Simply Beautiful Art's realm of calculus and analysis

ZION

00:18

Simply what tag do you put on a question if your stuck on creating a parituclar proof for a problem

Simply Beautiful Art

proof explanation?

@ZION proof writing

one of those two or both if you wish

ZION

all right

Simply it's up

0

Q: Verifying the Indictor Function:$X_{[a,b]}$ can be expressed as a Fourier Series?

In the text "Fourier Analysis: An Introduction" by Elias M. Stein and Rami Shakarchi. I'm having trouble attempting to verify the that $f(x)$ can be written as a Fourier Series in $Propostion \, \, (1.2).$ Note my initial approach to verify $Proposition \, (1.2)$ can be seen within, $Lemma \, \,...

Simply Beautiful Art

Pooey you are faster than me

I can't help you with that question, sorry D:

ZION

Simply it's all right

Simply Beautiful Art

Any recommendations on how to learn about fourier series? Its on my bucket list and I didn't get to it ytet

ZION

00:23

Simply pick up Stiein's FOurier Analysis book it's really good

Simply Beautiful Art

Okay, thanks for the recommendation

I made up this function in an attempt to produce something that grows magnitudes beyond the fast growing hierarchy

and I can't even tell if it eventually computes

ZION

interesting is the function real or complex

Simply Beautiful Art

Real. It takes in a computable ordinal and three whole numbers

ZION

what is a ordinal

Simply Beautiful Art

Its like a name-tag for stuff. For example, it could be the number on a drawing ticket

it says "you are this and you lie here" kind of thing

ZION

00:26

ahh ok

Simply Beautiful Art

and it comes in two (more, but these are the basic ones) forms: successor or limit ordinal

successor is like 5 and 4. 5 is the successor of 4

ZION

interesting

Simply Beautiful Art

In general, α is a successor ordinal if α = ß + 1 for some ß

Then we have limit ordinals. I like to think of them as long lists

ω = sup {1,2,3,...}
This is the smallest non-finite ordinal, and it is defined as the limit of the naturals

If you look at my function, it has on the last line ß[n]. This means to take the list that defines ß and extract the n-th item on the list

For example, ω[3] = 3, since 3 is the third item on the list that defines ω

ZION

interesting

can you take the integral of an ordinal

Simply Beautiful Art

No, ordinals are like 'whole numbers' in the sense that they are well-ordered and you can't go between an ordinal and its successor.

That is, 3.5 is not an ordinal.

ZION

00:32

ahhh ok

just looked it up on Wikipedia

Simply Beautiful Art

Also, since I didn't clarify on the notation, when I raise a function to a power (second to bottom line), it means the following:
f^k(n;a,b) = f(f^(k-1)(n;a,b),a,b)

Basically, iterate the function in the first argument of the funciton

ZION

Simply this would make an interesting question on stackexchange

Simply Beautiful Art

It would, but I already have a nine page PDF on this

ZION

Dang nine pages, on this function

Simply Beautiful Art

Oh no, the last 5 pages are completely on how to make ordinals

particularly, if you put crazy large ordinals in... you get very large numbers

files.acrobat.com/a/preview/…

Purely for the goal of large numbers, we make functions like these

ZION

00:37

still 4 pages, that's mathematically heavy even for set theoretic stuff

Simply Beautiful Art

nah. I don't think I went into much of the math

I explained what was necessary to make large numbers for a layman and a hint more

ZION

ahh ok

Simply Beautiful Art

@ZION Oh yeah, don't take too much from the PDF before playing the game

ZION

Simply there could be some techniques from analysis that coudhelp with this

Simply Beautiful Art

@ZION Actually, I find discrete things to be the most useful. And a tip? Don't over-think it.

ZION

00:45

all right, i'll just pull something simple

But i'll need some math breaktime

Simply Beautiful Art

lol

ZION

Simply lol

Simply but i'm happy my questions are getting positive response :)

Simply Beautiful Art

@Benjamín Hello and welcome to my realm...

@ZION Always a good thing

Simply Beautiful Art

01:17

@BrevanEllefsen Good day sir

ZION

01:29

Simply turns out my question was good after all got another upvote

feels good to learn and know your getting closer to answers

Simply Beautiful Art

@ZION Haha, yup

ZION

Turns out it was a latex error and a grammer error that threw the question off

2

Q: Verifying the Indictor Function:$X_{[a,b]}$ can be expressed as a Fourier Series?

In the text "Fourier Analysis: An Introduction" by Elias M. Stein and Rami Shakarchi. I'm having trouble attempting to verify the that $f(x)$ can be written as a Fourier Series in $Propostion \, \, (1.2).$ Note my initial approach to verify $Proposition \, (1.2)$ can be seen within, $Lemma \, \,...

real-analysis proof-writing fourier-analysis

Simply Beautiful Art

lol

ZION

Simply what's so funny

Simply Beautiful Art

that such things should hold us back against the tide of math

ZION

01:31

?

Simply Beautiful Art

grammar and latex

ZION

tell me about it one latex error could mean -5 rep down on you stackexchange profile, but mathematical communication is important

Simply Beautiful Art

yup lol

Brevan Ellefsen

@SimplyBeautifulArt Good day. How goest thou

Simply Beautiful Art

Large number-ly as usual @BrevanEllefsen

ZION

01:34

Simply lol

Brevan Ellefsen

Fantastic. Studying Ruby and SQL and PHP right now myself and then taking a Music History final and then figuring out how $\cot \theta$ comes up in this answer math.stackexchange.com/questions/2191510/…

Simply Beautiful Art

:O

Moving pictures!

$Mathematics$ This is the Realm of Simply Beautiful…

Room for totally bored people to hang. Open discussions.

Large number business going down

ZION

Brevan that looks like a read :)

$Mathematics$ This is the Realm of Simply Beautiful…

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