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You are currently reading a thread in /sci/ - Science & Math

The other one is 300+ so starting new one

I'll start:

How the hell do you guys keep up with all that terminology in probability theory?
Namely, how do you tell apart and remember those: Probability distribution, probability mass, probability density, probability distribution function, probability function, cumulative density, cumulative distribution function
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>>7795379
It might help if you disregard the word Probability in all those. If a probability theory question pops up, you just imply it includes that and not just ordinary "mass, density, distribution" etc
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>>7795379
the names are pretty clear
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if you have, for example, $F^E$, what does that mean?
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>>7795433
Functions from E to F
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When adding two polynomials $p_1(x), p_2(x)$, how do I denote adding them? Just $(p_1+p_2)(x)$?
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With a gpa of 3.44 or lower, would it makes sense to apply for a phd or am I just wasting everyone's time?
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Is it true that the dimensions of the intersection of different objects must be less than or equal to the of 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?
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>>7795646
Yes.
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>>7795649
proofs?
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>>7795544
That notation seems fine.
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>>7795658
You really need proof? Its a very intuitive to understand idea
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>>7795658
Sorry, can't think of any right now, although I'm fairly certain I had to find one while in uni.
For some reason, people tend to get confused by higher dimensions. You shouldn't; if something works in a "low"-dimensional space, it can pretty much always be expanded to a higher amount of dimensions.
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>>7795673
intuition isn't always right
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>>7795646
>>7795649
>>7795658
>>7795673
>>7795680
>>7795697
goddamit faggots.

let A and B be two objects of dimension p and q (with p<q, without loss of generality).

the intersection C of A and B is:
included in A, so dim(C)<= dim(A) = p
included in B, so dim(C)<= dim(B) = q
therefore dim(C)<= min(p,q).

Another way to see this is: an object A can be described by a certain set of constraints. an object B can be described by another set of constraints. The intersection is the combination of both sets of constraints, which results in an object with at most the same dimension as min(dim(A),dim(B))
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>>7795720
what the fuck does ln(x) do.
what the fuck does it do to x to give you ln(x).
how is it used, except for ln(e)=1 ?
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>>7795720
>>7796036

wasn't supposed to be quote.
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How do I solve pic related?

>mfw I can solve double integrals but can't do basic algebra
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>>7796184
a sum of two non negative things is non negative.
there is no solution to that question.
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>>7796036
Well, actually, ln(x) is defined to be de the inverse function of e^x (by the genera definition of logaritms). It was first introduced to solve problems that imply the usage of this exponentials. Now, because many natural processes seem to follow this same exponential function, its widely used to modelate them
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>>7796186
But x could have a negative value:

x = -1
-x = 1
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>>7796303
Whichever x is irrelevant in this case as the absolute value always produces a non-negative number and the sum of two non negatives is always non negative.
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>>7796303
>what is absolute value
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>>7796303
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>>7796367
This is called closure. An operation is "closed" on a set if the operation maps elements from the set onto itself. Has nothing to do with the psychological concept. Pwomise. ;)
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>>7796384
Then how do I solve it?
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>>7796401
There is no solution, you could make x infinitely negative, the solution would still be greater than 0, because the fractions both become positive either way, and when adding two positive numbers, there is no way it can be negative.

$x \rightarrow -\infty , f(x) \rightarrow \infty$
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Is there a name for this identity?
A ^ not B = (A U B) ^ not B

I would assume you usually see it the opposite way around.
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>>7796489
I don't think you it has a name, it's straightforward
A^notB = (A^not(B))U(B^not(B)) = (AUB)^(not(B))
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From the perspective of one point in the universe, can matter and energy be said to have been "destroyed", once it exits the particle horizon of that point?

I feel like this is an example of two scientific dogmas clashing. I recall (perhaps incorrectly, I don't know) most scientists dislike considering the existence of unobservable stuff, yet the first law of thermodynamics states that absolutely unobservable stuff nevertheless does exist.

Or is there already a term for this and I just didn't google the right words? Or can no matter or energy pass beyond the particle horizon?
>>
How do you pronounce "acetyl?"
Is is "ass-ee-till" or "ass-ih-tuhl"

Also, how do you pronounce "pyrolidinone?" Is it "peeroh" or "pie-roh" and "lih-DEEn-ohn" or "LID-ihn-ohn?"
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>>7796511
k thanks. I'm using it to prove another identity and all my other steps have the names of the things I used to make the step next to them in the proof, so I wanted to name that one too. Too bad.
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>>7796551

The only person I've ever heard pronounce it sort of like the second way was my organic chemistry teacher in community college. She said "ass-uh-teal"

Before that I just assumed it was "ass-ee-tuhl", and now I don't know what to think.
>>
how do i prove that (1-cos(x))/x^2 < 1/2? i can't seem to bound it properly for x<2
>>7796036
>what the fuck does ln(x) do.
it lets you solve the equation e^x = y for some given y. if e^x=y, then x=ln(y). for example, if you have e^x=2 then x=ln(2)
>what the fuck does it do to x to give you ln(x).
if you know calculus, it evaluates the integral from 1 to x of 1/t
>how is it used, except for ln(e)=1 ?
it's used widely. whenever you have e^(f(x))=y for some function f and some value y, then you take logarithms. this is used, for example, when solving analytically differential equations
>>7796184
just use a plotting calculator
>>
>>7796551
>>7796576

In Periodic Videos they say "ASS-ih-tile," but that's funky British pronunciation.
>>
It seems Library Genesis is dead.

http://gen.lib.rus.ec/

What's the next one? The other ones on the /sci/ section suck.
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>>7796631
>http://gen.lib.rus.ec/

That's the link for search I've always used. Lately I've had to use their bookfi and bookzz mirrors though.
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>>7796631
>not having written a script to download all the books and having a backup now

oy vey
>>
A farmer can plow a certain field in 6 hours. Using a smaller tractor a hired hand can plow the same field in 10 hours. If the hired hand works 2 hours before being joined by the farmer, how long will the farmer have to work to finish the job?
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>>7796688

4.8 hrs
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>>7796693
How do you figure
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>>7796693
nope.jpeg
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>>7796700
>>7796703
In 1 hour the form hand plows 1/10 of the field.

In two hours the farm hand plows 2/10 of the field.

In one hour the farmer plows 1/6 of the field.

8/10 divided by 1/6 is how long it will take the farmer to finish.

8*6 = 48

48 / 10 = 4.8
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How can I find the solutions to this?
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>>7796586
find rel/abs min/maxes, show they're all < 1/2
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>>7796750
this looks like the type of problem that is clearly solved using the thrice iterated integral method
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>>7796750
intuitively, you want x-3 to be a power of two so that shit has some hope of working. So set y^2 = x-3 which turns x = y^2+3. So it becomes...

sqrt(y^2+3+1-4sqrt(y^2)) + sqrt(y^2+3+22+10sqrt(y^2)) = 7

At which point the inner sqrts become just y, then you can factor the outer sqrts.

This easily simplifies to
[spoiler]y=2[/spoiler]
and substitituting back in for x...
[spoiler]x=7[/spoiler]
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>>7796750
x=4
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>>7796762
dammit messed up and didn't get you the second solution. see
>>7796763
>>
a lot of times it helps actually understanding the concepts ;)
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>>7796036
ln(x) is defined either as the inverse function of e^x (duh, logarithm to base e) or the integral from 1 to x of (1/x). As for what it's used for, take a math class.
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>>7796688
Wait. Does the hand work 2 hours and then leave after the farmer arrives or do they work together at that point?
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>>7796750
Square both sides twice, then do appropriate solving methods.
If you can use a graphing calculator see where the left part of the equation is equal to 7.
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I need help from anyone with excel knowledge.

How would I go about randomizing 300 cars in a table based off their make and color, with the final list not having any repetitions? (a red car doesn't follow a red car, a ford doesnt follow a ford).
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>>7796788

I'm brainstorming your question and inviting you to think, and be a little more precise.

Basically you want 300/600 inputs to output elsewhere in a particular way, with two constraints. It would be helpful if you could give an exact number on the data sets (50 colors? 50 makes?). There are various RAND-type functions in Excel that you can get to do what you want, I reckon.
>>
http://www.amazon.com/Campbell-Essential-Biology-Physiology-Edition/dp/0321967674/ref=dp_ob_title_bk

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>>7795379
How do I do basic algebra with extreme ADHD?

[spoiler] I'm college age and only made it through High school by the skin of my teeth. I don't think I'm stupid but math is just something I can't wrap my head around but some day I'd like to be good at it for my own benefit. [/spoiler]
>>
Not asking for an answer here just asking what the fuck the professor means when they posted this:

Let {w1, . . . wn} ⊂ V be a list of linearly dependent vectors. Prove that
there exists j ∈ {1, . . . , n} such that wj ∈ Sp {w1, w2, . . . , wj−1}.
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>>7796891
Become friends with your professors. They'll probably tell you as long as you don't go blabbing your mouth about it.
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>>7796931
jk I'm retarded. the coefficient for wj can be zero.
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>>7796942
Protip: you still don't understand the problem.
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>>7796947
Then do you have a suggestion for how to go about doing this?

The sad part is this is supposed to be review
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>>>/wsr/36495
I emailed my professor too, but he hasn't replied yet.
For instance, for the difference in proportionality question I'm trying to do, I get a difference of 0.17, but I'm not sure how to use this to find the standard error.
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>>7796948
Start by using the definition of linear dependence on the wi. The result should follow in one or two steps.
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>>7795379
>How the hell do you guys keep up
Constant effort.
srsly, that's what it takes
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>>7795608

Acceptance is not based solely on GPA by any means. 3.4 is fine in most cases, but it will also depend on your degree, school (both where you're coming from and where you're trying to get into), GRE, work experience, recommendations, etc.

If you think it all comes down to GPA, you probably don't know enough about statistics to be in such a program.
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>>7796952
Oh wow shit I'm retarded I thought it said a list of linearly INdependent vectors.... I probably shouldn't be taking functional analysis ;_______;
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>>7796036

Do you understand what different "base"s are? Like base 2, base 8, base 12 etc (our usual numbers are "base 10" because units of 10 form the structure: 13 = 1 "ten" + 3 "ones", etc.

Then you have "powers": 10 squared = 10^2 = 100; the logarithm is kind of the converse, where log(100) in base 10 = 2. For most numbers, log(x) is not a rational number unless X is a power of the base, so log(44) in base 10 = 1.6434.... meaning 1o to the power (1.6434...) is 44.

ln(x), i.e. "natural logarithm" of x, is using base "e" instead of base 10. "e" is a special number, 2.71828182846... that does "magic" things in mathemathics.

Simply, the ln(x) ("natural log of x") is "e to the WHAT = x?" So the ln(44) = 3.784... because e to the (3.784....) = 44.
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>>7796184

It's kind of a trick question, more logic-based than algebraic.

1) absolute values are always 0 or positive
2) no matter what is inside, you cannot add two of them an be LESS than zero.

> YA DONE GOOFED

> THE END
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>>7796368

Absolute value = stripping off the + or - ign, meaning effectively stripping off the "-" sign.

|4| = 4
|-4| = 4

So the lowest you can ever have for an abs value is 0, it doesn't matter what is inside.
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>>7796688

So the hired hand has done 1/5 of it already, meaning the two of them together are only covering 4/5.

The farmer can do 1/6 of the job per hr, the hand does 1/10th. Add these together and you get 10/60+ 6/60=16/60=4/15 per hour

At that rate, how long to do 4/5 which is 12/15?

3 hours.

This is presuming the farmer and the filed hand keep working together.
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>>7796724

I think you are expected to keep the hired hand working WITH the farmer; otherwise it's elementary. I solved it above.
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>>7796971
There's actually a solution, but it's by cases getting the intervals of each absolute values.
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>>7796986

Please provide--would love to see. Been many years since I had Calc
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>>7796994
Tomorrow, I'm already in bed, but I'll do.
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Assume a cube with the dimensions (0.5, 0.5, 0.5)

Surface : 6 x 0.5^2 = 1.5
Volume : 0.125

How does Volume < Surface make any sense?
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>>7797210
Same as how sometimes x^2 < x.

Volume only breaks even when the dimension is 6 units.
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Besides the obvious, "it's because he looks like he's trying to figure something out and then finally figures it out", can someone explain this joke to me?
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>>7797236
anybody?

I've been asking this question for a few months now, and given the number of higher math artists on this board I have yet to receive anything close to an inkling of an answer.

I HATE HOW SLOW MATH IS.
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>>7796903
learn self-discipline

i wouldn't say i have "extreme ADHD" but i was diagonsed with ADHD-PI, and I'm not currently taking medication, but I am a final year undergrad doing a STEM degree and I had quite a bit of success with self-discipline and time organization methods
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>>7797236
>>7797248
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>>7797228
I understand that the volume gets smaller for x<1.0, but I cannot grasp the concept of the surface area being bigger than the volume for small solids.
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>>7797210
>>7797255
you compare uncomparable things.

You are saying something like "I don't understand why 30 cm is less than 50°C" when talking about a hot ruler.
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>>7797257
Are you saying volume for x>1.0 are different to volumes for x<1.0?
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>>7797253
I assumed this was a common joke around these parts. My mistake!

Anyway, I can't imagine that context wouldn't do this reference justice so I'll just wait a bit longer.

Also, I don't want an exact answer. I assumed some people here are capable of working with the concept. I couldn't use a response versed in the calculus of differential equations anyway!

I was really thinking it would go something like:
>As stated, we have a vacuum of space
>the reciprocal of that state being E(x t)
>You are going to jail
>proofed

"Woah shit, so that's what the math meant"
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>>7797261
no, he starts from a wave equation, goes on to introducing the energy of a particle (photon), then sees that it verifies a version of the schrodinger equation and his mind is blown but it's not that funny.
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Why everything seems quieter when there is fresh snow on the ground? Scientific explanations only please.
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>>7797263
lol thanks for that! It's kind of a giggle bc schrodinger but I guess I still have to finish those courses to see what the big deal is.

>>7797264
Maybe because since the average temperature is much lower even the lights seem dimmer and there are fewer perturbations about the air?
>>
Ok smart guys when do I NOT use principal component analysis on a data set?
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>>7797264
Short version: Snow is porous, and porous materials tend to be good absorbers of sound.
>>
Final year EE here doing final year project with Biomed department

The core of my project is seeing whether multisensory integration in the dorsal cochlear nucleus can enhance certainty of hearing, so the experimentation will involve exposing people to auditory stimulus and an electrode on their tongue and seeing if it helps them hear a coherent band in an acoustic stochastic figureground. Only right no my problem is that I have to write up my preliminary report and I have no idea of the kind of language I should be using to describe the experimental stage. Can anyone throw me some appropriate terminology that I could start looking into?
>>
>>
Is set theory a prerequisite of real analysis?
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Hey guys, I have this really burning question on Water Conservation
Most people say that
>water gets wasted if we let the taps running, use excess water for cleaning cars etc.
But at the end won't all the water just evaporate and get restored to the water cycle and in effect not be wasted?
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>>7797464
When you pump water to put it in your faucet:
1/you take it from somewhere else that might be able to use that water. (which costs energy as well btw)
2/it might evaporate again, but more water won't evaporate because there is more water. Say the sea contains 100L and 1L evaporates each hour. You have 1L of fresh water each day that you bring from a source of 10L that has a refill rate of 0.5L per day. Through rain. You use 0.5 and throw 0.5 in the sea.
The sea now contains 100.5L, the lake contains 9L, and you contain 0.5L.

At the end of the day, you pee the intake, the sea contains 100.5+0.5-1=100L, the lake contains 9.5L and you contain 0.
Where did the missing 0.5L go? Well part is sea water, and part is lost on useless rain somewhere else, that could have been made purely from evaporated sea water.

You just wasted 0.5L of fresh water.
>>
Explain this shit to me? Why are the p-values so low?

>> [rho, pval] = corrcoef(inputs)
why are the pval so low for correlations like 0.195...
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>>7797504
because p-value is a bad indicator and that's why all science based on p-values is unreliable.
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>>7797479
Granted that happens. But chances are that someone else's wasted water rains here and restores balance. Right ?
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>>7797509
I don't think it's [just] that
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>>7797249
I'm currently on Adderall and it does help but not to the extent which I need it to help. I love literature and I have an overactive mind that shuts down anything I don't want to do, including math. Congrats though! It makes me hopeful knowing that someone that has the same disorder(?) as me is able to do so well. What methods do you use to self-discipline and time organization? I've tried a plethora of different techniques but nothing seems to stick to me. Good luck though and thanks.
>>
>>7797449
What are you talking about? Most lists of exponentiation start with 0 because anything (bar 0) to the 0 is 1 and 1 is a basic number
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>>7797063
Are we dealing with nonreals here or something? Because no absolute value is negative
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>>7797260
no, I'm saying surfaces and volumes are different things without even the same units.
>>
>get rejected by my first choice for grad school
>today my exam results came and i got a shit grade
blow after blow. what the fuck do i do. i literally thought for a second to get out of academia after this year. if i get rejected by my other choices i don't think i can take this shit anymore. i'm sad asf rn, i was even prepared to ace that fucking exam i dont even know what happened
>>
>>7797452
Not beyond understanding the meaning of $\in$ and $\subseteq$. So no.
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>>7797825
Nah, we are dealing with intervals.
>>
>>7796872
300 vehicles total, that need to listed with no repeats in colors, or makes.
Think of it more as 300 pairs of data (Make, Color).
I've tried =rand() function, but I could only sort column A randomly.
>>
>>7797255
>but I cannot grasp the concept of the surface area being bigger than the volume for small solids.
>gee, why is 30 m/s heavier than 25 K
>>
>>7797236
>Besides the obvious, "it's because he looks like he's trying to figure something out and then finally figures it out"
That's pretty much it though. The maths behind it is fairly complex, but the Schrödinger equation turns out to be easily readable when simplified.
>>
>>7798008
>tfw the never ending wait just to hear back one way or other from any school I applied to
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>>7798317
Ok, then explain
>>
why cant they just plug the hole up with cement?

>>
Why don't we just blow up mountains and move the excess land to the coast to expand our overall land mass for the world?
>>
How feasible would it be to drill to the core of the planet and to harness the thermal energy of our core to power the planet, at least partially.
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>>7798838
impossible apparently when we cant even stop methan gas from leaking from a 7 inch hole in the ground for last 3 plus month
>>7798822
>>
>>7798841
Ah, so the area surrounding a hole of that size would be poison pretty much.
>>
>>7798830
yeah and while were at why not just tow antarctica to the pacific to stop el nino.
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>>7798830
Why not? We moved pyramids with slave labor. Moving Antartica with current machinery should only take a millennia.
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>>7798845
theyve had to evacuate at least 2200 households so yeah its pretty bad. its a ghost town right now and for who knows how long
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>>7798847
see
>>7798851
>>
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>>7798876
jakes on you global warming will make sure theres nothing to tow long before then.
>>
What do you guys think is a sustainable population. I don't think we can sustain what we have now in the world. A worldwide one child policy would significantly help lower global temperatures.
>>
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HOW THE FUCK DO I GET FACTORING DOWN TO A SCIENCE

>>
>>7797818
I mean when you have 0 as an exponent, you divide your base by itself once, giving 0 like when the exponent is 2, you multiply the base by itself.
>>
Is the transformation that continuously takes the exponent of a function from 1 to -1, going through the reals in that interval and transforming the function into its inverse, a homeomorphism?
Please post some graphics of functions transforming into their inverses, if you have any.
>>
>>7798899
facts:
-the world produces enough food for 11 billion people
-1 billion people are starving though
-an american middle class person consumes 32 times as much resources as an ethiopian middle class person

Solution: prevent americans, europeans and japanese from reproducing.
>>
How do biologists/paleontologists estimate the number of species (nevermind individual populations) that have lived in the past with any accuracy if the fossil record is so incomplete?
>>
Where can I learn about physics without calculus?

Not saying pop-sci, but even just a light algebraic treatment of EMR, E&M, Atomic physics, etc

I haven't learned to do triple integrals yet, so some calc is OK
>>
Does anyone know of an archive of chemical reaction mechanisms or something? I need a source for my proposed mechanism since apparently it being correct isn't enough and all I can find is some autistic guy's shady blog, which I'm obviously not going to use as a source.
>>
>>7799607
Evolution. It's complex but really not that much of an issue if you genuinely understand evolution and the history of our planet.
>>
>>7799607
>>7799634
>evolution is true therefore evolution is true according to evolution
>>
>>7799637
Muh straw man
>>
>>7799585

This doesn't even make sense and if I asked you for context or motivation, you couldn't give one.

Maths isn't meant to be some douche competition of who can throw the most buzzwords around at each other, it's meant to be about understanding ideas and concepts then using them to solve problems.

If you want to use a bunch of big words and equations to sound smart, do something else. Maths will bitterly disappoint you in the end.

>>7799613
>physics without calculus

The only reason Calculus is in Physics is to deal with continuous functions.

The whole point of Calculus (or Analysis which is the formalised field) is to abstract discrete concepts to a infinite sets of numbers. Just take a step back and try to look at it as you would a discrete object and don't be afraid to ask for help.

>i haven't learned triple integrals yet

If you know how to integrate in one dimension, then three dimensions is just the logical extension of that. Path integrals are probably the greatest departure from the intuition you should have from where you already are.
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>>7799637
Cute strawman. They deduce the facts based on a proven theory which is the best explanation we have. This happens many times in science. If what the theory suggests is happening or happened and can be proven, the theory can very well be used to deduce other facts. These in turn don't prove the theory right because there is no further need and it's always stated as what they are. Deductions based on a theory.

Therefor you are an idiot for implying this was what I meant.
Also implying evolution is wrong shows what a dunce you are
>>
>>7799640
>>7799675
>strawman
it's obviously not one.
>>7799675
>proven theory
cute oxymoron

yes, good goyim. Keep gobbling darwin's cock.
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>>7799679
>we people from /pol/ don't know the difference between a hypothesis and a theory with one of the largest amounts of substantial evidence
I can tell

>obviously no strawman
Good comeback. Great argument. I stand defeated
>>
>>7799679
JIDF detected
>>
>>7799682
>we people from /pol/
I know you're not even remotely close to being a scientist. You know why? Because you can't understand that you can't prove a theory, you can only disprove it. You can find all the evidence you want, it doesn't mean the theory is true. It only means it's still valid. You can't even explain macrofuckingevolution. Bigger problem: you're not even trying to test the theory, only to find "large amounts of substantial evidence".
Look up "confirmation bias". You're the kind of people who would have sent astronauts to die in the columbia accident.
>>
>>7799653
>This doesn't even make sense
How come? It's a very simple question. I'm only starting university level mathematics.
>if I asked you for context
This example is the context: Continuously transform y=x into y=1/x, or any other function.
>Maths isn't meant to be some douche competition of who can throw the most buzzwords around at each other
Which are the buzzwords?
>>
>>7799679
if evolution is not true, then what is ?
>>
>>7799713
>you can't explain macro evolution
sorry your holyness. I meant creation is true. Please don't stone me
>>
>>7799737
>moving the goalposts

this game is too easy. I win again.
>>
>>7799746
You haven't won a thing.

>you can't explain macro evolution
There is no such thing. It's just evolution. Many small changes amount to big changes eventually. You call it micro/macroevolution. No one with scientific background does that because it's just evolution. If this concept is that hard to grasp for you, you should get back to bibleschool.

>you can't prove a theory
Ish. The more substantial evidence a theory has, the more believable it becomes. Just because you don't know how evolution can be tested, doesn't mean it can't be you ignorant fool. Being able to be tested is a fundamental requirement for hypothesis to ever be able to be considered theories. Read it up somewhere that isn't answersingenesis.com

>conformation bias
This doesn't apply to evolution. Read up what conformatiom bias means and learn what evolution is. Don't learn it on answersingenesis.com because that's not what scientists mean when talking about evolution.
Read the actual source, not summaries by bogus blogs

You've presented nothing to debunk evolution, you've presented nothing to support your claim of your argument not being a strawman.
What could you possibly have won except for "bait of the day"?
>>
>>7799763
There are a couple of rogue memesters running wild around /sci/, effectively trolling people with "we can't know nuthin". Simply ignore them because they are only here to bait.
>>
>>7799768
Cheers for the heads up. Has it always been like that?
>>
>>7799770
It was a tradition of /b/ to troll /sci/ with jesus baits. I think they evolved now and they're using the "we can't know nuthin" since /sci/ is more prone to prove their points no matter how autistic people are or how unwilling to understand logic.
>>
>>7799777
Which is why I came to /sci/. In every remotely science related discussion on /b/, there were a select few who weren't trolling or just being retarded by nature. I was guessing I'd find more of them here. There are things I know and many many more things I don't and I hope to keep learning through discussions with people. Whether it's by research I conduct after my curiousity was peaked or by things my conversation partner has to say
>>
>>7795379
my dad has moderate to severe fetal alcohol syndrome. how do epigenetics work and did it fuck me up?
>>
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How do I integrate this? preferably by substitution
>>
how do you put an equation in the form of ax^2 + bx + c in the form of (a-b)^2 instead?
>>
>>7796973
>mfw you don't generalise it to the complex numbers.

when x = a+b*i, |x|=sqrt(a^2+b^2)
>>
>>7799999
>>7800000
wew
>>
>>7799999
>get on sci
Kek
>>
>>7799973
Use 2 sin(x) cos(x) = sin(2x)
>>
>>7799999
>GET
>penta on /sci/
Fuck off, that's nothing.
>>
>>7800036
It's quints and dubs though.
gb2 memeology class friendo :^)
>>
>>7800053
I'll have you know i'm a high ranking memester, i'm in the inner fucking circle kid. I bet you didn't get about a 200 on your memies, still in meme grad school? Ha, fuck off and think before you tell me to go back to memeology class you little cunt.
>>
What happens to the current during self-induction?
I understand that via Lenz's rule the induced current acts against the original current, but why does it progressively get less?
>>
Could we form a hierarchy of categories? I mean, after large categories there would be very large categories, and after that very very large categories. Or is there some paradox waiting or is it just unnecessary?
>>
>>7800098
because the original current gets less as well.

it's basically fricition but for currents.
>>
>>7800311
A "very large category" would be, I assume, a category whose objects are large categories, or something like that.

The problem is that such a category wouldn't even be a class.

I suppose one could define it as a class of formulas with parameters, each formula corresponding to a class. This class of formulas would itself be defined by some formula. Thus, while technically a class, such a class can be metamathematically interpreted as a class of classes.

By encoding the "meta-level", as an ordinal, into each formula, we can extending this to inductively define $\alpha$-large categories, for $\alpha$ an ordinal.

So sure, why not.
>>
>>7799162
Factoring what?
>>
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College Freshman unsure of what I want to study, currently taking classes a chemistry major would take.

My problem is I don't know if I get personal satisfaction out of doing chemical research. I also have interest in astronomy and related courses, but I'm probably just in the "Bill Nye and Neil DeGrasse Tyson and Spacetime and Black Holes are so COOOOOOL" category. The concepts are neat, but I imagine the math behind them is fucking unbearable. As it is, I found basic physics really tedious and it can only get worse from there I imagine.

So my question is, chemists and physicists, what do you do on a day to day basis in your job, and how do you feel about it?

Sorry for blog post
>>
What exactly is a probability distribution? Say X is a random variable, and by x i denote values that it takes. Is P(X = x) is a probability distribution? So probability distribution is just a number (that expresses a probability)? Or the whole graph P(X) is a probability distribution? I see people referring to both P(X) and P(x) as probability distributions even though the first one actually shows a distribution of the variable X, and the other one shows just a probability value...
>>
>>7800565

P(X)
>>
>>7800570
But that's inconsistent with my slides
>>
>>7800565
Let's say you have a probability space $(\Omega, \mathscr{A}, P)$ and a measurable space $(\Omega', \mathscr{A}')$
The probability distribution of a random variable $X: \Omega \to \Omega'$ is $P_X := P \circ X^{-1}$.

The important thing about this definition is that it makes $(\Omega', \mathscr{A}', P_X)$ to a probability space too.
>>
>>7800596
If no idea what your post means, sorry
>>
Reposting the question here by another anon, but I'm rephrasing it.

For Rolle's theoem to apply, the function must be continuous on [a,b] and differentiable on (a,b), and f(a) = f(b). Does it still apply for a function which is continuous on (a,b) and $\lim_{a' \to a^+}f(a') = \lim_{b' \to b^-}f(b')$? If so, on what interval must the function be differentiable? Is it $(\lim_{a' \to a^+} a', \lim_{b' \to b^-} b')$?
>>
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I need help with 8 on Evaluate box here.
So, I did the first scalar product using the |vector|*|vector|*cos theta, which was:
520N * 1,50m * cos 55° = 4.5 x 10^2N.m
Now, I can't do the second way of doing scalar product, which is using compontes.
W = 520N.
Wx = 298N, Wy = 426N
Now, I believe Sx = 1,23m and Sy = 0,86m. However, using those two for S components, it doesn't gives me the same answer. Can someone help me here telling me what I doing wrong? Sorry for not using TEX, I never used it so I don't know how.
>>
Why is this supposedly 2/3? I need to study for an exam and this is in the list of exercises.
>>
for the equation 64n lg n where there's no log base given, what should i assume it is?
>>
>>7800565
Using P for the probability distribution seems like very poor notation.

Use f for the probability distribution; this is the function with a graph that you were thinking of. P(X=x) is a specific probability.
>>
>>7800845
If no base is given for log you assume it is 10
>>
>>7800841
I don't know, maybe L'hôpital's rule? Yeah, that's it. The derivative of sin(2x) is 2cos(2x) and d/dx [sin (3x)]=3cos (3x), so lim x->0 sin (2x)/sin (3x)= limx->0 2cos (2x)/3cos (3x)=2/3.

As for a method other than that, I dunno or care to figure it out right now, sorry
>>
>>7800841
divide and multiply by x, recognize derivatives at 0.
>>
>>7801010
Wrong answer, since base e is the only relevant base.
>>
>>7800845
log = base 10
ln = Log = base e
lg = cancer (but probably base e as well, depends on the context)
>>
Can someone recommend some good books for differential equations:

I got these, can you also recommend which one do you prefer and why:

[Boyce_DiPrima]_Elementary_Differential_Equations_10th_edition.pdf
[Boyce_DiPrima]_Elementary_Differential_Equations_7th_edition.pdf
[Boyce_DiPrima]_Elementary_Differential_Equations_7th_edition_solutions.pdf
[Coddington]_An_introduction_to_ordinary_differential_equations.djvu
[Coddington]_Linear_Ordinary_Differential_Equaitons.pdf
[Coddington]_Theory_of_Ordinary_Differential_Equations.djvu
[Coddington]_Theory_of_ordinary_differential_equations.pdf
[Shepley_Ross]_Differential_equations.djvu
[Tenenbaum]_Ordinary_differential_equations.djvu
[Teschl_G.]_Ordinary_differential_equations_and_dynamical_systems.pdf

I have get Ordinary differential equations by Vladmir Arnold (Silverman translation)
>>
>>7801070
>[Tenenbaum]_Ordinary_differential_equations.djvu
>[Shepley_Ross]_Differential_equations.djvu
>Ordinary differential equations by Vladmir Arnold (Silverman translation)

These in that order
>>
/sci/, what notation is this?

I don't need the answer, just what to Google. This was supposed to be a basic math review, and most of it was piss easy, but I've literally never seen this before, nor have I ever seen matrices like this.

Thanks.
>>
>>7801197
The notation is the determinant of a matrix. Each of those polynomials is the entries of the matrix.
When you take the determinant, you'll get a polynomial in x, for which you'll use to solve for x.
>>
>>7799989
Bumping this question
>>
>>7801016
>>7801041
Sorry, I forgot to say no L'Hopital was allowed.
>>
>>7801623
You factorize.
>>
>>7800841
>>7801625
You shouldn't have left out something so important m8.

Use double- and triple-angle formulae here and the answer will be obvious.

[eqn]\displaystyle \lim_{x \to 0} \frac{ \sin{2x} }{ \sin{3x} } = \lim_{x \to 0} \frac{ 2 \sin{x} \cos{x} }{3 \sin{x} - 4\sin^{3}{x} } = \lim_{x \to 0} \frac{ 2 \cos{x} }{3 - 4 \sin^{2}{x} } = \frac{ 2 \cos{0} }{3 - 4 \sin^{2}{0} } = \frac{2}{3}[/eqn]
>>
>>7801643
you stink
>>
>>7801651
Thanks bae
>>
>>7799989
>>7801623
Stupid questions are stupid, but they still have answers. Do you mean this?

[eqn]\displaystyle ax^2 + bx + c = \left( \sqrt{a} x + \frac{b}{2 \sqrt{a} } \right)^2 + c - \frac{b^2}{4a}[/eqn]
>>
>>7801674
I've never seen that before
I'm just in calc 3 and when you're putting the coordinates for the center of a sphere obv you want it to be in standard for but after completing the square you have a quadratic and idk how to put that in the terms they want [ie something like (x-3)^2 + (y-5)^2 + (z-7)^2 = r^2]
>>
>>7801678
I have no idea whether you wanted to complete the square or not. You'll have to make your question clearer.

>idk how to put that in the terms they want [ie something like (x-3)^2 + (y-5)^2 + (z-7)^2 = r^2]
General formula is

[eqn]\displaystyle (x-x_1)^2 + (y-y_1)^2 + (z-z_1)^2 = r^2[/eqn]

where
$r$ is the radius of the sphere,
$x, y, z$ are variables and
$(x_1, y_1, z_1)$ is the coordinate of the centre of the sphere.
>>
>>7801678
And yes I know how to do this crap when you have something like (x^2 + 8x + 15) that's easy but when its, idk, (x^2 -(3/2)x + 9/16) then it's not as obvious where to start, at least for me cuz I never did that
>>
>>7801651
The fuck are you doing?

sin(2x)/sin(3x)=(sin(2x)/(2x))/(sin(3x)/(3x))*2x/(3x)

and sin(x)/x tends to 1 as x tends to 0.
>>
>>7801688
Pic related, the only problem is the quadratic isn't always so obvious to factor into that general formula
>>
>>7801693
>Pic related
>>
>>7801693
Fuck im retarded. sorry its 5am and I appreciate your patience
>>
>>7801691
Well, that's another way. But what if he has to prove that $\frac{ \sin{x} }{x} = 1$ first?

Assuming he doesn't:
[eqn]\displaystyle \lim_{x \to 0} \frac{ \sin{2x} }{ \sin{3x} } = \lim_{x \to 0} \frac{ \frac{ \sin{2x} }{x} }{ \frac{ \sin{3x} }{x} } = \lim_{x \to 0} \frac{ \frac{2 \sin{2x} }{2x} }{ \frac{3 \sin{3x} }{3x} } = \lim_{x \to 0} \frac{2}{3} = \frac{2}{3}[/eqn]
>>
>>7801690
>when its, idk, (x^2 -(3/2)x + 9/16) then it's not as obvious where to start
Wut? Just halve -3/2 and you get -3/4. It's just (x - 3/4)^2.
>>
>>7801702
Or you can say that sin(cx) behaves like cx near 0
>>
>>7801711
This lack of rigour won't hold up in a calculus class m8.
>>
>>7801709
The thing is idk why that's true
>>
>>7801718
Why not just try expanding it again after contracting it.
>>
>>7801717
it does if you study physics tbqf
>>
>>7801720
I'm more looking for a proof than anything, just a pet peeve but thank you that helped a lot
Is there a name for that I can just google?
>>
>>7801728
Physicists are a joke tbqhwy
>>
>>7801725
>>7801729
Just google for "completing the square" or something.
>>
>>7801735
bit rude tbchf
>>
>>7801736
tyvm
>>
>>7795379
Why do we need eigenvectors?
I just don't understand the theory behind them.
What do they do and why do they do it?
>>
>>7799746
>Haha gotcha, I win again. Damn, I'm good.
Cringeworthy attitude.
>>
>>7801753
check out PCA
>>
>>7801625
>>7801041
this is not l'Hopital rule, this is an algebraic manipulation.
but ok, serves me right for trying to help the wrong people.
>>
>>7801755
>assblasted
>>
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What base do I change to?
>>
Okay guys, how come bootstrapping and cross-validation are said to be used for the same thing i.e. testing and validating a model? FWIW I'm coming from a computer science background and this is in the context of neural networks. I don't have much formal stats training

Maybe I have a super basic misunderstanding of the concepts, but the way I see it, in k-fold CV, I pick a K (say 10) then I do K number of tests and train the model on K-1 sections and validate it against the remaining section. Then I get an error from this, and I do this K-1 more times and get an average error; thus I know how likely is for the model to generalize to a population (ish)

Now with bootstrapping, it seems like I simply select a random number of data points and then calculate some parameters like mean and variance, and maybe try to fit them if it's a regression problem. Then I keep doing this and I eventually get a function that solves the problem by using all the fits I got. Or something.

However, the CV seems to VALIDATE an already existing, trained model; and bootstrapping seems to actually TRAIN a dataset? How do people use bootstrapping for validation then?
>>
>>7801775
>recognize derivatives at 0
It's not l'Hopital's rule?

>>7801816
Base √5 would be your best bet.
>>
>>7801842
no it's really not l'Hopital.

seriously bro.
f(0+h)-f(0)/h tends towards f'(0), this is the definition of a derivative if it exists.

now apply this to f(x) = sin(2x) and f(x) = sin(3x).
>>
So this has been bugging me for a while. When taking a derivative with respect to covariant or contravariant coordinates hitting on a contracted object e.g. $F^{\mu \nu} F_{\mu \nu}$ or $U^{\nu} U_{nu}$ (with $U^{\nu}$ being the 4-velocity), answers tend to look like chain-rule results $2 U^{\nu}\partial_{\{mu}}U{_\nu}$. How can I see why this works? I also expect this to be because a flat minkowski metric. is the result more contrived in curved spaces?
>>
>>7801860
I mean using derivatives to find the limit.
>>
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>>7801866
This should obviously be $U^{\nu} U_{\nu}$ and pic related.
Test:$2U_{\nu}\partial_{\mu}U^{\nu}$
>>
>>7796724

I would expect that the working hand is kept.

Then you could keep adding the fractions together. Where you get:

the farmer working for 3 hours and the hand for 5 hours. Where it is:

3/6 + 5/10 = 1
>>
Is there any way to represent a line in 3 dimensions with only one equation?
>>
>>7801916
yes, a parametric equation
>>
>>7801925
emphasis on "only one equation"
>>
>>7801964
well a+ t*v is only one fucking equation

emphasis on fucking.
>>
Is having a +3.5 GPA and good recommendations enough to get accepted into a PhD or Masters program for Computer Science?

I have no interest in working outside of academia, so I haven't looked for any internships.
>>
>>7799718
>Continuously transform y=x into y=1/x, or any other function.

what's your definition of "continuous transformation of function f(.) to Tf(.)"? what sorts of functions are we talking about here (that is, x and y are elements of which sets)? your question lacks essential information on the objects we want to talk about, so you'll need to specify this, if you want any sort of sensible answer. there are very different classes of functions and of definitions for "continuous transformation", so there is no general answer other than: it depends on what you mean by those terms.
>>
>>7801916
A line has codimension 2, so you need at least 2 equations.
>>
>>7800629
if you had a real-valued f() that's differentiable (and therefore also continuous) on the real interval (a,b) and also satisfied your limit condition, then you could take a value close to the limit, and may then argue (intermediate value theorem will help here) that there are x=/=x in (a,b), such that f(x)=f(y). then apply Rolle to f() on [x,y]. note that this even works for the limits +/-inf.

violating differentiability in just a single point will break the argument, as shown by the everywhere-but-in-zero differentiable function abs() on the interval [-1,1].
>>
>>7801088
Thank you
>>
>>7801916
what sort of equations are allowed? if only linear, then >>7802055 has a point. otherwise:
{(x,y,z) in R^3 such that x^2+y^2=0} is the z-axis.
>>
Does:

[eqn] \int_{\mathbb{R}} \frac{dx}{x} = 0 [/eqn]

???????????
>>
>>7802101
>x=0 doesn't compute

or is it a cauchy principal value
>>
>>7802101
$\int\limits_\mathbb{R} {\frac{{dx}}{x}} = \mathop {\lim }\limits_{\varepsilon \to \infty } \int\limits_{ - \varepsilon }^\varepsilon {\frac{{dx}}{x} = } \mathop {\lim }\limits_{\varepsilon \to \infty } \left[ {\int\limits_0^\varepsilon {\frac{{dx}}{x} + \int\limits_{ - \varepsilon }^0 {\frac{{dx}}{x}} } } \right] \to \infty$
>>
>>7802135
Thank you
>>
>>7802135
How the fuck does the second integral even make sense? Starting at 0 to a negative positive number? What the fuck are you even saying? It's not defined on any such interval over R.
>>
Why study EE?
What kind of job should I expect?
Having a fucking existential crisis over here
>>
>>7802140
it's bullshit btw, I seriously hope you don't use that lol
>>
How can I identify/know which books are horrible for learning? There's thousands of books for math, for example, how can I know which is good and which is not? Amazon reviews are not the best source for this, sadly.
>>
>>7802326
>>
I hate statistics.

I'm busy getting on with my life learning linear algebra and the algorithm I'm working on suddenly needs to correlate one set of features with another set of features.

So the simplest solution being used is the "Sum of Squared Differences", however the problem I'm having is that nowhere on Google actually proves that the sum of squared differences can be used to correlate things together.
To me it's just an opaque math expression and I don't know where the fuck these people are getting this.

Can anyone tell me how the sum of squared differences works, or at least link me to a proof of it being worked out? Google isn't working for me right now. They're too busy trying to prove the sum of squares.
>>
>>7802339
That would be easy if I was in school/college.
>>
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/g/ was no help. I'm trying to write a simple guess-the-number game on my TI-84, but it isn't working. It picks a random number, then prompts the user for a guess, but for some reason it skips the while loop and just ends the program there. This is my code:

X→randInt(0,100)
prompt Y
while Y≠X
if Y<X
then display "LOW"
if Y>X
then display "HIGH"
if Y=X
then display "WIN"
prompt Y
end
>>
>>7802363
why are there two "prompt Y"

try to display the value of Y after you take it, to see if that works.
>>
>>7802345
Another question:
How does one perform the "sum of squared differences" between pixels?
Declaring the obvious here: The residual error of each pixel can be found by subtracting two images, and the "sum of squared differences" is the result squared and then summed together.

But a pixel has three values.
How do you get the residual error of a pixel?
There's tons of options to choose from. Luminance, chroma, possibly some things I'm missing, but there's no obvious way to compare pixels together since they have three dimensions to them.

Do people just pick a metric that fits their use case?
>>
>>7802363
Is there a endwhile tag or something similar?
>>
>>7802363
X→randInt(0,100)
Y→-1
while Y≠X
prompt Y
if Y<X
then display "LOW"
if Y>X
then display "HIGH"
if Y=X
then display "WIN"
end
end
>>
>>7802345
This is the answer I was looking for:
>>
>>7802443
Also, declare a min and max variable at the beginning and make x=rand(min,max)
Then in the loop check y for bounds
If(y<min or y>max)
then display "out of bounds (",min,"-",max,")"
Or however the TI BASIC should look.
>>
Given a parabolic span which has height y1 at x1, y2 at x2, and ym at the midpoint between x1 and x2, how to prove the area under the curve on the interval [x1, x2] is 1/6 * (x2-x1)*(y1+4ym+y2), without using calculus?
>>
why doesn't the universe have any "bugs" ? any anomaly at all ?

for instance , you can make a simulation crash by fucking up the numbers, you can fuck up maths by dividing by zero in certain cases, why the fuck is the universe so perfect, or seem like it ?

another thing , do we know if the model we established for the universe constant, or could it be different very far away ? (as in further away from the observable universe)

the more i think about thoses things , the more i realise they are more tied to philosophy than to science but meh , this is the only place to ask i guess.
>>
>>7802485
The answer to the first question is tautological. Any statement true of some aspect of the universe is true, and any contradiction is false. Therefore a contradiction cannot be true of any aspect of the universe.

For your second question, science never proves the verity of any of its theories; given a theory, the best the science can do is fail to falsify it. If a model is not constant, it is not true, as truth is universal truth. Therefore, because science cannot prove the truth of any model, it cannot prove the constancy of any model. So not only do we not know, we cannot know.
>>
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how do I get from this to that?
>>
How much money can I make with Survey Statistics? I got a bachelor in sociology and am currently doing a Master in Survey Statistics. It's a Master of Arts.
>>
>>7802551
csc x = 1/sin x, sec x = 1/cos x
(csc x sec x)^2 = 1/(sin x cos x)^2 = 1/(0.5 sin 2x)^2
>>
>>7802485
>simulations have bugs
>humans create simulations
>universe contains humans
Universe has bugs, bro.
>>
>>7802485
>second question
>simulations
Simulations crash because garbage in, garbage out, or that some external influence, i.e. background radiation, causes memory corruption, which cascades into huge errors when that sector of memory is accessed.
Because we cannot actually know that there are other universes, we can't be certain that our universe can be influenced by outside forces, therefore the first example holds no merit.
>dividing by zero
Division by zero is "not allowed", because the logic written on our calculators triggers an interrupt in the CPU datapath, which the CPU then has to handle. The CPU then runs a routine that brings the error to the program's attention. The program then either chooses to pretend the operation never happened and possibly alert the user, or alternatively severely crash.
The reason this chain of events occurs is because the calculator does not have a definition for "division by zero." It logically does not exist given the common interpretation offered by compulsory education.
Calculators that are more aware of infinity will sometimes choose to use the calculus interpretation.

It cannot be said that universe performs "division." How would a chaotic set of particles perform an abstract operation such as "division", and even if it could, why wouldn't it use the infinity-aware interpretation?
So the example is irrelevant.
>>
>>7802565
Computer bugs aren't physics bugs, stupid.
>>
Hello friendos
Can someone explain to me how the simplex algorithm works, mostly what the slack variables represent in a graph of the constraints.
Been trying to wrap my head around it for an hour and all the explanations I can find say the same thing, but i'm probably just retarded.
>>
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>>7802571
wut
>>
>>7802571
but they are.

it's called noise.

If you set a threshold between 0V and 5V, below which you call a bit "0", and above which you call a bit "1", then if there is too much noise (or if you're very unlucky), a bit "0" could turn into a "1" and vice-versa. And there is nothing you can do about it, this is embedded in the physics of the universe.
>>
>>7802662
You start in one corner of the polytope and then keep moving to a better adjacent corner until you have reched the optimal point.
>>
>>7802684
Yes, I understand that bit, I want to know what the slack variables represent in the graph of the constraints
>>
Anyone here did Andrew Ng's course with the all the assessment? How long did it take? I find it hard to do everything while doing my degree
>>
>>7802135
How does one define ln(x) at x=0?
>>7802101
It's not continuous on (-inf, inf), so not integrable
>>
What are the odds that an enormous gamma ray burst is on its way to destroy us, but its so far away we haven't detected it yet?
>>
>>7802662
>>7802694
Noone on /sci/ has studied linear programming?
Help a nigga out
>>
>>7802822
I have, but I passed the exam without understanding shit about that because fuck it
>>
>>7802680
There is nothing about a computer bug that violates the laws of physics. The fact that computer bugs are computer bugs is a consequence of the laws of physics. I can scarcely even.
>>
>what are the odds
Well since it hasn't happened yet we can't compute those odds.
>>
So there is no such thing as true "touching", right? Then how do things cut?
>>
The Earth curves.
Aeroplanes travel far enough that the curvature actually changes. Why don't they have to realign their planes when they travel long distances? Or is keeping it aligned already part of normal duties so the additional deviation made by Earth's curvature is not even noticed?

>>7803058
You just push at a distancely roughly enough that it gives in. If you have a really repellent magnet there's no reason why you should be able to break metal bar with it right? It's the same thing on a smaller scale.
>>
Okay, I had to mail official transcript for the supplemental requirement to CP Pomona. I requested four to be mailed from the CCs to the University and two have arrived. The other two still have not been received. What happens if the two that have not arrived arrive past the deadline? The one with over 70 credits has already been received from CP Pomona.
>>
Given an arbitrary system of equations, why is direction in space "stored" in the variables when considering the system as linear equations, but "stored" in vectors when considering the system as a vector equation? For example suppose we have a system of three equations in three variables where each equation is of the form (a_i)x + (b_i)y + (c_i)z = d_i. Lets also suppose they represent three distinct planes in R^3. In the context of the system representing planes in space (a system of equations), it seems to me that dimension/direction is sort of "stored" in the variables x, y and z. Considering the system as a linear combination of vectors, say

xV1 + yV2 + zV3 = D, where

V1 = < (a_1), (a_2), (a_3) >, etc.

the coefficients associated with any one variable make a column vector. In this context it seems as though dimension/direction is stored in the vectors, and the variables x,y, and z now just scale them. I realize that both contexts have the same solution set, and both take place in R^3, but is there a more intuitive explanation for this relatedness?

Also, considering those same arbitrary planes associated with the system above, we could express any given plane as the set of points that satisfy the dot product of a vector parallel to the plane and perpendicular to it set equal to zero (and this makes intuitive sense to me why this is). I also see that how they are expressed in the system is similar to just doing the dot product operation. Any underlying connection here too? Sorry if this isn't a very coherent or well formed question. It has been a rough week.
>>
Anyone wanna play chess with me before I study? http://lichess.org/aCmnVatA
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>>7797529
Not the same person, but if you simply think about water purification from sea, you use resources such as electricity to de-salinate and make it usable. some amount of it gets lost through entropy which can't be recovered. So even if water quantity remains same in this scenario, resources are being wasted.
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>>7802662
in a 2d problem + slack you can see the slack variables as (differently scaled) normal vectors coming from the constraints, so the size of the slack variable says how far you moved from the constraint
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>>7803058
The strength of the bonds between metal molecules are stronger than the strength of the bond of paper molecules.

In a more macro sense, it can be said that because the only thing that keeps lengths of string together is intense friction between the jumbled-up fibers, if you pull hard enough, you'll eventually overcome either the friction or the strength of the bonds.
>>
>>7803760
also it helps that bladed materials apply lots of force at a single point.
There's also other things to be considered. Shear strength, tensile strength. Those should all be a property of the bonds between molecules.
>>
>>7803293
Planes don't fly straight from A to B.
As you said, long distance planes/missiles are made to follow the curvature.

So on the earth viewed as a rectangular projection, the path of a missile from Moscow to Los Angeles may be seen taking the scenic route over the Arctic Ocean.
And that's because it's taking advantage of the earth's spin.
>>
>>7803769
also planes keep a constant altitude, they don't fly straight out of the atmosphere.
>>
Are there any good autobiographies or articles written by really smart people about their work that would help me get a glimpse into what it's like not to be a genetically inferior brainlet?
>>
>>7799162
look up 'completing the square'. always helps me when i get stuck.
>>
>>7802363
I decided to pull out my TI-83 to figure out how this worked, and you have a few syntax errors.

Here's my successful program. The // symbol is for comments that aren't part of the actual code and white space between lines is for readability.

:
: randInt(0,100) → X // The syntax is Value → Variable. The variable needs to be on the right.
: -1 → Y // Yes, I know other programming languages use variable = value. But this is for teenagers, and they would get confused reading from right to left.
:
: While Y≠X
:
: Prompt Y // This is placed inside while loop to ensure "WIN" occurs on lucky guess. Setting Y to -1 earlier ensures Y≠X.
:
: If Y<X
: Then
: Disp "LOW"
: End // If-statements and while loops are not complete without an End at the end.
:
: If Y>X
: Then
: Disp "HIGH" // My TI-83 doesn't let me have Then and Disp on the same line. It might work differently on a TI-84.
: End
:
: If Y=X
: Then
: Disp "WIN"
: End
:
: End // This End is for the while loop. It's not here to end the program: the program ends automatically after running all the lines.
:
>>
Say you have a neural network or something... and you're doing supervised learning and try to evaluate your results.. The algorithms use euclidian distance so you want to standardize your inputs

Do you also standardize the outputs? I get super high MSE if i don't standardize the outputs, but if I do, my MSE is always under 1. Anyone knows?
>>
How do I measure time by the shadow of a satellite on Mars?
>>
>>7803854
Also if I don't standardize anything I get the most "correct" results.. But it feels wrong cause some of the inputs are between 0 and 300, and some are between 0 and 1, so surely the first group gets more weight given that I'm using Euclidian distance..

Also, when standardizing, I'm standardizing the inputs/columns, not the rows/data points

What am I doing wrong? Using z-score btw
>>
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Can this be solve or do you need a adjacent and opposite?
>>
>>7804285

Can what be solved? What are you looking for?
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>>7804295
The hypotenuse t1 & t2.
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>>7804298
You can figure out the last angle, then split the triangle into two right triangles.
>>
>>7804285
All information you can use is that the sum of forces are 0:

cos(53°) T1 = cos(53°) T2
sin(53°) T1 + sin(53°) T2 = T3

Two linear equations and three variables so it's not enough information.
>>
>>7804298
T means tension, you are looking for tension.
>>
>>7804311
yeah but then all you have are angles, with no length.
>>7804319
oh so you can't solve it. thanks
>>
>>7804285
sin53.0 = t1 / (fg/2) ;)
>>
>>7804319
well, he probably have the weight and he can find fg>>7804323
>>
>>7804285
>>7804322

Assuming you know the value of "weight" then this can be solved. If the angles are the same you know that the problem is symmetric. Therefore the tension T1 is the same as T2.

T1 = T2
T1 sin(53°) + T2 sin(53°) = T3
2 T1 sin(53°) = T3
Weight = T3
T1 = Weight / (2 sin(53°))
>>
ODE question: suppose I have a non-linear equation with an initial condition. I know the RHS is continuous, therefore a solution exists locally around t_0. How do I prove that it is globally defined ?

(I have a particular exercise, I'm asking for some direction, not for a general proof which obviously doesn't exist. Just in case of misunderstanding)
>>
>>7805024
any chance you could use something like this?
I think your question can't really be answered without the precise example, it's too vague.
>>
>>7805040
>like this
https://en.wikipedia.org/wiki/Picard%E2%80%93Lindel%C3%B6f_theorem
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>>7805024
You have to prove that the solution stays bounded on every finite time interval.
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>>7805057
thanks, could you explain why is this sufficient ?
>>
Are the two fractions $\frac{1}{1}$ and $\frac{100}{100}$ considered two seperate elements in the set of $\mathbb{Q}$?
>>
>>7805993
No, certainly not. Rigorously, $\mathbb{Q}$ is defined as the field of fractions of the integers, whose construction involves an equivalence relation among equivalent representations of the same fraction.
>>
>>7805993

No.

I will add to this in a later post, but your big takeaway for right now is that the answer to your question (and related questions) is "No".
>>
>>7806077

In naive set theory, if for whatever reason the expression of a set involves multiple instances in the enumeration (where each element or representation is understood to mean the same thing), a simplification of the set entails expressing the element exactly once. For example...

$\{ 2,3,3,3,4 \} = \{ 2,3,4 \} \\ \{ \pi , 3.1415... \} = \{ \pi \} \\ \{ 0.999... , 1 \} = \{ 1 \} \\ \{ \{ \} , \emptyset \} = \{ \emptyset \}$

where the third item puts trolls firmly in their place. Such a convention of banishing multiplicity extends to the rationals, as another anon alluded. And the reason why this is so, is because at its simplest level, "two-valued" (that is, 'is a member of' OR, 'is not a member of') naive set theory, like two-valued logic, is simply concerned to say whether a thing IS or IS NOT in a particular set. Questions of ordering, multiplicity, etc are dealt with in other (nearby) areas.
>>
>>7805993
No. Q is a set of equivalence relations: a/b = c/d iff ad = bc. And clearly, 100 = 100 so both of those represent the same fraction: 1 (= 1/1)
>>
>>7802558
If you've got free time and charisma to start a company, 200k/yr after 3-5 year startup period. Otherwise, probably 60-75k+benefits working for someone else. Unless you don't wanna be in marketing, then 70k max.
>>
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How does the graph look? I'm terrible at this
>>
>>7806869
Just construct such a function for example:

f(x) = |(x-3)^3 + 343|
>>
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>>7806884
... eeeh? what?
>>
Can you "redo" college? I was pretty average in high school (no homework, decent test grades) and graduated decently. went to a community college for Mathematics and did alright until my gf of 4 years at the time broke up with me, my grades dropped, lost motivation, but I kept going while depressed and GPA went from a 3.8 and is now a 2.2 or so. Had to retake some calc classes and still didn't do well with them (I can't show work for shit but got correct answers).

Im 23, and been working the past two years and want to go back after dealing with the shit of working manual labor jobs. The job is actually decent 40k/yr, benefits and loads of time off while job takes care of housing and food while working, but I want to try to go back. Keep a decent GPA up and perhaps go to a European college that specializes in maths, engineering and sciences, like Tartu or something.

I just don't know where to start or what to do at this point in time.
>>
>>7805993
Are you familiar with equivalence relations? It's essentially a way of comparing elements of some set that behaves just like "=" does.

We can define an equivalence relation $\sim$ on $\mathbb Z^2$ by saying that $(a,b) \sim (c,d)$ if $ad = bc$. What this is saying is that two fractions are equal if we can cross multiply and get the same thing.

So we define $\mathbb Q = \{(a,b)\in\mathbb Z^2 : b\ne 0\}/\sim$, which means that we take all ordered pairs (these are what we consider to be the fractions, i.e. $(a,b)$ is just $\frac {a} {b}$) and declare that any two are the same fraction, and hence equal in $\mathbb Q$, if $(a,b)\sim(c,d)$
>>
>>7806890
You know two conditions of the derivative, f'(-4) is undefined and f'(3)=0, and the original function is continuous. So it has to be some kind of absolute value function with its vertex at x=-4 and some function that changes from decreasing to decreasing or increasing to increasing at x=3. Knowing this you can make up a function
>>
>>7806902
wait
why would we define Q with b non-zero?
Why can't we just define a fucking class with b=0
1/0 = -1/0 = 2/0 = ...
call it THE infinity and be done with it.

division by 0 solved right here in this thread, please gib fields medal
>>
>>7807230
Have you verified a consistent extension of the field operations to this extended domain?
>>
>>7807230
As >>7807242, I'll give you a hint: you can't.
>>
>>7807230
There's a way to allow 0 in the denominator, but you get the 0 ring. Is this what you'd like from the rational numbers?
>>
>>7807242
how would you do that?
>>
If I get a tank of air. Remove all its water molecules. Put a single one in there. Is the water molecule more likely to go up or down?
>>
>>7808002
>>7807247