Well Yea Forums ?

go play with the mud people or better yet the psychics
should be around your playground

She's ass.

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> here's some arbitrary symbols put together
You just need to put a little effort into understanding the mathematical notations.

x cannot be an exponent so it is not a polynomial.
The math itself doesn't matter since it is not the question, the question is whether it is a polynomial or not.

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Here comes the obligatory condescending faggot on a 4channel thread.

I bet you don't even know half the notation written in the image, stop projecting your insecurities here.

It's just another language. By the same logic you can call English 'arbitrary' if you wanted to.

The question is whether f is a polynomial function, not x
And besides, there's no question, there's something to prove

Kurisu's got a great butt.

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absolutely correct
obviously op is the one not getting ridiculed on basis in his uni, assuming he even attends one

why, my peenus weanus of course :)

hahah! :D

it's my weeeeeenus peanus! :) hahah

my answer is, of course, my peanus weenus :D

hahaha!

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By Induction

encyclopedia.ushmm.org/content/en/article/germany-jewish-population-in-1933

K E K
E
K

>It's just another language. By the same logic you can call English 'arbitrary' if you wanted to.
The point is that the problem becomes "can you read mathematician well enough to understand what this actually says?". And judging someone's thinking skills based on that is kinda like judging them based on their ability to quote the correct post on Yea Forums.

>fails to define how big a batch is

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Let k = supremum of n_x for all x in I. If k isn't infinity, taking the derivative of f, k times shows that f is a polynomial. Moreover, k must be finite, since if it was infinite, and since I is a finite interval, the pigeonhole principle shows that there exist points arbitrarily close with non vanishing derivatives for all n_x arbitrarily large, which contradicts the fact that f is infinitely smooth .

I think I understand the problem but I'm too dumb to actually prove it

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This is a highschool level problem.

>high school dropout detected
f has to be polynomial for the condition to be met you animal. You can't have (a^b)c=0 unless c is 0 or (a^b) is zero. Since it has to work for all elements of I, c won't always be zero, so it follows that the (a^b) must be able to make it 0 always with some combination of values. This cannot happen with a monomy because you simply can't have c^x=0, so it's necessary that instead of c a polynomial exists in which its terms cancel each other with at least some values.

If f wasn't a polynomial function, then I wouldn't be able to solve the problem. Given the assumption that I can solve the problem, f is necessarily a polynomial function.

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LMAO
That's a very well known theorem that was proved in 1970. And later even for a more stringent condition of x from [a,b] and x from R.

Suppose f is not a polynomial. Let
C = {x: there is no neighbourhood of x on which f is a polynomial}.
A_n = {x: f^(n)(x) = 0}.

Clearly C is closed and nonempty, and A_n closed with union_n A_n = [0,1].
Applying the Baire Category Theorem to C, A_n intersect C has nonempty interior
in C for some n, i.e. there exist x0 in C and delta > 0 such that
C intersect (x0 - delta, x0 + delta) is contained in A_n.

Suppose f^(k)(x0) 0 for some k > n. By Taylor's Theorem, we get f^(n)(x) 0
for 0 < |x - x0| < eta (for some eta > 0). Taking eta < delta, this implies
C intersect (x0 - eta, x0 + eta) = { x0 }, but then f is a polynomial on
(x0 - eta, x0) and on (x0, x0 + eta) and hence on (x0 - eta, x0 + eta),
contradicting x0 in C. So we must conclude that f^(k)(x0) = 0 for all k >= n.
The same is true for all points in C intersect (x0 - delta, x0 + delta).

Now suppose c in (x0 - delta, x0 + delta) \ C. Then f is a polynomial on some
neighbourhood of c. Let [a,b] be the maximal interval containing c on which
f is a polynomial. Then a or b (say b) is in
(x0 - delta, x0 + delta) intersect C, so that f^(k)(b) = 0 for all k >= n.
Now if f has degree p on [a,b], f^(p) 0 on [a,b] so p < n, and then
f^(k)(c) = 0 for all k >= n.

We conclude that f^(k)(x) = 0 for all k >= n and all x in (x0 - delta, x0 + delta). But then f is a polynomial on (x0 - delta, x0 + delta), contradiction.

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P.S. It's called the "polynomial problem" btw

Nowadays, it seems the math degree requires being an avid anime fan

that's irrelevant for the question

Can confirm.
t. Masters in pure math -kun

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>0 < |x - x0| < eta (for some eta > 0). Taking eta < delta
Why does this appear so often in math and why does this always break my brain

What do you mean? That's a fairly common practice. How otherwise do you compare two unknown values?

>comparing two unknown values
well, now at least I know what it is for but my brain stops processing it anyway
t. going to computer science

2439.02439024 get rekt user

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i couldn't understand your post because it was just some arbitrary symbols put together
post it in a less pretentious fashion

you literally run into that every time you use floating point numbers in computing

28*3 for a regular oven=84 *15 ovens=1260 cookies/batch
24h*60=1440 mins/day
1440/20mins=72 batches/day
365*5= 1825 + 2 days in 5 years
1260 cookies/batch*72batches/day=90,720 cookies/day*1827 days = 165,745,440 cookies in 5 years

what?

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What?

if you want to bait brainlets you should use problems that brainlets could actually understand, like diophantine equations.

math confusing
math people understand
other people don't understand
math people smug

Why are you dividing by 20 min? it’s an hour per batch.

Right goes up since the tension of the string is in the same direction as the buoyant force.

More like highschool problems.

People who don't understand high school and freshman year math should not procreate desu.

I would expect the scale not to tip if the weight of the ping pong ball can be ignored.
the crane contraption would not influence a glass filled with air, and in an air filled glass the same buoyant effects apply as in a water filled glass.

it all comes down to wether the ping pong ball is considered weightless, in which case the scale stays balanced, or if it weighs a little bit, in which case the ping pong ball's side lowers.

Right side goes down. Just compare the difference in potential energy when one side moves down a bit. The steel ball doesn't actually affect anything, while the ping pong ball does.

>baking cookies for an hour
If you want nothing but smoke and carbon coming out of your oven, sure

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Why is she offering the kid a graphics card and what is this from? Has Nvidia marketing reached a new level?

alternatively, the left ball could be filled with a gas lighter than air

Wow...that is so far removed from my domain of expertise I don't even know some of the terminology you're using.

Wrong. Think of the weight the string holding the steel ball has to support. As you lower it into the water, the tension decreases by the bouyant force of the steel ball. As long as this is greater than the weight of the ping pong ball (it should be), then the right side will drop.

With the defined constraints (15 ovens working 24 hours a day, 365 days a year (with one leap year at 366 days), the cookie monster could only make 657,360 batches of cookies. to reach the desired 6,000,000 a batch of cookies must contain 9.127418765972983 cookies. since the cookie monster won't make fractional cookies, we'll round this up to 10 and say:

Cookie Monster can make a batch of 10 cookies. A batch takes 1 hour to cook from start to finish. As soon as a batch is done a new batch is going in at the exact same second. He can cook 15 batches at a time. These ovens run 24 hours a day for 5 years straight.

10 (cookies) * 15 (batches) per hour = 150 cookies per hour.
150 batches per hour * 24 hours per day = 3,600 cookies per day.
3,600 cookies per day * 365 days per year = 1,314,000 cookies per year (and 1,317,600 cookies on a leap year).
1,314,000 cookies per year * 4 years (to later account for the leap year) = 5,256,000 cookies over 4 years + 1,317,600 for a leap year = 6,573,600 jews in 5 full years.

For each x\in I I will form an open cover U = {U_x}_{x\in I} of I such that m_x > n_x has f^{(m_x)} = 0 in U_x. Since f is smooth, such derivatives exist and such open neighborhoods of x exist. Now since I is compact, there's a finite subcover of U determined by a finite index set A. By taking m = max_{i \in A} (m_{x_i}) we see that f^{(m)} = 0 for all x \in I. As f is smooth we see that by Stone-Weierestrass approximation f is a polynomial of degree less than or equal to m. QED.

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Now calculate the mass of all the cookies then divide by the mass of a Jew to get the actual jew amount that was baked.

Fuck you you little shit

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Making the force diagram for the water:
Left side has the weight of the water itself, the downward force due to buoyancy B1 and the upward force due to string tension T1.
Right side has the weight of the water and the downward force of the buoyancy B2.
The right beaker therefore has has an "increased weight" equal to the volume of displaced water, equal to B2. For the left side, we have to take into account the tension which pulls up the beaker, which is equal to B1 - m1 (m1 is the mass of the ping pong ball); therefore the left side has an increased weight of B1 - (B1 - m1*g) = m1*g.
Since both balls have the same volume, B2 = B1 = B, so the left side increases it's weight by the mass of the ping-pong ball (as is expected), while the right side increases it's weight by the volume of displaced water, so taking in account real-life situations, the right side goes down.

got a question for you instead math lady
When am I actually gonna use this in my life? In my job? Out on the field? Experimenting in the lab and filling out spreadsheets?

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Just search what each of them means,it's easy when they are universal

youtube.com/watch?v=OZzIvl1tbPo

> but muh usefulness!!1
If you can't appreciate the beauty of mathematics then you probably won't use anything you learned in school in real life because you'll never amount to anything more than a drone.

are you underage? because that kind of argument tends to come from lazy school kids or people working a mcjob because they were lazy in school

meant for

Thanks, I tried for a couple minutes but I couldn't get anywhere. I can't really understand the proof either, I'm at least glad I understood what the problem was asking.

What’s the use?

anything remotely related to anything STEM or statistics

There are several conditions that need to be either "given" or "abstracted out" and even though one could just reduce everything else to "zero time, quantity one", it still is annoying for those who are used to "trick questions":
>The amount of cookie batches per oven needs to be defined (or otherwise the amount of ovens per batch)
>The issue of maintainance and lifespan of the ovens needs to be clarified
>The pre-heating time of the ovens from room temperature to the regular baking temperature needs to be defined (likewise time to cool down for maintainence if neccessary)
>The issue of how much time it takes to switch out oven sliders (i.e. putting in and taking out the cookies) needs to be defined
>Any unexpected factors (supply shortages, mistakes committed by employees or cookiemonster himself, blackouts, etc.) need to be clarified or abstracted out
>etc.

>Any unexpected factors (supply shortages, mistakes committed by employees or cookiemonster himself, blackouts, etc.) need to be clarified or abstracted out
okay but anything like this which isn't explicitly mentioned in the first place will only exist if the person asking needs to be kicked in the dick and then ignored

>avatarfags with a genius
>is a dumbo
classic

The polpost doesn't define size of batch because it never mentions individual cookies, just batches of them

the pic asks for time for 6 million batches of cookies, not 6 million cookies

Huh, I somehow skipped over that. If that's the case you can't reach 6 million in 5 years.

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i admire your effort to interact with polpost, but there's no point in that
nazi apologists will never admit that Nazi genocide spree happened, and good goyim will never admit it was typical purge of undesirables that happened in pretty much every socialist totalitarian regime

5th year EE and there was literally no reason for me to take any differentials or any of the calc classes, the applications are so basic they might as well be taught with the theory classes

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>Taking 5 years to do a 4 year degree
>Not having any knowledge of signal processing which uses fourier transforms the way most people use a comma
Knowing how to wire a plug doesn't make you an "EE", son.

>but you don't like math like me so you're not a real engineer!!
grow up, child

>doesnt even tell you what time he left.
The answer is indefinite.

He begins going home at the moment the presented scenario occurs, because Tanaka's bed is his home now.

You don't have to like math, you have to acknowledge the immense use it has in allowing modern life.

Are you from a balkan country? Never heard anyone else say 5th year EE

Amerilard
It's been really shitty, gonna spare you the details but I really, really hate school

I graduated in computer science 2 years ago. I know I should be able to solve this, but I can't.

You're missing the point. It's established that it takes one hour for one batch, and the final answer is asking about the number of batches. Whether each batch is one cookie or one hundred doesn't matter.

If it's C-infinity I guess you could just do a Taylor series expansion, and after you get to n_x all the coefficients are 0, so BAM! there's your polynominal.

not everything in life has an immediate direct application you bloody buffoon.

I get the picture, these concepts are a retard filter, so people who don't want to deal with those concepts can't get good work. Life sure would be luxurious if you could just get trained by whatever company you wanna work at but I realize they have to filter out morons.

Well to be fair, universities have to teach you this stuff, because in the first place, university prepares you to become a scientific researcher, and you may end up needing this stuff in science. University is not supposed to be job training, even though in practice it totally is.
So that's kind of the issue.

the cookiemonster didn't finish his job

The proof follows trivially.

This implies that all cookies are baked in ovens. In fact, if you had the cookie dough near one of the 15 ovens, you would just go ahead and bake it, it's a total no brainer. But what if you found a family of cookie dough somewhere else, they resisted, and you shoot them in the head? Do you drag the cookie dough all the way to an oven, or do you just bury it somewhere, or something.

Jews came from all over Europe, not just Germany. Think Poland, France, Austria. Etc.

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Who is that girl?

What is a C-Infinity class function and N-Star.

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What I dont get is why holocaust victims have more consdieration and attention the the 81 million people that died on the war that werent jews

The answer is that it is the jews and women's fault.

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Your mum is already taking care of that for us (the world)

We're just waiting our turn on the line

So are you though.

You use it to show off on Yea Forums and brag about how smart you are in threads like these.

Virginity in women is seen as good and valuable.

Virginity in men is seen as bad and making the man worthy of mockery.

>Catholic clergy bad

>5th year EE
>no reason for me to take any differentials or any of the calc classes
What fucking kind of
>education
allows this?

I'm not a scientist, I'm a MAD scientist. Stupid joushu!

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Are you claiming that those corrupt child molesters are good?

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Who are you implying to be joushu? I am not joushu!

>when am I going to have to understand a problem symbolically generate an understanding of the mechanics behind it and use my prior knowledge to provide a solution

You'll probably never use it because you're a fucking weeb who uses his neetbux to get fat and retarded

So basically, we have a real, infinitely differentiable function in [0, 1]. Assuming that one of the function's derivatives is zero, then we must prove that the function must be a polynomial. Is that right?

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Clearly it works for all polynomial functions. Assume that f is not a polynomial function, clearly we get a contradiction.

Q.E.D

Not quite, we're assuming that for every argument there is a derivative of the function that will return 0

I'm gonna take a stab at this. Not sure if this is correct but if we integrate both sides of fn(x)=0 n times we should get a polynomial like f(x)=ax^n+bx^(n-1)+cx^(n-2)... etc. Am I missing something here?

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Yes

Elaborate

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engineering or compsci brainlet spotted

Physics, but still kys

no. It says that at each point the derivative of some order vanishes. That's a very different statement from saying that the nth derivative vanishes.

Lel at that convoluted shit. Just apply Tychonoff's theorem and basic functional analysis and the proof is only a couple lines.

may allah have mercy on you

Go on then

shota gets devoured by thirsty cougar

Oh shit that's actually completely different.

I think this user has the best proof from what I've seen in here then

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You would be fucking them too if you could get away with it.

I couldn't come up with a proof because I don't really know any functional analysis so I can't really throw stones, but this proof is terrible. What's the point of doing a proof by contradiction here? Why the splitting into cases? Why can you invoke Baire's theorem? Are you making an appeal to Sard's theorem?

Oh, I'm retarded and didn't remove the first line. I didn't mean to invoke contradiction at the beginning. Also, which cases?

twitter.com/Complex/status/1138466155767717888

You should be able to solve this.

In most Americans, deep down, lives the eternal fishmonger whose interests are fundamentally and ultimately fish-related.
For Americans, excellence is the continuous murder of the fishmonger within.

I want a doujin out of this
>Has Nvidia marketing reached a new level?
kek

What's the problem?

45 years