July 1st, 2011, 08:33 PM  #1 
Member Joined: Mar 2011 Posts: 49 Thanks: 1  1+2+3+4... = 1/12, what the fresh hell is this?
Hey, I don't even know where to post this, maybe it could be moved to where it belongs. So when I look at very complex mathematical forumals, they look like gibberish to me, and I'm quite happy to find that they are gibberish, but this seems to quite directly conflict with my logic.. so I'm not asking to be explained this in a way that I understand, I would be more than happy if someone could translate this, which in my head right now is a fatal critical error contradiction, into just regular gibberish.. or something like that.. tell me it's something I must be misunderstanding.. or something lol http://en.wikipedia.org/wiki/1_%2B_2_%2 ... _%E2%80%A6 This is the wiki article about it. 
July 1st, 2011, 08:39 PM  #2 
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 520 Math Focus: Calculus/ODEs  Re: 1+2+3+4... = 1/12, what the fresh hell is this? where the notation indicates Ramanujan summation. http://en.wikipedia.org/wiki/Ramanujan_summation I moved this to Real Analysis & Topology. 
July 2nd, 2011, 12:27 AM  #3 
Senior Member Joined: Apr 2007 Posts: 2,140 Thanks: 0 
Assuming no advanced mathematics knowledge, wouldn't 1 + 2 + 3 + ... diverge to infinity?

July 2nd, 2011, 05:41 AM  #4 
Global Moderator Joined: Nov 2009 From: Northwest Arkansas Posts: 2,766 Thanks: 4  Re: 1+2+3+4... = 1/12, what the fresh hell is this?
Or it converges to some padic number, perhaps

July 8th, 2011, 02:07 AM  #5 
Member Joined: Mar 2011 Posts: 49 Thanks: 1  Re: 1+2+3+4... = 1/12, what the fresh hell is this?
Okay, I think I'll leave this as it is for now, I was showed it by someone who just wanted to annoy me xD

December 15th, 2015, 09:36 AM  #6 
Senior Member Joined: Dec 2015 From: holland Posts: 162 Thanks: 37 Math Focus: tetration 
S1 = 1 − 1 + 1 − 1 + 1 − 1 + 1 − 1 + … = 1/2 this is not true 11+11....=0 or 11+11....=1 the outcomes can not be mediated. On the other hand true is .....99999.0 = 1 so 9+90+900+..... = 1 and 1+10+100.....=1/9 
December 15th, 2015, 10:00 AM  #7  
Math Team Joined: Dec 2013 From: Colombia Posts: 7,599 Thanks: 2587 Math Focus: Mainly analysis and algebra  Quote:
What does this mean?  
December 15th, 2015, 11:48 AM  #8 
Senior Member Joined: Dec 2015 From: holland Posts: 162 Thanks: 37 Math Focus: tetration 
Informally, nonterminating decimals are easily understood, because it is clear that a real number can be approximated to any required degree of precision by a terminating decimal. If two decimal expansions differ only after the 10th decimal place, they are quite close to one another; and if they differ only after the 20th decimal place, they are even closer. 10adic numbers use a similar nonterminating expansion, but with a different concept of "closeness". Whereas two decimal expansions are close to one another if their difference is a large negative power of 10, two 10adic expansions are close if their difference is a large positive power of 10. Thus 3333 and 4333, which differ by 10^3, are close in the 10adic world, and 33333333 and 43333333 are even closer, differing by 10 ^7. More precisely, a positive rational number r can be expressed as 10^e·(p/q), where p and q are positive integers and q is relatively prime to p and to 10. For each r ≠ 0 there exists the maximal e such that this representation is possible. Let the 10adic absolute value of r to be r= 10^e 0 = 0. Closeness in any number system is defined by a metric. Using the 10adic metric the distance between numbers x and y is given by x − y. An interesting consequence of the 10adic metric (or of a padic metric) is that there is no longer a need for the negative sign. As an example, by examining the following sequence we can see how unsigned 10adics can get progressively closer and closer to the number −1: 9=1+10 so 9(1)= 0.1 99=1+10^2, so 99(1)=0.01 999=1+10^3 so 999(1)= 0.001 9999=1+10^4 so 9999(1)=0.0001 and taking this sequence to its limit, we can say that the 10adic expansion of −1 is ...... 9999=1 Last edited by manus; December 15th, 2015 at 12:10 PM. 
December 15th, 2015, 12:13 PM  #9 
Senior Member Joined: Dec 2015 From: holland Posts: 162 Thanks: 37 Math Focus: tetration 
5adic: 1 = .......444 i = .......12013233 i = ......32431212 
December 15th, 2015, 02:48 PM  #10 
Math Team Joined: Dec 2013 From: Colombia Posts: 7,599 Thanks: 2587 Math Focus: Mainly analysis and algebra 
That's a completely different number system, so it's rather muddying the waters here.


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