heres another thing. some infinities are bigger than others. there is an infinite number of decimals between 0 and 1, so the real numbers infinity is bigger than the whole numbers infinity
Math like this is really interesting
I am probably dumb and I didnt read any of is other videos, but this only makes sense if you make the assumption that the first sum is actually equal to 0.5
From what I saw the equation was basically that you cannot determine if the sum stops at 1 or 0, so the assumption is that an average of the possibilities is the solution.
But logically I feel an infinite sum is still infinite.
[QUOTE=Zelacks;43494785]I am probably dumb and I didnt read any of is other videos, but this only makes sense if you make the assumption that the first sum is actually equal to 0.5
From what I saw the equation was basically that you cannot determine if the sum stops at 1 or 0, so the assumption is that an average of the possibilities is the solution.
But logically I feel an infinite sum is still infinite.[/QUOTE]
Quick rundown of the proof of S1 = 1/2
1 - S1 = 1 - (1 - 1 + 1 - 1 + ...) = 1 - 1 + 1 - 1 + .... = S1 [b]->[/b] 1 - S1 = S1
1 = 2 * S1
S1 =1/2
fyi for anyone who's confused, these are all what are called divergent series and does not return a "sum" in the normal sense
[QUOTE=Zelacks;43494785]I am probably dumb and I didnt read any of is other videos, but this only makes sense if you make the assumption that the first sum is actually equal to 0.5
From what I saw the equation was basically that you cannot determine if the sum stops at 1 or 0, so the assumption is that an average of the possibilities is the solution.
But logically I feel an infinite sum is still infinite.[/QUOTE]
He says at the end of the video that you really have to apply this to physics to see past that. It makes a lot of sense if you do: Nothing anywhere lasts forever. It all comes to an end eventually. Something may last a seemingly infinite amount of time, but it always ends somewhere.
But this is as far as we know currently. Maybe we'll make a groundbreaking discovery of something that lasts forever.
Man I keep knowing less and less about math...
Fuck it. I hate math.
I'm done.
what i dont get, is how they can just move the second part of S2, what kind of rule is that?
why did he start subtracting from the 1+2+3+4+5+6...
he lost me there
[QUOTE=Lazore;43496026]what i dont get, is how they can just move the second part of S2, what kind of rule is that?[/QUOTE]
No rule. This is how I see it. It's not the same numbers, but the idea is the same.
[img]https://dl.dropboxusercontent.com/u/99717/MathStuff.png[/img]
Fantastic.
[QUOTE=Zyx;43496105]No rule. This is how I see it. It's not the same numbers, but the idea is the same.
[img]https://dl.dropboxusercontent.com/u/99717/MathStuff.png[/img][/QUOTE]
No, you know what... Fuck you all.
[editline]11th January 2014[/editline]
I'm done.
[IMG]http://i.imgur.com/nrFmkCd.png[/IMG]
I need to get back into Rudin dangit.
Oh and I'll just leave [URL="http://en.wikipedia.org/wiki/Riemann_series_theorem"]this[/URL] here...
[QUOTE=Quiet;43496691][IMG]http://i.imgur.com/nrFmkCd.png[/IMG][/QUOTE]
That is a good point.
(About the video)
I'm not sure if I am using this term correctly, but as they guy in the video is shifting an infinite series before he does the subtraction, then the two series will not have the same number of elements. The series being subtracted surely tends towards a "smaller" infinity than the first series?
[QUOTE=Mattz333;43497007]That is a good point.
(About the video)
I'm not sure if I am using this term correctly, but as they guy in the video is shifting an infinite series before he does the subtraction, then the two series will not have the same number of elements. The series being subtracted surely tends towards a "smaller" infinity than the first series?[/QUOTE]
It is more of a heuristic approach to deriving the result. Note that this is not the right answer is mathematical terms but it has physical applications and so this is what is commonly stated as the right answer. Because in reality you are summing a divergent series and it is hard to define what this resummation is.
heres a more complicated proof.
[video=youtube]http://www.youtube.com/watch?v=E-d9mgo8FGk&feature=youtu.be[/video]
this is why i prefer humanities
Maybe you should just start using your brain instead of instantly being scared away from maths. This whole [URL="http://www.theatlantic.com/education/archive/2013/10/the-myth-of-im-bad-at-math/280914/"]"I'm not a maths person" is a western bullshit mentality. [/URL]
I admit, maths can be hard, and it can make you feel dumb, but that's just part of it. Everyone assumes that when you see a mathematical expression or some reasoning, you're supposed to get it instantly. That's completely untrue. You work hard on it until you get it, and then you continue. You don't read a maths book like any other book, it's rather some sort of "crawling through it". I'm getting my master's in physics (started with a high school degree that allegedly wasn't even good enough for psychology, math-wise) and I still feel dumb on a regular basis . You just accept it and try to do your best.
I'm not saying that everyone is equally talented in maths, it's just that the belief that it's solely talent is not true at all. It's the same with music, you don't get skill for free in either of these fields. Some people get a head start, some don't, with hard work you'll get somewhere (kinda cliché I admit)
/rant
I've studied infinite sums last semester and i still have no idea how the fuck this is possible.
I feel violated, can someone call johnnymo already?
[QUOTE=Quiet;43496691][IMG]http://i.imgur.com/nrFmkCd.png[/IMG][/QUOTE]
no it works fine. you just forgot that you have to do 0-1 at the end, making the total 0. e.g.
(1+1+1+1)-(1+1+1+1) is the same as
1+1+1+1+0 -
0+1+1+1+1
notice how you have 1-0 at the start and 0-1 at the end, this totals up to 0.
[QUOTE=Quiet;43496691][IMG]http://i.imgur.com/nrFmkCd.png[/IMG][/QUOTE]
Except in "Theoretical end" of the non-shiftet S there will be a +0, making the result 0 again. Will there not?
Hi. I'll just leave this here.
[url]http://en.wikipedia.org/wiki/Ces%C3%A0ro_summation[/url]
[url]http://en.wikipedia.org/wiki/Ramanujan_summation[/url]
This video came up at my work. I consider it a form of intellectual dishonesty -- they're not making it clear that the method of summation is entirely different from what any normal person would consider 'summation'.
Their answer to 1-1+1-1+1... is likewise suspect outside of Cesaro's method. That is a nonconvergent series, meaning that it does not have a finite sum.