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2023-11: Warosu is now out of extended maintenance.

/sci/ - Science & Math

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5858447 No.5858447 [Reply] [Original]

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>> No.5858449

Undefined.

>> No.5858450

Either undefined or 0 depending on which definition of sequence convergence you are using.

>> No.5858452

>>5858450
What about 1?
1 + (-1+1) + (-1+1) + ...

>> No.5858454

>writing undefined sums
<span class="math">\sum_{n=0}^{\infty} (-1)^n = sage[/spoiler]

>> No.5858458

obviously <span class="math"> \frac{1}{2}[/spoiler]

>> No.5858460

>>5858452

That's not how sequence convergence works.

>> No.5858459

>>5858450

Correction: this should have read "either undefined or 1/2 depending on which definition of sequence convergence you are using."

>> No.5858464
File: 112 KB, 584x600, Penn_Teller_Bullshit_P_48edb326c031a.jpg [View same] [iqdb] [saucenao] [google]
5858464

>>5858459
>>5858458

>quantum mechanics

>> No.5858466
File: 73 KB, 356x357, reported.jpg [View same] [iqdb] [saucenao] [google]
5858466

Is dat sum Grandi's Series

>> No.5859574

It converges by alternating series test.

>> No.5859730

http://www.youtube.com/watch?v=PCu_BNNI5x4

>> No.5860389

>>5858447
the answers in the bracket bro
pi()ligion

>> No.5860806

>>5860389
The answer is -1?

>> No.5860812

>>5859574
It doesn't converge at all you dipshit.

>> No.5862014

>>5860812
Of course it does.

>> No.5862916

1/2

>> No.5863006

Lrn2convergence

>> No.5863015

>>5860812
>>5862014
This is why I hate /sci/.
>>5860812
show how it doesn't converge.
>>5862014
Show how it converges.

If you can't or won't you are automatically wrong.

>> No.5863028

The Alternating Series Test for convergence says that an alternating series converges if and only if the SEQUENCE converges to 0. The sequence is oscillating between -1 and 1, and does not converge to 0, therefore, the series diverges.

>> No.5863068
File: 11 KB, 198x72, 1.jpg [View same] [iqdb] [saucenao] [google]
5863068

>> No.5863071

1,0 and 1/2.

>> No.5863075

>>5858458
Bitches love Cesàro summability.

>> No.5864117

>>5863075
What is Cesaro summation and why do we need it?

>> No.5864121

0.5

>> No.5864131

>>5864117
Useful in QM apparently. Don't know much more about it.

>> No.5864139
File: 13 KB, 772x425, chanchanchan.png [View same] [iqdb] [saucenao] [google]
5864139

>> No.5864804

>>5858464
Why is quantum mechanics 'bullshit'?

>> No.5865927

>>5864804
Not the poster you're replying to, but our current theories of QM have a lot of flaws.

>> No.5865961

>>5858454
/thread

>>5858458
>>5858459
you mean Cesaro-sum fucktwat

sure is engineer in here

>> No.5865963

Well, I derped, best I can say is that it never converges.

>> No.5866021

>>5865961
>Someone posts something correct
>That makes him a fucktwat

Get out, kid.

>> No.5866759

>>5865927
What sort of flaws?

>> No.5867086

>>5858447
i believe that the answer is -1 due to infiniti being equal to 99999.... all the digits
of infinti should be 9 due to it being the largest single digit number.

>> No.5867090

>>5864131
I don't know where you got that idea.

>>5864117
There's this neat website called wikipedia. It's free, and openly available to anyone. Even you.

>> No.5867115

>>5867086
in base 10

>> No.5867925

>>5867086
What field are you working in? Surely not the real numbers.

>> No.5867969

listen up you fuckig retards

the sum is undefined because it does not converge because its an alternating series

And that's the bottom line

>> No.5868256

>>5867969
>the sum does not converge because its an alternating series
this guy knows some shit

>> No.5868304

>>5867969

Unless you're using cesaro summation as your definition of convergence of a sequence, in which case it converges to 1/2.

>> No.5868316

>>5867969
You're right that it doesn't converge, but the reason is wrong.

Alternating series can still converge. But this one does not.

>> No.5868319

>>5868316

Speaking of which, conditionally convergent series are fucking spooky. Rearrangement theorem and whatnot.

>> No.5868520

>>5867969
http://en.wikipedia.org/wiki/Alternating_series_test

>> No.5868746

doesn't converge by alt series test so you can re arrange terms to equal anything

>> No.5868774

>>5863068
You can't full me, the limit does not exist.

>> No.5868776

>>5868774
I'm going to pretend that I didn't just type full instead of fool.

>> No.5868841

divergent

>> No.5868850

>>5858447
Just graph it. If you step through the integers, it jumps between -1 and 1 forever. The next term in the series will never be closer to some limit than the current term, so it doesn't converge. If you graph it continuously, you'll see it's just a sine wave, which also won't converge unless there it is multiplied by an ever-decreasing fraction.

>> No.5868891

>>5868776
fool

>> No.5868893

This whole stupid post is no more interesting than the "does .99999... = 1" crap that's always around here.

Imagine if one guy defines a "fizbin number" to be an integer greater than 5, and another guy defines a "fizbin number" to be an integer greater than 10. Then imagine endless posts debating whether or not 8 is a fizbin number. Yes it is! No it isn't! Yes it is! No it isn't. Get a fucking clue.

>> No.5869163

>>5868774
Why not?

>> No.5870657

>>5868893
Isn't that what math is about? Definitions?

>> No.5870672
File: 170 KB, 611x390, ____69.jpg [View same] [iqdb] [saucenao] [google]
5870672

Diverges because the limit goes to 1 and 0. Two limits, limit does not exist.

Just like the sum of sin(n*pi).

>> No.5870676

>>5870672
sin(n*pi/2). My bad.

>> No.5870684

>>5870672
Hi there! Welcome to /sci/! If you hadn't noticed, you are responding to an old thread that was just necrobumped by a troll. Please use the catalog to find interesting threads rather than relying on the front page.

>> No.5870705

>>5870684
antisage

>> No.5871384

>>5870657
Yes, but only if the definitions are useful.

>> No.5871391
File: 8 KB, 225x225, 1372245358887s[1].jpg [View same] [iqdb] [saucenao] [google]
5871391

>>5870705
>top lel

>> No.5873159

>>5871384
>implying it isn't useful

>> No.5873758

>>5873159
Why is it useful?

>> No.5875339

>>5873758
Because it solves problems.

>> No.5875849

>>5870657

Sure, definitions are important. But when two people use the same symbol but have different definitions of its meaning, it is pointless to argue who is "right."

If one person uses log() for natural log, and someone else uses log() for base 10 log, it's a waste of time to argue weather log(100)=2 is "right" or log(100)=4.6052... is "right"

>> No.5876209

>>5875849
>it is pointless to argue who is "right."
Yes it is. Notation should not be unnecessarily complex.

>> No.5876482

This thread was supposed to be about typesetting color.

>> No.5876487

>>5876482
This thread was supposed to die a week ago

>> No.5876549

0.7499999...

>> No.5877582

>>5876549
How did you come to this result?

>> No.5878848

>>5876482
Oh, now I see. The file name.

>> No.5880009

>>5876487
How do you know?

>> No.5880670

>>5875339
What problems?

>> No.5882085

>>5858450
What definition would make it zero?

>> No.5882096

>>5865927
What? Explain?

>> No.5882714

>>5882096
For example cuantum mechanics predicts entanglement cannot be used to superluminally transmit information. This has been experimentally discredited.

>> No.5882721
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5882721

>>5882714
>>"This has been experimentally discredited"
>> implying "cuantum mechanics" predicts this
>> implying experiments show entanglement can superluminally transmit information
> faggot logic and woman lies

Wrong on every count

>> No.5882733

>>5865927
Nigger. There are no "theories of QM." There is Quantum Mechanics, just like there is Classical Mechanics. And QM (singular) doesn't have any of the flaws you ascribe to it. You're much too stupid to comprehend anything that could weaken QM.

>> No.5884179

>>5882733
>There are no "theories of QM."
QM consists of several distinct theories.

>doesn't have any of the flaws
Yes, it does. If you knew the math, you wouldn't post such ignorant comments.

You should take a real university course on the topic instead of listening to shallow pop sci youtube channels for children.

>> No.5884797

>>5882721
>>>"This has been experimentally discredited"
It has.
>>> implying "cuantum mechanics" predicts this
It does.
>>> implying experiments show entanglement can superluminally transmit information
They do.
>>> faggot logic and woman lies
Homophobia and misogyny.
>Wrong on every count
Why are you so uneducated? Do you have a severe learning disability?

>> No.5885067

http://www.wolframalpha.com/input/?i=sum_{n%3D0}^\infty+%28-1%29^n

>> No.5885072

>>5884797
Um, source for any record at all of someone who knows their stuff stating that quantum entanglement experiments have shown superluminal information transfer?

>> No.5886235

>>5885067
>mfw wolfram alpha can't into Cesaro summation

>> No.5886244

>>5858447
0.5

>> No.5886295

>>5885072
I just emailed the references to you. You should get it yesterday.

>> No.5887291

>>5885072
Watch Carl Sagan's "Cosmos". It is explained well.

>> No.5887609

>>5858452
I actually tried that, and shown that to my lecturer.
He said that this will only work with a finite amount of terms,

>> No.5888796

>>5887609
Was it your calculus lecturer or your biology lecturer?

>> No.5889229 [DELETED] 
File: 50 KB, 1296x720, 5858447.png [View same] [iqdb] [saucenao] [google]
5889229

Someone is keeping at least 36 threads like this alive
by bumping them twice a day. Compare the post times of
>>5864117 >>5864804 >>5865927 >>5866759 >>5867925 >>5870657
>>5871384 >>5873159 >>5873758 >>5875339 >>5876209 >>5877582
>>5878848 >>5880009 >>5880670 >>5882085 >>5882714 >>5884179
>>5884797 >>5886235 >>5887291 >>5888796
to the post times in other threads.
It's clear most of these are the same person.
The threads being bumped:
>>5858447 >>5861383 >>5862983 >>5863249 >>5865823 >>5866853
>>5867452 >>5867640 >>5868097 >>5868460 >>5868538 >>5869504
>>5869595 >>5869759 >>5869946 >>5872951 >>5873166 >>5873829
>>5874378 >>5874727 >>5875025 >>5876410 >>5876819 >>5878449
>>5878607 >>5878684 >>5878722 >>5880041 >>5880453 >>5880775
>>5881738 >>5883998 >>5884116 >>5884625 >>5884717 >>5885545
Write to moot@4chan.org if you want it to stop.

>> No.5889254 [DELETED] 
File: 49 KB, 1296x720, 5858447.png [View same] [iqdb] [saucenao] [google]
5889254

Someone is keeping at least 36 threads like this alive
by bumping them twice a day. Compare the post times of
>>5864117 >>5864804 >>5865927 >>5866759 >>5867925 >>5870657
>>5871384 >>5873159 >>5873758 >>5875339 >>5876209 >>5877582
>>5878848 >>5880009 >>5880670 >>5882085 >>5882714 >>5886235
>>5887291 >>5888796
to the post times in other threads.
It's clear most of these are the same person.
The threads being bumped:
>>5858447 >>5861383 >>5862983 >>5863249 >>5865823 >>5866853
>>5867452 >>5867640 >>5868097 >>5868460 >>5868538 >>5869504
>>5869595 >>5869759 >>5869946 >>5872951 >>5873166 >>5873829
>>5874378 >>5874727 >>5875025 >>5876410 >>5876819 >>5878449
>>5878607 >>5878684 >>5878722 >>5880041 >>5880453 >>5880775
>>5881738 >>5883998 >>5884116 >>5884625 >>5884717 >>5885545
Write to moot@4chan.org if you want it to stop.

>> No.5889295

>>5889254
nice.jpg

& >>5858447
The answer is the Brackets as a notation in single series, <-> style

>> No.5889329
File: 49 KB, 1296x720, 5858447.png [View same] [iqdb] [saucenao] [google]
5889329

Someone has been keeping at least 35 threads alive
by bumping them twice a day. Compare the post times of
>>5864117 >>5864804 >>5865927 >>5866759 >>5867925 >>5870657
>>5871384 >>5873159 >>5873758 >>5875339 >>5876209 >>5877582
>>5878848 >>5880009 >>5880670 >>5882085 >>5882714 >>5886235
>>5887291 >>5888796
to the post times in other threads.
It's clear most of these are the same person.
The threads being bumped:
>>5858447 >>5861383 >>5862983 >>5863249 >>5865823 >>5866853
>>5867452 >>5867640 >>5868097 >>5868460 >>5868538 >>5869504
>>5869595 >>5869759 >>5869946 >>5872951 >>5873166 >>5873829
>>5874378 >>5874727 >>5875025 >>5876410 >>5876819 >>5878449
>>5878607 >>5878684 >>5878722 >>5880041 >>5880453 >>5880775
>>5881738 >>5883998 >>5884116 >>5884625 >>5885545
Write to moot@4chan.org if you want it to stop.

>> No.5889641

>>5884179
What are the theories?

>> No.5889675

hey faggots

if the limit of the nth term does not approach 0, the sum of the partials does not exist. (ie series does not converge)

lim (-1)^n as n->inf does not = 0

>> No.5889676

Oh however the best approximation for this sum is 1/2

>> No.5890651

>>5889676
Why is it the best approximation? Can you prove there isn't a better one?

>> No.5891346

>>5888796
It was algebra.

>> No.5892021

0 is the "best one on average" if you measure with a mean square error. If measuring with mean of absolute differences any number within [-1,1] would be equally good. Pick a different error measure and you probably get another result.

>> No.5893119

>>5891346
What kind of algebra?

>> No.5893761

>>5893119
Uniformly hyperfinite algebra.

>> No.5893766

>>5893761
Welp, board's down for an hour.
Get treatment.

>> No.5893782

The answer is obviously integer infinity modulo two.

>> No.5894902

>>5893782
Infinity is not an integer.

>> No.5894926

Depends on how big the infinity is.

>> No.5894961

>>5894902
It's an infinite integer.

>> No.5895767

>>5894961
That makes no sense.

>> No.5896988

>>5894961
Do you even know what an integer is?

>> No.5897023

>>5858447
>fucking /m/ invented a new field of math where infinity is a number and 1 = 0.99999999999...

>> No.5897048

>>5897023
> >>5897023
lol
>/n/

>> No.5897216

>>5858447
Non convergent so anything \thread

>> No.5897247

>>5897216
>\thread
Nope, see >>5889329

>> No.5897848

>>5897023
The field always existed. /m/ simply discovered it.

>> No.5899307

>>5897848
What field did /m/ invent?

>> No.5899822

>>5899307
Mechamatics.

>> No.5901015

>>5899822
What's that?

>> No.5901848

>>5901015
A new field of maths where infinity is a number and 1 = 0.99999999999...

>> No.5903252

>>5901848
Isn't that already true in the reals?

>> No.5903283

>>5858447

1 doesn't equal .9999....

.9 repeating can't be infinite

since it's not infinite, there's always a number inbetween 1 and the furthest out you've went in the repeating .9999

1 =/= .9999

>> No.5903302

>>5903283
>>5903283
>irememberwhentrollingmeantsomething.jp9999999999....

>> No.5903991

>>5903252
Absolutely, but it is tedious to prove. Here we take them as axioms.

>> No.5905488

>>5903283
This is a very elegant proof. Thanks for posting it, anon.

>> No.5906283

>>5903302
>.jp9999999999...
What applications use this file format?

>> No.5907533

>>5903283
.9999... = .(9) is just an alternative form of writing down 1. By the fucking definition.

>> No.5908037

>>5907533
This is not a definition but a theorem.

>> No.5908068

3.4448913

>> No.5908225

Why can't it converge to multiple things just like square root of 1 is + and - 1?

>> No.5908687

>>5908037
How am I able to prove it?

>> No.5908720

>>5908037
Depends on how we define expressions like 0.(9) .
Natural way for me is as a limit of {0.9, 0.99, 0.999, ...} sequence. Which is indeed 1. The main problem with such expressions is that people misunderstand what they mean, and tend to think that they're some concepts of a number "infinitely close to 1" rather than actual elements of R. Our school math education is shit, sadly.

>> No.5908746

http://www.scribd.com/doc/109954775/how-euler-did-it
page 229

>> No.5908751

>>5908225
Because limits are unique.

>> No.5909837

>>5860812
>not conditionally convergent by alternating series test
Do you even Calc?

>> No.5909902

>>5908720
it is 1.
there are like a gazillion proofs for that..
same thing with the 6/2(1+2) thing. if you look at it with a math education levl higher than high school you know the only possible answer is 9

>> No.5910201

>>5858447
By the definition of distance functions/metrics that I've learned, it won't converge in any conventional sense. However, that's just, like after a year or so at university.

>> No.5911897

>>5910201
>However, that's just, like after a year or so at university.

You'll be surprised what kind of math you're gonna learn in your second year.

>> No.5912862

>>5911897
What will I learn?

>> No.5914207

>>5912862
You will learn math with letters instead of numbers.

>> No.5914814 [DELETED] 

You have been visited by the Spooky Skeleton!
Repost this to 3 other threads or your mom will die in the next 24 hours.
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>> No.5916009

>>5914207
That sounds hard.

>> No.5917449

>>5916009
It's called "higher math" for a reason.

>> No.5917452

>>5912862
>>5916009
>>5917449
samefag