) with trying to destroy the chiropractic industry.

Neither is concerned about advancing medicine or science. They exist to maximize profits for a select few organizations.

I made some ferrous Chloride by reacting Iron with HCl, but of course there's some unreacted HCl left.
Can I just boil it all off?
I mean Hydrochloric Acid is just a gas dissolved in water.
Shouldn't it evaporate completely leaving me with the pure salt?

>>7788012
>wanting to breathe in HCl fumes
Why not just use excess iron nigga

>>7787938
Thank fuck someone understands this.

>>7787575
(1st and 3rd poster you replied to speaking)

yeah I'm gonna, it starts next semester, I just had to learn some very basics on my own (I'm writing my bachelor's work on differential topology) and love it so far.

btw differential topology is fucking awesome. milnor's book is a bedtime reading, I suggest it to everyone interested in topology or differential geometry.

I finished the Calculus 1 and 2 parts of Stewart's book. Where do I find good practice questions/exams that really challenge my knowledge? Not looking for anything that involves proofs, I'm too dumb for that.

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Why does the imaginary part of that function vanish when integration. V(t)dt namely.

>>7787563
I'd check out Applied Numerical Linear Algebra by Demmel.

I'm studying function of a complex variable and ran into a bit of a conundrum.

When explaining the algebraic properties the text says "The existence of multiplicative inverses enables us to show that if a product z1*z2 = 0 then at least z1=0 or z2=0."

Its easy for me to see why the implication z1*z2 = 0 then at least z1=0 or z2=0 is true, but why/how does this follow from the existence of multiplicative inverses?

>>7788357
Two complex numbers are the same iff real parts and imaginary parts are the same.
[math] |I| [/math] has an imaginary part of [math] 0 [/math].

>>7788576
Wait, nevermind. I think I see why now.

>>7787563
http://4chan-science.wikia.com/wiki/Mathematics#Applied_Linear_Algebra

I'm autistic /sci/. I'm studying for my GED because I'm a degenerate who spent high school doing drugs and dropped out.

2 adults and three children are going to the movies. Adult tickets cost twice as much as children tickets and the total cost of the tickets is 14 dollars. How much are the adult tickets?

I figured out the answer was 4 since the question was multiple choice but how would you go about solving this more efficiently?

Tl;dr
>a = 1/2b
>2b + 3a = 14
>How to find value of b

>>7788736
Use GauB

how can i calculate the range of this function?

[math]f(x)=cos^2x+2sinx(sinx-1)[/math]

>>7788736
adult = 2*child
14 = 2*adult + 3*child = 2*2*child + 3*child = 4*child + 3*child = 7*child
child = 2
adult = 2*child = 4

>>7788736
Never mind, after scribbling for like 20 minutes I figured it out. Did the "substitution method" like so

>2b + 3(1/2b) = 14
Substituted
>2b + 3/2b = 14
>7/2b = 14
>14 / (7/2) --> 14 • (2/7) = 28/7 = 4 = b
Wew lads, it's all coming back to me.

>>7788584
Christ why do I grasp the complicated shit but I hurr durr with trivial stuff like this?

>>7788790
Because you actually don't. Restart studying maths from arithmetics. This time take it seriously tho

>>7789089
It's usually symptomatic of me needing a break. Nice meme though.

>>7788760
draw it

here's a good question

Prove that:
[math]
\frac{d^n}{dx^n}(xe^{\lambda x})=e^{\lambda x}(\lambda^nx+n\lambda ^{n-1})[/math]
for all [math]n \in \mathbb{N}[/math]

>>7789127
Simple proof by induction.

>>7788760
not sure why your tex didn't render

did you mean

[math]f(x)=cos^2(x)+2sin(x)(sin(x)-1)[/math]

?


because if it is...
multiply out the brackets

[math]f(x)=cos^2(x)+2sin^2(x) - 2sin(x)[/math]

use identity

[math]f(x)=1+sin^2(x)-2sin(x)[/math]

then plot it

>>7789147
LaTex has been fucking up on /sci/ lately.

>>7788760
well you can simplify it down to

[math] f(x) = (sin(x)-1)^2 [/math]

since sin(x) has a range of -1 to 1 inclusive, the range of f(x) is 0 to 4

>>7779489

I want to turn my life around and become an engineer. How can I find out if I have the intellectual ability beforehand? I never did any work in school, so I can't use that as a predictor.

>>7788736

Let [math] a,c [/math] be the cost of an adult and child ticket respectively

The question tells us that adult tickets cost twice as much as child ticket

That is [math] a = 2c [/math] and we'll call this equation 1

It also tells us the price of 2 adult tickets and three children tickets

That is [math] 2a + 3c = 14 [/math] we'll call equation 2

Since this equation has 2 unknown variables, it isn't very helpful on its own. However, if we can change it to only contain 1 variable then it can solve for that variable.

If you look at equation 1, it tells us that the price of 1 adult ticket is the same as the price of 2 child tickets, so i follows that the price of 2 adult tickets is the same price as 4 childrens tickets, we've just multiplied both sides of the equation by 2, giving us [math] 2a = 4c [/math]

now if you look at equation 2, we can switch out that pesky 2a for the 4c from equation 1, which gives us

[math] 4c + 3c = 7c = 14 [/math]

So 7 child tickets costs 14 tickets, which means 1 child ticket costs $2, attained by dividing both sides by 7.

now that we have [math] c = 2 [/math], we can put it into our original equation to get [math] a [/math], the price of an adult ticket

[math] a = 2c = 2*2 = 4 [/math]

and so an adult ticket is $4. With these type of problems first lay out what the question tells you in a mathematical way, and the look to eliminate variables.

>>7787339
>implying 0 is a natural number

>>7789280
This.

Being a number theorist at heart, I'm also opposed to 0 being counted as a "natural number".

>>7783720
factorise

[math] k! \times k + k! = k! (k + 1) = (k+1)! [/math]

first step is similar to
[math] a\times b + a = a(b+1) [/math]

second step is because if you have for instance
[math] 3! = 1\times 2\times 3 [/math]
it follows that
[math] 3! \times 4 = 1\times 2\times 3\times 4 = 4! [/math]

>>7789280
Man I had a number theory professor say in class something like "There are many reasons why 0 should be a natural number, so in this class remember that I will be considering 0 a natural number."

>Ok...so how am I supposed to interpret the textbook, which mentions natural numbers.

Also had an analysis teacher say
>Just pretend infinity is a number for this and now the proof works.

>>7789301
This is for you too: >>7789294

Some of these people have ivy league PhDs.

>>7789301
>>7789294

yeah proof by induction is less pleasing if to prove something for all [math] n \in \mathbb{N} [/math] you had to start at [math]P(0)[/math]

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>>7789301
>>Just pretend infinity is a number for this and now the proof works.

>>7789294
As a set theorist, you disgust me. Each number is the set of its predecessors, and zero has no predecessors.

[math]\mathbb{N} = \omega = \{0,1,2,\ldots \} [/math]

>>7789307
I think you're missing something simple at the heart of induction. You can start at any point n and prove it for all numbers at least n, so it doesn't matter.

In any case, I just never use the phrase "natural numbers." Use either [math]\mathbb Z_{\ge 0}[/math] out [math]\mathbb Z_{> 0}[/math] .

>>7789338
I find [math] \mathbb{N} [/math] and [math] \mathbb{N}_0 [/math] more elegant and easier to write, especially small

Clearly it is logicians, who work at the foundation of mathematics, who should decide if [math]0\in\mathbb{N}[/math], and all logicians define the natural numbers to include 0.

>>7789345
But when some people see [math]\mathbb N[/math], they're always going to think that 0 is included. Might as well be explicit.

Another point is that it usually doesn't really matter whether 0 is included; it's often a small technicality.

>>7789345
>>7789367
I prefer [math]\mathbb{N}^+[/math] and [math]\mathbb{N}_0[/math] desu

>>7779714
I'm not your mate, friend

>>7789147
thought I had done everything right but it didnt render correctly. and yeah, that's what I meant>>7789147
>>7789233
>>7789127
thanks for the replies senpai

I modified the Weierstrass function a bit. Is it still continuous everywhere and differentiable nowhere?

[math]f(x)=\sum_{n=1}^{∞}\frac{n}{π^n}\sin{(π^nx)}[/math]

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>>7789535
>the city of leltex

>>7787631
as implied in the first post, it's rolling friction. I can tell you haven't finished freshman physics yet.

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I'm stumped with this.
Obviously
[math] N_\text{Ba}(t) = N_\text{Ba}(0) \exp (-t \lambda_\text{Ba}) [/math]
and
[math] N_\text{La}(t) = N_\text{Ba}(0) - N_\text{Ba}(t) - N_\text{Ce}(t) = N_\text{Ba}(0) (1 - \mathrm{e}^{-t \lambda_\text{Ba}} ) - N_\text{Ce}(t) [/math]
but beyond that I have no idea.

How do I study 10+ hours a day?
I have a scholarship test on june and the syllabi is pretty extensive, at least for math. Also have to study another language, since the scholarship is in Japan. Planning to do my undergrad there because my country's education is a piece of shit. I'd appreciate some advice.

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I'm not sure how to start with Pic related and it's really important for me to solve it properly.

So does this mean i just have to figure out if it converges (if the sequence of it converges to 0) and (with the root or ratio test) if it converges absolute? or do i have to do more than that and find the limit too?

>>7790241
It's me again, apperantly i can solve this with cauchys condensation test.
Altough i will only know if it converges or diverges, my question if this is enough still remains.

>>7790241
you just have to compare it to the harmonic series, and realise that log(n)^B<n^B or something

I have a function that satisfies:
f(0)=0 , f"(x)>=0 for x>=0.
I need to show that for all a>=0 , b>=0
f(a+b)>=f(a)+f(b)
This is probably a stupid question, but does f"(x)>=0 imply that f"(x) even exists for all x>=0?

>>7790292
f(x)=a^x-1
a>1

Anyone know about math research in Complex Analysis? I'm currently thinking about what field I might want to pursue and I'm in Complex Analysis 2 right now thinking this stuff is pretty sweet.

I have a differentiable function [a,b] \to R, how to show that f[[a,b]] is an interval? a,b are real

>>7790610
[math]f[/math] is continuous, so its range must be an interval (there cannot be any "jumps"). By "interval" in this context, we include that f([a,b]) could be an open interval, half-open interval, or closed interval.

But, furthermore, f([a,b]) must be a closed interval by the compactness of [a,b]. Are you to just show it must be an interval, or show it must be a closed interval?

>>7790549
so?

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I am having some issues regarding Fourier's law/the heat equation. I had some document when the top equation was used (with q being the thermal flux, with units of J/s), but I had some issues with it, and from what I could find in google, the thing in the bottom seems to be the correct one, but I am not sure.

Sorry if the question isn't clear.

>>7790549
Not true. Note the inequalities.

>>7790292
Yes, if we look at the rigorous definition of derivative, f''(x) >=0 does imply that f''(x) exists.

>>7790755
It is true, though.

>>7790760
>I have a function that satisfies:
>f(0)=0 , f"(x)>=0 for x>=0.

f(x) = x^2 also works, as do so many others. I don't even know what you're thinking.

>>7790755
thanks bby

>>7790674
it says just to prove that it is an interval.

>>7790821
If f(x_1) = a and f(x_2) = b, then by continuity for any c between a and b there is an x between x_1 and x_2 such that f(x) = c.

>>7790963
Thank you!

>>7789708
[math] t_{\frac{1}{2}} = \frac{ln(2)}{\lambda} [/math]

Stupid video though
https://www.youtube.com/watch?v=SgQc4ZkVeMY

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What does Wendelstein7-X mean for fusion research?

>>7791270
[math]t_{{1}\over{2}} = {{\ln 2}\over{\lambda}}[/math]

>>7779489
I've got one that's dumb beyond belief.

Let's say I'm trying to prove Taylor's Theorem by some integration.

Is this valid?
[math] f(x)=f(x_0)+\int^x _{x_0} f'(t) dt \\[/math]
Trick: Write f'(t) as 1*f'(t) and integrate by parts, differentiating f'(t) and integrating 1.

Here's the part I'm unsure of. Is it ok take the indefinite integral of 1, setting the arbitrary constant to -x? So, I integrate 1 to get t-x?

So, to continue my working, I get:
[math] f(x)=f(x_0)+\int^x _{x_0} f'(t) dt \ = f(x_0)+ [f'(t)*(t-x)]^x _{x_0} - \int^x _{x_0} f''(t)*(t-x) dt \\ = f(x_0) +(x-x_0)f'(x_0)+ \int^x _{x_0} f''(t)(x-t) dt [/math]

My thinking is that the constant of integration is arbitrary, I can set it to anything I want, but I'm just here to double check.

>>7791693
What do you going to do with that linear factor you introduced when you have to integrate again?

If you're actually going to prove the theorem fully it needs to work for an arbitrary number of derivatives

>>7791724
I'm doing it with integral remainder but for now I'm only curious as to the validity of my arbitrary constant maneuver.

>>7791270
>>7791443
I'm sorry, this doesn't help me at all.
I need to calculate the rate at which Barium decays into Ce, by first decaying into La with a particular half life, then decaying from La into Ce.
Obviously you can't just say [math] N_\text{Ce}(t) = N_\text{La}(0) \, \mathrm{e}^{-t \lambda_\text{La}} [/math] because at time t = 0 there [math] N_\text{La}(0) = 0 [/math]. I'm thinking you need to construct then solve some sort of differential equation relating the decay rates of La and Be, as clearly [math] \frac{dN_\text{La (t)}}{dt} \propto N_\text{Ba}(t)[/math] and [math] \frac{dN_\text{La} (t)}{dt} = -\frac{dN_\text{Ba} (t)}{dt} - \frac{dN_\text{Ce} (t)}{dt} [/math]

>>7791751
*Obviously you can't just say [math] N_\text{Ce}(t)=N_\text{La}(0) \, ( 1 - e^{−tλ_\text{La}} ) [/math]

i'm struggling with fucking trig ids; i realize i am mentally deficient

how does (1-tanx)/(sinx-cosx) = -secx? this should be so straightforward; i understand that i need to sub in sinx/cosx for tanx, but i don't see how it simplifies from there

>>7791693
I think that might work. I remember slightly that you can prove Taylor inductively, probably like that.

>>7791758
Multiply top and bottom by sin x + cos x
(sin+cos)(1-tan) / (sin^2+cos^2)
=(sin+cos)(1-tan) as sin^2+cos^2=1
=sin - sin tan +cos - cos tan
=cos - sin tan (since cos tan= sin)
=cos - (sin^2 / cos)
=cos - (1-cos^2 / cos)
=cos - sec + cos
= 2 cos - sec
Hm, weird.

>>7791820
Fuck me, I made a mistake on the very first line, disregard that post.

>>7791758
[eqn] - \sec(x) (\sin(x) - \cos(x)) = \frac{\cos(x) - \sin(x)}{\cos(x)} = 1 - \tan(x) [/eqn]

>>7791758
Hope Leltex holds up this time.

[eqn]\frac{1-\tan{x}}{\sin{x}-\cos{x}}=\frac{\frac{\cos{x}}{\cos{x}}-\frac{\sin{x}}{\cos{x}}}{\sin{x}-\cos{x}}=\frac{-(\sin{x}-\cos{x})}{\cos{x}(\sin{x}-\cos{x})}=-\frac{1}{\cos{x}}=-\sec{x}[/eqn]

>>7791846
...nope it doesn't.

>>7791847
Here, this should work.
[eqn]\frac{1-\tan{x}}{\sin{x}-\cos{x}} \\ =\frac{\frac{\cos{x}}{\cos{x}}-\frac{\sin{x}}{\cos{x}}}{\sin{x}-\cos{x}} \\=\frac{-(\sin{x}-\cos{x})}{\cos{x}(\sin{x}-\cos{x})} \\ = -\frac{1}{\cos{x}} \\ =-\sec{x}[/eqn]

>>7791856
...try again.
[math] \frac{1-\tan{x}}{\sin{x}-\cos{x}} \\ =\frac{\frac{\cos{x}}{\cos{x}}-\frac{\sin{x}}{\cos{x}}}{\sin{x}-\cos{x}} \\=\frac{-(\sin{x}-\cos{x})}{\cos{x}(\sin{x}-\cos{x})} \\ = -\frac{1}{\cos{x}} \\ =-\sec{x} [/math]

>>7791856
>>7791858
Don't bother, >leltex isn't going to fix itself anytime soon.

Seems like it still works in the archives though. As well as in the TeX preview so just copy and paste or something.

>>7791858

Another anon who is fairly good at writing LaTeX in /sci/'s dialect takes the code from the above post, and attempts an unsolicited re-post.

[math] \displaystyle \frac{ 1 - \tan{x} }{ \sin{x} - \cos{x} } = \frac{ \frac{ \cos{x} }{ \cos{x} } - \frac{ \sin{x} }{ \cos{x} } }{ \sin{x} - \cos{x} } = \frac{ - ( \sin{x} - \cos{x} ) }{ \cos{x} ( \sin{x} - \cos{x} ) } = - \frac{1}{ \cos{x} } = - \sec{x} [/math]

In the event that the above re-post was successful in this post, the following should be noted:

-always declare "\displaystyle" right at the top, esp. when working with large operators and complex fractions like the above posters'. This makes everything three times as legible, and it looks sexy to boot.
-to improve odds of success (on /sci/), space out arithmetic operators, other characters and such from the syntactic and functional LaTeX delimiters { and }. When in doubt, add whitespace. 4chan's implementation often complains, for want of a single space mark.
-I made a personal gut choice to eliminate the superfluous line breaks. I can't recall ever having good luck with them, though 'math' was actually improved in recent months.

>>7791934
Well shit.

It's high time /sci/'s LaTeX needs fixing.

>>7791934
Ironically it doesn't seem to be working in the archives if you do that.

>>7791934

Pushing my luck (now that I've had some (You)s), I will now attempt to repost the code directly from the above post, adding only the line breaks that the other poster had originally intended.

[math] \displaystyle \frac{ 1 - \tan{x} }{ \sin{x} - \cos{x} } \\ = \frac{ \frac{ \cos{x} }{ \cos{x} } - \frac{ \sin{x} }{ \cos{x} } }{ \sin{x} - \cos{x} } \\ = \frac{ - ( \sin{x} - \cos{x} ) }{ \cos{x} ( \sin{x} - \cos{x} ) } \\ = - \frac{1}{ \cos{x} } \\ = - \sec{x} [/math]

Should the above prove successful, since we're in a sandbox SQTDDTOThread-thread, I shall re-post a long-form version of the celebrated Barnett Identity, which is rarely seen in its full splendor.

just space

https://www.youtube.com/watch?v=8FaziD_7i24

>>7779489
Say mcm is the minimum common multiple.
What's a very simple proof that mcm(a,b)=mcm(a,b+na)?

Consider the celebrated Barnett Identity, which relates five important numbers in mathematics. Due to its status as a meme, the subject lately causes /sci/ to groan. But this /remarkable/ pop-/sci/ equation :^) is amenable to rearrangement which gives me an excuse to funpost with LaTeX, and actually brings out a comparable number of operations and dummy variables, which replace the constants themselves when re-arranged.

Consider that e may be written as an infinite series of reciprocals of factorials. Pulling the first such term out, "1", both side-steps the 0! topic, and more importantly allows the series to be re-indexed in such a way that definitive product notation can replace a factorial symbol. Moreover, pi can be replaced with an integral corresponding to integration over the unit circle (or arc length if you like), and i can be re-written in terms of its definition. The result is Barnett's Identity in its beauty, entailing the understanding of series, products, limits, and integrals, couched in terms of three dummy variables. Thus,

[math] \displaystyle e^{ i \pi } + 1 = { \Bigg( 1 + \sum\limits_{n=1}^{ \infty } \frac{1}{ \prod\limits_{k=1}^{n} k } \Bigg) }^{ 2 \sqrt{-1} \int\limits_{-1}^{1} \sqrt{1-x^2} \; dx } + 1 = 0 [/math]

Of course, I'm having a meme more than anything else, but inspection of the tex source will show that my above formatting suggestions are being followed in the coding of this meme. The above can even be plugged into Wolfram Alpha without it breaking.

>>7792126
Can you repost the equation you used without the [eqn][/eqn] tag?

>>7792145
Oops, I meant the [eqn] tag.

>>7792145

Way to stay on-topic with the thread. :^)

But seriously, if you're asking about the code, you can just right-click on my autism - "see Tex" or whatever, then copy that, and paste it inside [math] tags, and riposte. This is left to the reader as an exercise.

>>7792161
>Show Math As
>TeX Commands
I see, thanks.

>Way to stay on-topic with the thread. :^)
It is a stupid question after all. Damn am I slow on the uptake.

Sorry posted as a reply.
Does anyone have a simple proof that least common multiple lcm(a,b)=lcm(a,b+na)?

>>7792204

Where a,b and n are all arbitrary nonzero natural numbers, no such proof is available.

For suppose a = 2, b = 3, c = 1. Then

lcm(2,3) = 6 =/= 10 = lcm(2,3+1x2) = lcm(2,5).

Thus, the premise is false.

>>7792212
Yep, thanks. Should have checked it more carefuly.

>>7792204
>>7792419
Not that anon who solved it but were you thinking of a different question?

As in prove that gcd(a,b) = gcd(a,b+na)?

What does 'In' mean in this equation? The book I'm reading doesn't say and googling this is very hard. Or is it '1n'? The lower case l and 1 look the fucking same.

In[A] - In[A](subscript)0 = -kt

>>7792462
Natural log. As in [math]\displaystyle \ln{x} = \log_e{x}[/math]

>>7783799
benzene is very stable, and is aromatic. it can incorporate itself into the nitrogenous bases of dna (which are all aromatic as well), this disruption causes irregularities in the dna structure, and can alter things like dna replication and cell division

>>7792469
i forgot to mention--the bases are stabilized by h-bonds, and pi-pi stacking due to the aromaticity, but benzene can disrupt the pi-pi stacking by incorporating itself into the structure

>>7792468
Thank you very much

>>7792436
More or less. I knew about that one but for some reason I thought I saw the other one somewhere.

I might as well ask. It seems the concept of integer combinations is extremely useful yet my "book"/pdf never mentions them. Is my book the exception, cuz it seems damn useful.

eg, with I(a,b) being the integer combinations.
Prove gcd(a,b) = gcd(a,b+na).

Bezout's Theorem: gcd(x,y)=positivemin I(x,y)
And I(a,b)=I(a,b+na).
Therefore gcd(a,b) = positivemin I(a,b) = positivemin I(a,b+na) = gcd(a,b+na)

File: lattice_n5.png (8KB, 220x248px) Image search: [Google]

8KB, 220x248px

This is the lattice [math] N_{5} [/math]

I am having trouble finding a nice definition of [math] N_{n} [/math] because it is very hard to google and I don't see it anywhere in the "Introduction to Lattices and Order" book I'm trying to read.

Because this is called the "pentagon lattice" I'm assuming that [math] N_{n}[/math] is a lattice representing an n-gon, is this correct and is there a more formal way to define [math] N_{n}[/math] in terms of operations on smaller lattices?

>>7787612
You don't need it. Mathematicians hate it and engineers alike hate it and I can't imagine physicists don't like it either

>>7785740
Take a look at the extended complex numbers. Infinity is defined as the point (0,0,1) on the unit sphere and from here the property z/0 = infinity is assigned. Pretty mind boggling shit.

>>7790292
This time I actually need help solving this... I'm not getting anywhere

pls halp

>>7791693
Anyone able to verify this?

>>7792831
nvm solved it ;)

>>7787612
You don't need it but if you set things up the right way (protip you can reuse computations in clever ways) then Cramers rule will actually be much faster than other methods. Generally though you rarely need to compute this shit by hand. In mathematics you just abstract away all the computation and in everywhere else you use a computer with mathlab/octave/python.

Is there a term or phenomenon for when you're listening to someone but the words break up and go really slowly in your head? Almost as if everything is slowing down.

Help me choose an engineering degree, to you engineers. Why did you choose your field? Why should I go into that field?

>>7779489
It is short for a range of fatty acid types, " iC4-nC6 fatty acids". Just just like using, "GA3" instead of "gibberellic acid-3".

how do you calculate the change in temperature of water as the pressure increases?

Can anyone find the pattern here?

{ 4, 2, (16/9), 2, (64/25), ... }

if a given female is more likely to have sex than a given male, wouldn't that select for unbalanced gender ratios in babies?

>>7793679
Having a 1:1 ratio is an evolutionarily stable strategy, look up Fisher's principle for the details.

It is true however that most of your ancestors are female many of because your male ancestors mated with multiple women,
That is imagine there is only Adam, Eve, and Carol. Adam-Carol has a daughter and Adam-Eve has a son who marry to produce You. You now have 3 female ancestors and only 2 male ones.

>>7793634
[math]\frac{2^{n+1}}{n^2}[/math]

Does light refract/bend upon entering a gravitational field?

The fact that light cannot escape a black hole implies to me that it does but I dont know if I have ever seen the phenomenon referenced/talked about.

>>7790963
>>7790674
>>7790610 <- this guy
Just had prof send us an email, it was a mistake, it should have said f', thats what was confusing me, it made no sense since it was clear from the continuity.

Why do people deny evolution? Could someone give me a run-down on transitional fossils? I'm sorry guys, been in /his/ too much lately.

does it exist some kind of board like the 4chan style that discusses programming and such? can you guys please redirect me to some that you know?

>>7793801
Gravitational lensing has been a thing for about 40 years

>>7793782

where n does not equal 0.

>>7793897
where n > 0

>>7793897
>>7793900
I left out "for nth term" because I assumed that was trivial. Apparently not.

>>7793871
This is why Leibniz notation is superior.

>>7793884
That'll be /g/.

How do I algebraically evaluate the following limit?
lim (2x+5)/(x-3)
x->3

>>7793917
oh im a retard, thanks man

I've used the definition of continuity at x = 0 to obtain |w(x)| < ε. Can I then conclude that w(x) = 0 everywhere from this? Thinking that then I can say that |f(c+h)-f(c)| = 0, so f(c+h) = f(c) = some constant and is continuous at c.

Pretty sure that that's wrong, but I just want to get the w(x) = 0 or not out of the way first.

File: ss+(2016-01-18+at+09.44.52).png (32KB, 935x185px) Image search: [Google]

32KB, 935x185px

>>7794034
>forgets to upload file
not off to a great start

>>7794014
[eqn]\displaystyle \lim_{x\to3}\frac{2x+5}{x-3}=\lim_{x\to3}\left(2+\frac{11}{x-3}\right)=2+\lim_{x\to3}\frac{11}{x-3}=2+\lim_{x\to0}\frac{11}{x}[/eqn]

The rest is trivial.

>>7794014
>>7794055
And >leltex strikes again.

Just copy and paste it to the TeX preview.

>>7794058
>[math]\displaystyle \lim_{x\to3}\frac{2x+5}{x-3}=\lim_{x\to3}\left(2+\frac{11}{x-3}\right)=2+\lim_{x\to3}\frac{11}{x-3}=2+\lim_{x\to0}\frac{11}{x}[/math]
really dubt this would help him

>>7794077
without actually explaining the steps

>>7794079
coming from the less than 3 side it goes into -inf, when it;s coming from the 3+ side it's going into +inf.

>>7794105
That was the trivial bit anon.

>>7794055
>>7794077

Nice dubs. The LaTeX dude strikes again:

[math] \displaystyle \lim_{x \to 3} \frac{2x+5}{x-3} = \lim_{x \to 3} \left(2+ \frac{11}{x-3} \right) = 2 + \lim_{x \to 3} \frac{11}{x-3} = 2 + \lim_{x \to 0} \frac{11}{x} [/math]

(provided the above was successful, always) Remember: to make LaTeX behave on 4chan's /sci/:

1. ADD SPACES BETWEEN LATEX- BRACE AND BACKSLASH \ { } OPERATORS, and the items exterior to them (keep the operators themselves close together though).


" 2 + \latex{thing + \frac{a}{2 + b} }, NOT
"2+\latex{thing+\frac{a}{2+b}}"

>>7794563
I hate /sci/'s LaTeX.

Hiro-tan please fix.

>>7794567

As a matter of fact, as I suggested earlier >>7791934 , /sci/'s LaTeX implementation /actually was improved somewhat/ in recent months, during Hiro's administration (though I would imagine that the development had been a long ways along already). It's /actually less finicky right now/ than it used to be, and you can even easily do certain stuff that was not feasible before-particularly large arrays, which I will now attempt (again) by way of demonstration (getting ambitious...)

[math] \underbrace{
\begin{bmatrix}
16 & 3 & 2 & 13 \\
5 & 10 & 11 & 8 \\
9 & 6 & 7 & 12 \\
4 & 15 & 14 & 1 \\
\end{bmatrix} }_{Albrecht \; Dürer's \; magic \; square.} [/math]

Assuming that panned out, arrays larger than 2x2 were /nigh-impossible/ before they plugged in a different latex solution. I heard rumors that shitposters abused the feature, but who knows.

And a repost, with \displaystyle, which I uncharacteristically forgot (I want that subscript to read more nicely if possible):

[math] \displaystyle
\underbrace{
\begin{bmatrix}
16 & 3 & 2 & 13 \\
5 & 10 & 11 & 8 \\
9 & 6 & 7 & 12 \\
4 & 15 & 14 & 1 \\
\end{bmatrix} }_{Albrecht \; Dürer's \; magic \; square.} [/math]

File: semen demon question mark.jpg (41KB, 429x377px) Image search: [Google]

41KB, 429x377px

>>7794603
>>7794610
I don't see a difference?

>/sci/'s LaTeX implementation /actually was improved somewhat/ in recent months, during Hiro's administration (though I would imagine that the development had been a long ways along already)
Yeah, but it still sucks. I don't know why there's such a huge disparity between the quality of the TeX preview and what's actually posted.

>>7794621

I don't know all the tricks, I just know how to express things that I want "legibly" on /sci/, or else very quickly search how to do so. The-in-board sandbox test is a welcome improvement, but to your point, it's still not perfect. My central observation is that there is something wrong between 4chan's interface, and how whitespace is handled in in-board TeX code. In this case, it turns out that /displaystyle didn't improve anything noticeably, but it is still a killer switch on /sci/'s LaTeX, which should always be turned ON/be invoked by default (I just forgot this one time).

Sometime late last year, maybe november-ish, /sci/ migrated from a "jsmath" solution (which would display a little box at the page's bottom right) to something slightly better, which handles "math-mode" material more easily, whatever the details of that are. I used a bmatrix above to make brackets appear around my matrix-table, but the more generic "array" and similar creatures are also usable now, where they weren't before.

To your earlier point, the old "jsmath" box would link to an exterior sandbox, and I could usually translate what I wanted from the sandbox to a real 4chan post. But the principal disconnect between the two spaces were large matrices that I tried to render. My point being that the older solution also had its own disconnect, and you had to go to an exterior site to test your stuff.

It's still buggy (and frustrating), but they /have/ improved it over the past six months. I've noticed.

Rigorously, for some arbitrary constant c, how does
[math] \frac{d}{dx} G(y) = F(x) \frac{d}{dx} \implies G(y) = F(x) + c[/math] ?

I can tell I'm missing something simple here, but I'm looking for the rigorous answer.

>>7791758

take out a factor of [math] \frac{-1}{cos(x)} [/math] everything else is just one
[math] (\frac{-1}{cos(x)})(\frac{sin(x)-cos(x)}{sin(x)-cos(x)}) = -sec(x)[/math]

Is it true that the dimensions of the intersection of different objects must be less than or equal to the object with the least dimensions?

For example: the intersection of a line and a 3d object like a cube is always either a line or a point, does this also apply to higher dimensional objects?

>>7795132
Are you trying to say that two functions with the same derivative everywhere differ by a constant?

>>7789535
>>7789540
So I tried modifying the LaTeX like >>7791934 advised.
[eqn]\displaystyle f(x) = \sum_{n = 1}^{∞} \frac{n}{π^n} \sin{ (π^nx) }[/eqn]

So, anyone know?

>>7795595
Well one needs a definition of the "dimension" of an object. Intuitively it should certainly be true, and it is objectively true for common definitions of dimension such as Lebesgue Covering Dimension and Hausdorff Dimension.

>>7792126
I would like to see a single sentence+equation that synthesizes all of the following:

- Triple Integrals
- Barnett
- [math]\displaystyle \sum_{n=1}^\infty n = - \frac{1}{12} [/math]
- Inter-Universal Teichmüller theory
- .999... = 1
- anything else I forgot

Any thoughts on what the pattern is?

(3/5), (-2/3), (9/13), (-12/17), (5/7), (-18/25)

Clearly alternating, kind of looked pseudo-periodic when I plotted it; however I can't find the definite pattern.

>>7795610
I'm trying to state is as typed, the d/dx on both sides isn't a typo.

>>7795811
[math]\displaystyle \frac{ 3n (-1)^{n + 1} }{4n + 1}[/math] for nth term.

>>7795835

God damn, how do you deduce this? I'm struggling hard with this.

>>7795837
Eh, I just look at a pattern and bruteforce it.

I'm utterly screwed when it comes to the more complicated patterns.

>>7795132
>>7795830
>[math]G(y)[/math]
>[math]F(x) \frac{d}{dx}[/math]
Is it supposed to be like that? For the second one, is there a difference between putting [math]\frac{d}{dx}[/math] at the back, as opposed to putting it in front?

>>7795862
Oh shit yeah, they're both meant to be at the front.

>>7795862
>>7795920
But that being said... does it even matter?

>>7795921
For the first one, the variable is completely different, so yes.

For the second one, remember that [math]\frac{d}{dx}[/math] is an operator. I doubt the function is commutative with the operator here, at least in this case.

>>7795921
>does it even matter?
Can I write (x)F in place of F(x) and expect people to understand me?

In an alternator, what provides the current to produce the magnetic field?

My understanding is that the battery provides the initial current, and then the alternator sends some of the current it generates from that back through the field coil in the rotor, is that right?