Ynot Posted April 16, 2014 Share Posted April 16, 2014 Hmmm... At the moment, I remain on the shelf a little, although clearly minds immeasurably brighter than mine have 'proven' this. But apparently, 1+2+3+4+5+6+7+.... to infinity is NOT a huge infinitesimal result but in fact minus 1/12 Spend a few minutes watching this video and then tell me what you think..... https://www.youtube.com/watch?v=w-I6XTVZXww&feature=player_embedded Link to comment Share on other sites More sharing options...
matt_beal Posted April 17, 2014 Share Posted April 17, 2014 I found this really intriguing and spent a few minutes looking at this earlier and wondered about the conclusion that 2S2=1/2 ... Perhaps someone can explain...? In the part of the calculation where you calculate 2 S2, they said you have to move the numbers along one so that 1+0=1 and -2+1=-1 etc. What confused me is that this is surely not 2S2, rather S2+(S2+1), as they've shifted the second S2 up one at any given point. This I feel rather ruins the whole idea... I'm fairly secure in my wrongness but would like to know why?! :D Edited for typo. Link to comment Share on other sites More sharing options...
chelgrian Posted April 17, 2014 Share Posted April 17, 2014 At the moment, I remain on the shelf a little, although clearly minds immeasurably brighter than mine have 'proven' this. The natural numbers form a divergent series therefore the series cannot sum to a finite limit which is also a natural number(1). The big gaping hole in all of this is that the number he comes out with in the video with is actually a measurement function which has been applied to the series it is not the conventional algebraic sum of the series in any meaningful sense. That is not to say it's not useful. Assigning these values to the sum of divergent series is extremely useful and yields comprehensible results in several areas of physics. (1) Well it can but not without adding this as a new axiom in your system of mathematics and therefore potentially invaliding all results based on the conventional axioms. Link to comment Share on other sites More sharing options...
BlueShift Posted April 17, 2014 Share Posted April 17, 2014 Er. Basically. No. Read this: http://en.wikipedia.org/wiki/Ces%C3%A0ro_summation Unfortunately the internet has got hold of this and because Cesaro Summation has the word 'sum' in it, they have said that 1+2+3+....=-1/12. As many other have and will say, the series of all natural numbers is clearly divergent. It doesn't approach an answer. In fact as you add the 'next' natural number in the series, the true sum actually changes by an ever increasing amount. Hence the series is divergent, and has no sum. A Cesaro Summation is essentially a mathematical construct to enable mathematicians to deal with infinite series in a manageable way. Link to comment Share on other sites More sharing options...
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