Mathematics - 2016-02-07 (page 3 of 3)

9:00 PM

Illustrated, explains problems in simple terms

If $A$ and $B$ are events with $P(A)+P(B)>1$, why is it that largest possible value of $P(A \cap B)$ is $ \min(P(A), P(B))$?

Idle001

@I'manartist what is the qualifier for som1 to make a book ? having a rich history of mse answers ? having phd ? studying and reading too much ? just asking

Forever Mozart

usually you publish a book if you can put together lots of recent developments clearly and concisely

instead of having thousands of related research papers floating around, it's nice to publish a book that puts them together

Idle001

i have 3 papes until now

I'm an artist

@Idle001 Ramanujan didn't have a rich history of mse answers, neither phd, but he worked a lot on mathematics he liked, he really knew his mathematics and produced a lot of mind-blowing results.

Idle001

9:03 PM

and thousands of softwares

Forever Mozart

yes but they dont have to be your papers @Idle001

Idle001

@I'manartist ramanujan has inventions not books

well he has one in contribution with hardy

I'm an artist

@Idle001 Ramanujan had enough stuff to write tons of books, but it seems he wasn't too willing to share all his knowledge with the others. Many of his results don't have a proof.

Idle001

and a notebook (not sure if it is published when he was alive)

Forever Mozart

Like if I had to write a book, I'd write one about connectedness in topological spaces. And I could put together lots of interesting examples and theorems that have come out in the last 50 years.

a book specializing in connectedness

nothing like that exists really

user276387

9:07 PM

I've seen Ramanujan's notebooks. Frightening stuff!

Michael

Do it! I would buy it once my IQ becomes higher than that of a rock's.

Forever Mozart

lol your IQ is probably fine, you just need more studying

and they say IQ doesn't increase after age 20 anyway

I'm an artist

Stop blaming IQ for anything. With a resonable amount of IQ points and extremely hard work, passion and patience, one can get absolutely amazing results.

Work hark, very hard on what you like, put passion, never give up, be stubborn for years if needed.

Michael

Oki

Can I ask a question

Idle001

@ForeverMozart this s bullshit

Forever Mozart

9:10 PM

I am one Lemma away from a pretty cool result, but writing the proof is going to be hard...

Michael

Suppose $x$ is a vector in $\Bbb R^n$ and $x\cdot y = 0$ for all $y\in\Bbb R^n$. Prove that $x$ must be the zero vector.$

Forever Mozart

so I'm here procrastinating

Michael

Don't give me an answer

What is special about the zero vector?

Evinda

Hello!!!

Forever Mozart

@Idle001 what is?

Idle001

9:11 PM

iq doesnt increase

Forever Mozart

I don't think it does after a certain age

Evinda

What is Applied Algebra about?

Forever Mozart

not significantly anyway

Idle001

people told me before , u wont be that intelligent after ur 30s

that is crap

Michael

Oh ok I realized what it is

thanks anyways :)

Evinda

9:13 PM

Hey @IlmariKaronen
Are you familiar with Coding Theory?

Idle001

one can be relatively intelligent regarding how much he is informated

and brain is continuously evolving

Forever Mozart

@Idle001 I think the reason mathematicians accomplish more in their 20s and 30s is because they are more driven at that age. Driven to publish something original, get a reputation, get a job, etc. After they have that, most people will relax and not be quite as passionate.

Idle001

just try to solve mathematical problems, and puzzles and stuff like that, u would guarantee ur mental tact

@ForeverMozart yes not passionate, but still creative

Michael

@TedShifrin Can it be an informal proof?

Forever Mozart

I feel much smarter now, but on my last IQ test I got 134, the same as when I was 17.

so I sort of believe it will not increase

user276387

9:17 PM

Is anyone familiar with Apostol's Calculus (volume II)? I wonder whether I can use it for multivariable calculus and linear algebra (and in that order). As I understand, it starts with linear algebra, but I'm not sure whether I can read the multivariable calculus part without going through the linear algebra part first.

Idle001

and at social level, its recommended to keep in touch with real world, that would help to not detach one's mind from reality and cause a rupture in inner personna that would reflect on the inner unconscious

where uncounscious mind is a platform of conscious mind, and major part of decision making

Michael

@ForeverMozart what are some ways I can prove a theorem in general?

Evinda

Hey @abel
Do you know what Coding theory is about?

Forever Mozart

@Michael you must learn the basics first. Study definitions and examples, then later on you can try proving theorems.

Michael

@ForeverMozart what are some definitions I need to know for this proof: Suppose $x$ is a vector in $\Bbb R^n$ and $x\cdot y = 0$ for all $y\in\Bbb R^n$. Prove that $x$ must be the zero vector.

abel

9:23 PM

evinda, no.

Forever Mozart

that's my approach anyway. I read a new definition, think of some examples where it applies, look at properties of those examples, and then see if maybe they are related to the new term by a theorem.

@Michael Know the definition of $\mathbb R ^n$, the dot product, and zero vector.

Now apply some logic.

What if $x$ is not the zero vector?

can you find $y$ such that $x\cdot y\neq 0$?

Michael

no

well

if y is a zero vector

Forever Mozart

right you need $y$ to be nonzero obviously

do you see how I am trying to prove the statement?

Michael

Yep

I'll go review some definitions and I will be right back

@ForeverMozart thanks:)

Evinda

Guten Abend @TedShifrin
Do you maybe know what Coding theory is about?

Ted Shifrin

9:28 PM

Guten Abend, @evinda. Nope.

Evinda

Ok... Neither Applied Algebra?

Ted Shifrin

@user276387 The point is that to do multivariable calculus "right," you do need some linear algebra (not all of it). The whole point of calculus is to approximate general (differentiable) functions by linear functions, so we need to know what linear functions $\Bbb R^n\to\Bbb R^m$ are and how to use them.

@evinda: Mostly no.

Evinda

A ok... No problem... @TedShifrin

user276387

@TedShifrin I already have a semester's worth of linear algebra. Not sure if that's sufficient to skip the linear algebra and do multivariable calculus, though.

Michael

@TedShifrin are there some books you recommend that I read as I go through your lectures?

robjohn

9:43 PM

@JeSuis is $n$ fixed? If so, then $A(P)=P(1)=\sum\limits_{k=1}^na_k\le n^{1-\frac1p}\left(\sum\limits_{k=1}^n|a_k|^p\right)^{1/p}=n^{1-\frac1p}\|A\|_p$

JeSuis

10:02 PM

@robjohn I finally ask the question here math.stackexchange.com/questions/1645027/…

robjohn

@JeSuis So $n$ is not fixed.

JeSuis

@robjohn yes

I'm an artist

LOLLLLLL, you have to see that

Here is the test I took: arealme.com/iq-2016/en

Michael

@I'manartist ;)

I'm an artist

If you try it, take it only one time and be honest, don't cheat. Of course, I don't have that score, but this is the score I received from them.

Michael

10:10 PM

I legitamtely don't know what the first question wants me to do

I'm an artist

Let me know the scores you get. This is more of a joke although the questions are pretty hard, but nice at the same time.

Michael

Is it timed?

I'm an artist

@Michael No. I did it in 15 min, 20 cute questions.

Michael

oki

AM I allowed to use papers?

Forever Mozart

265 is not possible on a real IQ test

Michael

10:17 PM

Not unless ur @I'manartist

I remember doing a test that gave me 60 iq -.-

Forever Mozart

I think 160 is the highest

Idle001

i just read an article about most desastrous people who caused massive murders , a major part of them are motivated by a closet passive grudge that grew with age

I'm an artist

@ForeverMozart You should also get a huge IQ points on that test (since you get a lot on a real test). Just give it a try and see. :-)

Forever Mozart

lol ok

what the hell

Michael

ikr?

How on earth do you do the first question

I'm an artist

10:25 PM

lol :-)

Think a bit of the colours of the points. :-)

Idle001

sleepy, gonna hit the bed

see ya

JeSuis

isn't A because the small arrow is too advanced :p

I'm an artist

By the way, what is the meaning of nerd in the context above? nerd has many meaning.

Michael

Someone who likes integrals

I'm an artist

@Michael lol

Michael

10:31 PM

Someone help I still can't

It looks like D

I'm an artist

10:46 PM

Is any done with the IQ test?

Let me know the scores you get, it is just for fun. I'm working on the 2016 test version, I'm at the last 2 questions.

Forever Mozart

probably should have spent more time

and I totally guessed on the first problem

but it was fun, some good problems

Michael

11:05 PM

I didn't get the one with the box, and the one that was find X

Forever Mozart

how do you see which ones you missed?

aw hell I already closed the window

pretty sure I missed the first one... thought it was a joke

Michael

me 2

@ForeverMozart Does the order matter when multiplying two vectors in $\Bbb R^{n} $?

oh

Forever Mozart

you mean dot product?

I'm an artist

Here my second result

Forever Mozart

look at how dot product is defined

Michael

11:09 PM

In mathematics, the dot product or scalar product (sometimes inner product in the context of Euclidean space, or rarely projection product for emphasizing the geometric significance), is an algebraic operation that takes two equal-length sequences of numbers (usually coordinate vectors) and returns a single number.

Forever Mozart

removed in case someone else wants to try the test

I'm an artist

Forever Mozart

you beat me you bastard

I'm an artist

:-)

Michael

Can females be bastards?

Forever Mozart

11:10 PM

female?

Michael

wait

I thought I'manartist was a woman

I'm an artist

I could have done it perfectly, but I'm pretty tired now.

@ForeverMozart what did you score?

Forever Mozart

scroll up and see

my triangle is isosceles

I'm an artist

@ForeverMozart Nice!

@robjohn take some nice iq tests above for fun. They are very nice. :-)

Michael

It doesn't seem like order matters

Forever Mozart

11:12 PM

right it doesnt matter

I'm an artist

@ForeverMozart I wonder what is the meaning of those scores in a real test.

Michael

Suppose $x$ is a vector in $\Bbb R^n$ and $x\cdot y = 0$ for all $y\in\Bbb R^n$. Prove that $x$ must be the zero vector.

Forever Mozart

I dont know. On the real test there are many more problems, and it is divided into three sections if I remember correctly

they put blocks on the table, show you a picture for a few seconds, and then make you recreate the image from memory

I remember that part

Michael

hmm, is y not a vector?

Forever Mozart

@Michael suppose $x$ is NOT the zero vector.

can you find a vector $y$ such that $x\cdot y\neq 0$?

(yes)

Michael

11:17 PM

yep

Forever Mozart

ok, so what can $y$ be?

Michael

anything but the zero vector

Forever Mozart

no

I'm an artist

@ForeverMozart there should be a connection though with the real scores I suppose, not sure how strong. Also in real tests there are such questions.

Forever Mozart

$(1,1)\cdot(-1,1)=(0,0)$

I'm an artist

11:18 PM

According to the last test logic and number areas are perfect. At the visual part I did all in a hurry, but I could have done it perfectly.

Michael

ohhhhhhhhhhhhhh

Forever Mozart

what can $y$ be?

Michael

gimme a sec to collect my thoughts

im sorry

Forever Mozart

$x\neq 0$, find $y$ such that $x\cdot y\neq 0$

come on man!!!

Michael

I think I am just missing some definitions

ahh

ok ok ok

y is an element of the reals?

Forever Mozart

11:22 PM

$x$ and $y$ are vectors

like if $n=2$, $x=(x_1,x_2)$, $y=(y_1,y_2)$

Michael

yep

Forever Mozart

so by $x\neq 0$ I mean $(x_1,...,x_n)\neq (0,...0)$

Yep

what can $y$ be?

a zero vector

11:26 PM

then the product is $0$

I want $x\cdot y\neq 0$

I'm an artist

@ForeverMozart did you take the other test?

Forever Mozart

given that $x\neq 0$

@I'manartist no I dont think so

Michael

Well y can't be the zero vector, I know that now

I'm an artist

@ForeverMozart this one, and it is even nicer arealme.com/iq-2015/en. Very appealing questions.

Michael

I feel like I am missing a definition or a theorem

Forever Mozart

11:29 PM

ok I will do it a little later

I'm an artist

OK

Michael

Given that x is another vector, I need y to be a vector that can prevent the dot product from equaling zero

Forever Mozart

given that $x\neq 0$

Michael

yep

I honestly can't I am so sorry

I don't know enough properties of vector spaces

Forever Mozart

what is $x\cdot x$?

It is a sum of squares, right?

Michael

11:33 PM

oh that is the part of the lecture that I couldn't see

Forever Mozart

so if $x$ has a nonzero coordinate...

you get $x\cdot x>0$

Michael

Yah that makes sense

Forever Mozart

that's the proof

Michael

uh

so multiplying two vectors can never make a negative answer?

Forever Mozart

it can

but not if you multiply a vector by itself

cause then dot product is sum of squares

Michael

11:37 PM

Dot product

In mathematics, the dot product or scalar product (sometimes inner product in the context of Euclidean space, or rarely projection product for emphasizing the geometric significance), is an algebraic operation that takes two equal-length sequences of numbers (usually coordinate vectors) and returns a single number. This operation can be defined either algebraically or geometrically. Algebraically, it is the sum of the products of the corresponding entries of the two sequences of numbers. Geometrically, it is the product of the Euclidean magnitudes of the two vectors and the cosine of the angle...

Should I look at the geometric definition?

Forever Mozart

$x\cdot y=\sum_{i=1} ^n(x_i\cdot y_i)$

that is definition

Michael

Why is there nothing below the series

Oh no index

Ok I will review some definitions, I need to understand what the question is asking before proving :)

Thanks for sticking with me

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$Mathematics$ Mathematics