SQT thread

>>8314917
1. Draw a triangle

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It's been a little while so forgive any mistakes.

>>8314962


OP here
Wrong. 0.78 and -0.78 are the correct answers.

I did the same as you

are there any infinite fields where the multiplicative group is isomorphic to the additive group?

or any pair of infinite fields where the multiplicative group of one is the additive group of the other?

>>8314972
Those are the values of cos x and tan x when they are equal, but the values of x are what I gave. The way you phrased it implies you wanted x. What was the exact phrasing you were given?

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Help

>>8314917
cos x = tan x
cos x = sin x / cos x
cos^2 x = sin x
1 - sin^2 x = sin x
0 = sin^2 x + sin x - 1
sin (x ) = ( 1 +/- sqrt(5) )/2
discard the positive sqrt as this is greater than 1
inverse sin, etc

>>8314962
Line 3 do: cos4x = 1-cos2x
Solve the quadratic

>>8314972
sqrt((-1+sqrt(5))/2)
That's what you want

>>8316375
So Cos(x) = Tan(x) when Sin(x) equals the golden mean?

Mind blown.

>>8316375
missed a negatve, my bad

Working out of Bak and Newman's Complex Analysis book. The proposition is 7.3:
If f is an entire function satisfying [math] |f(z)|\leq 1/|Imz|[/math] for all z, then [math] f\equiv 0 [/math]. I fail to see how this is at all significant or what the point of it is. It seems intuitively to be a big "well no shit" result. The proof is also kind of obtuse. They pull a [math]g(z)=(z^2-R^2)f(z)[/math] out of their ass to prove it, I understand how it follows but how they popped that up at the start beats me.
Any insight would be amazing.

>>8316878
>They pull a g(z)=(z2−R2)f(z)g(z)=(z2−R2)f(z) out of their ass to prove it

from what I've heard this is pretty typical for analysis

I've got about a year and a half before I graduate with a B.S in Mathematics. Is there hope for me to get some kind of research experience before I graduate or am I fucked? Thinking about applying to grad schools and my chances of getting in is making me pretty nervous, especially since I go to a small and kind of shitty school.

If humanity learns to master the universe and do anything it. Would there be a reason to keep doing anything, or would humanity just chill for an eternity doing whatever it wanted?

I'm actually curious for an answer.

>>8314917
Biology is science... Right?
I have been looking everywhere and I haven't been able to find the answer to this question and my textbook is total shit

Q: Which has a greater effect on the rate of immigration? (talking about species coming to islands)
A: Distance
B: Size

i would appreciate any help

Can I have a fact check on Tesla being born in an electrical storm at the stroke of midnight plz senpai

>>8320593
should be true, sources say yes like this one
http://www.pbs.org/newshour/rundown/5-things-you-didnt-know-about-nikola-tesla/
didn't find any myth busting

>>8320583
I would guess distance

How close is humanity in radically extending its lifespan, and maybe reverse aging?

Are there any governments pouring funding into things like this?

Does anybody know of a good textbook to get started with modular arithmetic?

>>8320644
more number theoretic point of view:
An Introduction to the Theory of Numbers - niven/zuckeman/montgomery

more algebraic point of view:
hungerford - abstract algebra: an introduction

>>8320837
many thanks

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I can't decide.

Should I use Hoffman/Kunze or Friedberg to learn linear algebra?

>>8322403
bump

how do i measure the frequency of some sort of cyclic mechanical thing like a gearbox. i know i have to fourier a time signal, but how do i get the time signal?

>>8315006
The multiplicative can never be isomorphic to the additive group. Suppose there is an isomorphism [math]\varphi[/math] from the additive group to the multiplicative group for sake of contradiction. We can study this hypothetical isomorphism and show that it cannot exist. We know that [math]\varphi(a) = -1[/math] for some [math]a[/math], so [math]\varphi(2a) = [\varphi(a)]^2 = 1[/math]. This means that [math]2a = 0[/math], [math]a = 0[/math], and [math]1 = \varphi(0) = \varphi(a) = -1[/math]. Now let [math]\varphi(1) = m[/math] so that [math]m = \varphi(1) = \varphi(-1) = m^{-1}[/math]. This means that [math]m^2 = m \cdot m^{-1} = 1[/math], meaning that [math]m = \pm{1} = 1[/math]. Notice that [math]\varphi(1) = m = 1 = \varphi(0)[/math], so [math]\varphi[/math] cannot be injective. Q.E.D.

>>8314917
I'm learning Prolog at the moment, my question though is more related to logic qua science than programming.

When unification is done, from my understanding, it is simply finding a substitution that makes two expressions identical, for example, the most general unifier of:

f(X, g(Y))
f(h(U), V)

is, replacing X with h(U), and V with g(Y), and I understand this to be the most general unifier.

However, what I don't understand is why this is a valid inference, in predicate logic, X, Y, U and V are elements of the universal set, and g is a subset of the universal set, and f is a subset of (universal set) x (universal set).

So, g(Y) is supposed to be a truth value, it is either true or false, it is true if Y is an element of g, it is false otherwise.

So how can we sort of "replace" Y which is an element of the universal set, with something that is "outside" the universal set (something we call a truth value), why is that even valid?

>>8316878
Think about what the expression means and about what it does in the proof. If you still can't get the intuition behind [math](z^2 - R^2)f(z)[/math], try reading the proof backwards.

what if all my myelinated neurons were replaced by nonmyelinated ones but with the speed of the potential remaining constant?

>>8324089
durr, the question being, would I still look the same?

How come neanderthals and shit never have crazy long ass hair? Did they used to cut their hair as well? What?

When I transfer from community college to university, will my stinky GPA follow me and stain my degree?

>>8325211
NOPE

your shit gets reset, you will start with a zero GPA.

don't fuck it up this time.

>>8320641
yes anon, don't worry; you'll never die

>>8320476
how's your gpa?

>>8325218
>If you believe in special relativity, there is nothing receding faster from us than c. You can catch up to anything other than photons if you go faster than it.

I believe in SR but I also believe in observational cosmology, where we see galaxies receding from us faster than c.

From Earths PoV it's clear the ship won't ever reach those galaxies but what would it look like from within the ship?

>>8320481
just chill

>>8323955
you forgot about characteristic 2 >>8318726

What is similarity transformation from the geometrical pov? What is similarity coefficient?

No vectors pls

Does anyone knows how to do a linear control for a hovercraft?

HOO HOO HOO!

I'm going to explain how I can made a single core hyperthread, into six processors, due to the topic of trig.

Blazzin it in math

>>8325308
it means you make something bigger or smaller. the coefficient is how much bigger or smaller you make it. simple enough for you?

Thoughput to OUTput to output SHELL.

Break my streets network and analyse, like breaking into kiddie porn orgies happening by my foodstore

>>8325409
congrats Craig

>>8325418
So if we're taking ST of a plane, it's gonna be it's own invariant regardless of the k_s?

>>8325440
Define invariant and k_s, then I can answer your question.

>>8325446
Invariant of f from X to X is a subset of X that remains the same under f. k_s is similarity coefficient.

The reason we wake well is lack of decaf and a secured networking GIANT.

The Illinois economy recieved 42,000,000USD; I have a billion one third currencies today a Billion now.

Just saying we need to just take theor HugesNet box, upgrade, the destroy to secure.

My funds are prossesed.

In the next 11 years what can I most likely expect technology/medical wise /sci/?

>>8325650
mEMe drive

>>8325650
Probably nothing exciting. Everything will just be slightly higher quality. Think about how things are today compared to, say, 2006. Computers are faster, smartphones are much better, internet is better, and there have been slight cultural shifts because of that, but that's pretty much it. My guess is by the end of the 2020s the big new technology will be self-driving cars.

>>8325828
I see. Well thanks for the reply Anon.

Is there by chance any huge advancement you think will most likely happen 30-40 yrs by chance?

>>8314917
USE WOLFRAM ALPHA YOU NIGGER

Why do poor people have more children than richer people/people who are more taken care of?

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What on earth am I looking at

>>8326210
a test on whether or not you can apply the fundamental theorem of calculus

>>8326214
>taught something fucking forever ago
>not used for anything
>suddenly we need it
Why does university do this?

What are some ways an advance civilization can prevent the heat death without leaving the universe for another, or just getting out of it?

>>8326220
Radiating negative energy while creating positive energy maybe?

>>8326218
Every time you evaluate an integral
[math]\int_a^x f'(t) \mathrm{d}t = f(x) - f(a)[/math]
you're using the fundamental theorem of calculus.

If you then take the derivative of both sides
[math]\frac{\mathrm{d}}{\mathrm{d}x} \int_a^x f'(t) \mathrm{d}t = f'(x)[/math]
you get exactly what you posted.

>>8326323
Please explain that like I am a retarded caveman who is loudly banging two rocks together as you speak

>>8325459
A similarity transformation's invariants will be any linear subspace, or ray/halfsubspaces if the coefficient is nonnegative.

>>8326328
Suppose there is a function F(x) which when differentiated gives sin(e^x+2^x).
The fundamental theorem of calculus tells you that
[eqn]\int_a^x sin(e^t+2^t)dt=F(t)-F(a)[/eqn]
Now differentiate the LHS, that's what your picture wants you to do, then differentiate the RHS. Well, differentiating F(x) gives sin(e^x+2^x) and F(a) does not depend on x at all, so differentiating gives 0, so all you end up with on the RHS is the sine term.

>>8320583
http://jareddiamond.org/Jared_Diamond/Further_Reading_files/Diamond%201975.pdf
distance

>>8324630
bump

>>8326218
It's called the FUNDAMENTAL THEOREM of calculus. You should remember it.

>>8326032
One reason is poor people will be taken care of by their children.

Can someone explain the solution to this problem to me? I think I understand it.

Given events A and B are defined as follows:
A={It rains Monday}
B={It rains Monday and Thursday}
Which of the following is true?
A. B is a subset of A
B. A is a subset of B

The correct answet is B is a subset of A. Why is this? Is this because B is just a combination of A with additional events but will ultimately fall under it rains on monday?

>>8327035
>Is this because B is just a combination of A with additional events but will ultimately fall under it rains on monday?

Yes. B holds in less situations than A does, so it's a "smaller" set.

>>8327118

solution is

(It rains on monday)= (it rains on monday and thursday)U(it rains on monday and not thursday)

In the textbook but that notation doesn't make sense to me :/

>>8316383
Technically it's the golden ratio conjugate, but yes, that number is extremely prevalent.

>>8327144
I mean I understand what the notation is saying I just dont get how then union of those two gets rain today

>>8327154
>>8327144
union = or

>>8327174
I get that but I dont get how it simplifies down to just it rains on monday

>>8327183
If it rains on Monday, then it either rains on Thursday or it doesn't. In one of these cases you get the first set, in the other you get the other. Draw a Venn diagram and it will make more sense.

>>8322403
how about you just learn linear algebra through multiple sources you fucking procrastinator

dont ever get fat with a brain like yours

>>8327200
I see it now I guess anon. I just wouldn't have made that connection I guess. Thank you

Suppose we have the seires

[eqn]\sum_{i=0}^{\infty} \frac{5}{i^{3}+2}[/eqn]

Would these two forms of the direct comparison test be equally okay to prove the convergence?

>First:

Take the convergent p-series

[eqn]\sum_{i=1}^{\infty} \frac{5}{i^{3}}[/eqn]

Then consider:

[eqn] i^{3} < i^{3} + 2[/eqn]
[eqn]\frac{1}{i^{3}} > \frac{1}{i^{3}+2}[/eqn]
[eqn]\frac{5}{i^{3}} > \frac{5}{i^{3}+2}[/eqn]

Thus the original series must converge.

>Second:

I just think of it this way:

Same p-series:

[eqn]\sum_{i=1}^{\infty} \frac{5}{i^{3}}[/eqn]

But then the relation:

[eqn]\frac{5}{i^{3}+2} < \frac{5}{i^{3}} [/eqn]

Since clearly [math] i^{3}+2 > i^{3} [/math] which implies the former grow smaller much much faster than the latter. Same answer, but less inequality work.

What type of integration do I use for something like sqrt(d^2 + x^2) ?

>>8327949

trig sub

[eqn] \sqrt{a^{2}+bx^{2}} \implies x = \frac{a}{b}\tan\theta [/eqn]

>>8327974
I'm pretty sure there was another method though.

>>8327977

ibp, u=sqrt(d^2+x^2), dv = dx

>>8327983
Please use English on this British watercress-sampling imageboard.

>>8327984

Integration by parts you mong.

>>8327988
I thought that was for two things multiplied together.

>>8327992

In IBP it's often useful to use dv=dx. Consider this:

[eqn] \int \arcsin(3x) dx [/eqn]

where [math] u = \arcsin(3x) [/math] and dv=(1)dx

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How do interpolation periods and sample periods work? Trying to implement this algorithm:
https://www.researchgate.net/publication/258401146_Look-Ahead_Algorithm_with_Whole_S-Curve_Acceleration_and_Deceleration
I can`t figure out what Ts is supposed to be...

>>8326433
So what exactly does this coefficient represent?

>>8328001
I have absolutely no clue what you're talking about, and that still doesn't explain why you can use IBP without two things being multiplied together.

>>8327977
Mentally tried normal substituion, back substituion and by parts and there is no way.

Trig sub unless you have some genius identity.

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>>8328041
Hmm, and trigonometric substituation produces a gigantic mess.
Which leads me to suspect that I'm doing this question wrong.
I assumed the answer was to integrate the function for the distance of a part of the rod from P.

Why hasn't GR been superseded yet if it doesn't fit the Standard Model in quantum physics with gravity and with other phenomena like dark energy?

>>8328036
He is right.

You are multiplying by dx. You always multiply by dx.

>>8328036
>>8328036
>that still doesn't explain why you can use IBP without two things being multiplied together.
Uh.... yes it does. Did you actually read what he posted?

>>8328107
If I could understand it when it's written in such a shorthand way, I wouldn't be posting in a SQT.

>>8328036
The two things you are multiplying are [math]\arcsin(3x)[/math] and [math]dx[/math].

Let [math]u=\arcsin(3x)[/math] and [math]dv=dx[math].
Then [math]du=\frac{3}{\sqrt{1-9x^2}}dx[/math] and [math]v=x[/math] (since the antiderivative of 1 is x).

So we have...
[math]\int\arcsin(3x)dx=x\arcsin(3x)-\int\frac{3x\,dx}{\sqrt{1-9x^2}}[/math]
by integration by parts.

>>8328157
[math]\int\arcsin(3x)dx=x\arcsin(3x)-\int\frac{3x\,dx}{\sqrt{1-9x^2}}[/math]

jfc

>>8322403
Strang is the linear algebra god

>>8328159
[eqn]\int\arcsin(3x)dx=x\arcsin(3x)-\int\frac{3x\,dx}{\sqrt{1-9x^2}}[/eqn]

If this doesn't work I'm killing myself.

>>8328170
https://www.youtube.com/watch?v=muf774IVsTY

>>8328164
>Strang

Pretty pleb-tier to be honest family pie.

>>8328170
When you use latex on sci you usually want to put spaces EVERYWHERE.

[eqn]\int \ arcsin(3x)dx = x \arcsin(3x)-\int \frac{3x\,dx}{\sqrt{1-9x^2} } [/eqn]

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I know how to find pmfs but how do I conclude that whether it follows the binomial distribution?

Can someone explain what plasma is like I'm 5 years old? I realize it's essentially an ionized gas but I still can't wrap my head around it.

>>8328489
>but I still can't wrap my head around it.
Or rather how it behaves, what the effects of ionization has on it etc.

>>8328493
it conducts and you can use magnets on it.

How is the point of inflection for 1-2x-x^3 (0,0) and not (0,1)?

>>8328749
Probably just a mistake.

>>8328776
kek fucks sakes the worksheets uni gave me are hopeless

SQ here; what can i study in order to contribute to this?>>8320641

>>8325235
About 3.6, not too great I think.

Does the fact that solar radiation causes photosynthesis and D-vitamin production in the skin have to do with energy levels?

>>8329036
In atoms that is?

How to prove that square integrable functions are integrable?

>>8329255
The identity function is clearly square integrable. the result follows for arbitrary square integrable f.

Two of the five coins are counterfeit. One of those two is lighter and the
other is heavier than the genuine ones. How can you determine, in three weighings on
a balance scale, which coins are counterfeit?


I've been stuck on this for a while. I figured you probably start by weighing any two coins versus another two coins, but I can't figure out exactly how to explain or show it works if they aren't balanced.

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>>8329255

It's by definition. [eqn]L^2(D) := \left\{ f \colon D \to \mathbb{K} \mathrel{\Bigg|} \int_{D} |f|^2 \, d\mu < \infty \right\},[/eqn] where [math](D, \Sigma, \mu)[/math] is an appropriate measure space (wlog, we can just set the field [math]\mathbb{K} = \mathbb{C}[/math]).

If you're wondering about whether something like [math]\int f[/math] is well-defined, it's pretty trivial to show that [eqn]\left| \int_D f \, d\mu \right|^2 \leq \int_{D} |f|^2 \, d\mu[/eqn] using something like Jensen's inequality (there's probably a better choice for a slicker proof; Jensen's requires either rescaling your measure or introduces factors of [math]\mu(D)[/math], which is a bit messy (but is fine since you chose an appropriate measure, right?)).

I think what >>8329411 is alluding to is using Cauchy--Schwarz to show that, given that [math](L^2(D), \langle\cdot,\cdot\rangle)[/math] is a Hilbert space, [eqn]\left|\langle f, \mathrm{id}_D \rangle\right|^2 = \left| \int_D f \, d\mu \right|^2 \leq \left(\int_{D} |f|^2 \, d\mu\right) \left(\int_{D} |\mathrm{id}_D|^2 \, d\mu\right),[/eqn] where [math]\mathrm{id}_D \colon D \to D,\ x \mapsto x\ \forall x\in D[/math]. However, without specifying a particular measure on which [math]||\,\mathrm{id}_D||_{L^2}[/math] is finite, I fail to see how this proves existence for all choices of [math](D,\Sigma,\mu)[/math].

>>8329431
Off the top of my head ...

Suppose that you weigh 2 against 2.

If the scale balances, then
- the one left out is genuine, and both counterfeit coins are on the same pan.
- Replace one coin on the left pan with the left-out genuine coin.
- If the scale still balances, then
- - you replaced one genuine coin with another.
- - the two coins on the right pan are both counterfeit
- otherwise
- - you replaced a counterfeit coin with a genuine one
- - the two which were originally on the left pan are counterfeit

Otherwise, the one left out is counterfeit, but you don't (yet) know whether it's the heavy or the light one. Either you left out the light coin and the heavy coin is one of the coins on the heavier pan, and you left out the heavy coin and the light coin is one of the coins on the lighter pan.

You then need to tell whether the left-out coin is the light or heavy coin (which tells you which pan holds the other counterfeit coin), and which of the two coins on that pan is counterfeit. And you have two weighings left, which I'm not sure is enough.

The main question is whether the sum of the weights of the two counterfeit coins can be equal to the weights of two genuine coins. If they can, then I don't think 3 weighings is enough.

>>8314917
If I take quizzes 6 questions long, and get 1 wrong every time, am I truly a B student? Hear me out, if I get one out of every six questions wrong, then on 10 question quizzes couldn't I expect to get only 1 wrong, resulting in an A (90%)?

I ask because I've been getting 1 question wrong on 6 question quizzes for awhile now, and I feel as if the grades I get aren't an accurate representation of my abilities.

>>8323749
wut

>>8327823
you could squeeze with i^2 and i^4 pretty directly

Okay, I got the most SQT type question. My geometry professor left us 3 theorems to have some fun with but they are not homework so I am not really in a rush. Also, I don't need to prove it for me.

For context, this is specifically 3 dimensional euclidean geometry.

The theorem I am having problem is this one:

Prove that 3 different planes intersect each other at a single point, go through the same line or are all parallel to the same line.

My problem is, what does this mean? As I see it there are 2 interpretations.

Interpretation #1: Prove that these are the only possibilities. In other words, negate all 3 cases and find a contradiction with the axioms.

Interpretation #2: Prove that these 3 cases can happen in space. In other words, start with an empty space and do general constructions that lead to each of the results

Which one makes more sense? Has anyone seen this in a book before?

Am I being autistic by not being able to interpret this correctly?

>>8329795
>Also, I don't need to prove it for me.

I meant that whoever wants to answer me, you don't need to prove it for me. Just clarify what the theorem really means.

When you disrupt a gene in a plasmid via insertional inactivation and then introduce the plasmid into a cell, does the cell RNAP still attempt to bind to the intact promoter region and initiate transcription or what? How does it terminate?

Big sharks gone, I am eated.

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alright, easy peasy question for you, and i feel kind of dumb asking it.

i need a gently declining function with a max at 65536 and a floor at 100.

help me /sci/

here is a wendelstein in return.

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>>8314917
I had to find the adjA of matrix A, which I've done. Now I have to verify AdjA is correct by multiplying it by A, but I'm not getting a identy matrix

A *adjA=I
>plz help I'm dumb

>>8329431
I don't think that 2-against-2 can be made to work. But 1-against-1 can.

Label the coins A through E.

First weigh A against B. If they're equal, weigh A against C, otherwise weigh C against D. Finally, weigh D against E.

That gives you a 3-tuple from a set of 3^3=27 possibilities. It turns out that the 20 possible permutations of one light, one heavy and three medium coins yield 20 distinct 3-tuples.

I.e. not only does it tell you which two are counterfeit, but also which one is light and which one is heavy.

>>8330137
you didn't find the adjugate; you found the transpose

>>8330137
Adj(A)xA is not I bruh, the matrix M such that
MxA=I
is the inverse

>>8329431
this is not possible without more information

for instance suppose coins 1 and 2 are counterfeit and mass(1)+mass(2)=mass(3)+mass(4) and you use a balance as 1+2 versus 3+4 then learn nothing

>>8330137
[eqn]\begin{aligned}
\frac{1}{\det{A}} \text{adj} \, A &= A^{-1} \\
AA^{-1} &= I
\end{aligned}[/eqn]

>>8330222
>>8330224
>>8330278
whoops, I'm a dumbass

also does anyone know how to solve eigenvalues and eigenvectors quickly?

>>8330289
Row reduce into upper-triangular, check out your diagonals. They'll all be something like
[eqn]
\begin{pmatrix}
a - \lambda & loli & loli \\
0 & b - \lambda & loli \\
0 & 0 & c - \lambda
\end{pmatrix}
[/eqn]
But this usually DOES NOT reveal all the eigenvalues of a matrix.

>>8330300
loli? excuse me?

>>8330308
Hi. I was too lazy to add all the entire [math]A_{(m, n)}[/math] stuff so I decided to type in [math]loli[/math] instead.

>>8330300
what about eigen vectors?

>>8330195
> I don't think that 2-against-2 can be made to work

With 2-vs-2 and symmetric deviations (i.e. the sum of the weights of the light and heavy coins is the same as the weight of two normal coins), it's possible.

The first weighing splits the cases 8-4-8, the second splits 8 cases 3-2-3. The third weighing is 1-vs-1, but there's always a method which will distinguish the 3 cases.

With asymmetric deviations (i.e. the sum of the weights of the light and heavy coins isn't the same as for two genuine coins), 2-vs-2 can't work, as the first weighing splits the cases 10-0-10 (i.e. there's no way for it to balance) and there's no way to distinguish 10 cases with 2 remaining weighings (3^2=9, 9<10).

>>8314917
What is the difference between $\in and \subset$

>>8330506
A is in B if A is an element of the set B.

A is a subset of B if every element of the set A is an element of the set B.

>>8329795
Interpretation #1 is correct. Don't use a proof by contradiction though. IIRC A plane is the solution set of [math]m \cdot x + b = c[/math], so just show that one of those possibilities occurs depending on the vectors m, b, and c for the two planes. If you do that it will be trivial to come up with an example.

brainlet here

log 8 = a; log 5 = ?;
gotta write log 5 base 10 in terms of a.

not homework, just an exercise I picked up and couldn't do.

>>8322403
Why not both

>>8316351
Really dude? i is like a cofunction (sin(a-pi/2)=cos(a)) you can do it

>>8331006
never mind, solved it

log 8 = a;
log 2^3 = a;
3*log 2 = a;
log 2 = a/3;
log 5 = log 10/2 = log 10 - log2;
log 5 = 1 - a/3;

Could someone explain the concept of noosphere to me? I kinda understand the page in Wikipedia, but sufficiently well.

>>8330552
and obviously you can set c = 0 there, so you'll have to solve [math](m - m') \cdot x + b - b' = 0[/math].

>>8330552
You are probably right but this is not the way to do it.

In this class we don't give equations to anything. This is not analytical geometry. This is pure euclidean geometry. All proofs refer directly to logical statements of the axioms and you rarely see an equation and even then it is an equation that describes some part of a triangle.

>>8331443
Ah ok. The first two sentences still stand though.

Studying for a midterm.

Does sup A and inf A have to be a part of the set to exist?

eg if [math]A = {a : 0 < a < 2^{.5}, a \in \Q}[/math], is sup A sqrt(2) or does sup A not exist?

>>8331854
>Does sup A and inf A have to be a part of the set to exist?

yes

>>8331854
Too lazy for Latex, so let R denote the reals. Now -infinity = inf R and infinity = sup R, but neither is in R.

>>8331917
so is sup A = sqrt 2 in my post?

>>8331953
Yes it is. There is a reason why sup and max (and inf and min) are separate. For any subset of reals, max and min either are in the set or don't exist, but sup and inf always exist. This could be generalized, but it'd just confuse you and you are not ready yet.

>>8331969
>For any subset of reals, max and min either are in the set or don't exist, but sup and inf always exist.

...this is not true. It's sloppy to say that, e.g. sup R = infinity. sup_R R simply does not exist. You may be able to complete R so that it *does* exist, but this is a nontrivial fact and changing the set you're in tends to cause problems. Likewise, for the A above, sup_Q A does not exist.

File: Capture.png (41KB, 774x259px) Image search: [Google]

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I can't find any explanation of this notation.
What do I do here?

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Is this book trash, or am I a brainlet? I got an A in Calc2 and I'm going into Calc 3 next quarter. Been trying to read this a little bit to brush up on vectors and I can't fucking understand what the fuck is happening.

Anyone have a better book recommendation? Or is this one decent and I'm just stupid

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Why isn't the raddi (3)^(1/2)?

Should it be (3)^(1/2)-1? Because of the lower bound in the inequality statement?

>>8332262
>enter as a comma-separated list
hmm

>>8332251
>and I can't fucking understand what the fuck is happening
How far have you gotten in that book? Where are you getting stuck?

>>8332262
It's asking for multiple radii. The points are bounded by an inner sphere of radius 1 and an outer sphere of radius [math]\sqrt{3}[/math].

>>8314917
find all the natural numbers n that satisfy PHI(n) = 110, where phi is the euler totient function, pls guys im stupid

>>8332251

you're a brainlet

>>8332291

Tbh, I'm only on the first chapter, but I feel like the concepts aren't coming across very well. My previous teacher used Stewart, but now we're using this and I barely remember anything about vectors from pre-calculus.

So one of the questions was to describe a plane that spans between two vectors using vector notation, and after reading the first chapter I couldn't do it. Another question was asking if the points (2,3,-4), (2,1,-1) and (2,7,-10) were on the same line and I had no idea how to even start that one

>>8332318
I think it's generally recommended you take linear algebra before vector calculus.

>>8332272
>>8332301
Oh okay, thank you guys, so it is:

1, (3)^(1/2)? correct?

>>8332325
>>8332313

Perhaps, but I just looked at the reviews on Amazon and this book has an average of 2 stars. Spivak's for comparison, average of almost 5 stars.

Anyone else have a better multivariable book to use as an introduction?

>>8332318
You are using this textbook exclusively? I'm pretty sure Calc 3 doesn't usually have a huge focus on vector calculus. It's there, but more important is calculus on functions of multiple independent variables, partial derivatives, etc.

I don't have any specific recommendations, but I would certainly encourage you to find a better textbook. Maybe find a basic (and good) linear algebra text, too.

>>8331854
All of the answers you've received so far are awful. The way you've phrased the question is also a bit problematic in terms of what I believe you're asking, so I will change things slightly.

Let [math]A = \{x \in Q \mid 0 < x^2 <2 \}[/math].

When A is viewed as a subset of Q, A has no supremum. This is simply by to the definition of supremum. Given an upper bound of A in Q, you can always find a smaller upper bound. In this particular case, if x is an upper bound of A, then (2x + 2)/(x + 2) is smaller than x, and also an upper bound for A.

However, when A is viewed as a subset of R, the supremum of this set is sqrt(2). In general, R satisfies the follow property: "if A is a non empty subset of R which is bounded above, then there is an element of R which is the supremum of A."

What is Average Percentage Change. Google gives me nothing

I've been reading so much lately, in on lifetime I will redeem myself as a love based and blessed animal lion.I will read The Holy Bible fifty times this large and examinable lifetime.

Bizinga.

>>8332364
thank you, this answered my question and also you clarified the axiom of completeness in one sentence. ++

A anon posted this in another thread and it perked my interest
>there will be a civilization that is born so far into the future, that all other galaxies will have drifted beyond the universal event horizon
>they will never know that there was ever more than one galaxy
I then had a question but thread died
>I just had a light bulb go off. Can what you just said be theoretically possible? If so then it would be accurate to say that hundreds of millions of years ago that galaxies were closer (i.e. milky way and andromeda), so if there was a civilization back then that had space faring technology then they could have possibly reached destinations we cannot because of the lack of expansion that we observe today. So we are existing in a period where expansion hasn't totally isolated us like the galaxy you mentioned but the distances between points have grown so much that this intermediate period has fucked us over space travel wise.
If all of this is grounded in bullshit let me know. If not, an answer maybe?

>>8314972
but thats wrong, thats only an approximation

Why do my eyes become slightly bloodshot when I push my poop out via abdominal muscles