Wikipedia:Reference desk/Archives/Mathematics/2014 February 7

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February 7

Android "Places"/"Local" app: prevent automatic selection when nearby one of the search results?

It seems that if you happen to be near the highest ranking result, the app just automatically selects it to be displayed in a new page, without providing a link or whatnot to the original list of results (which may in fact contain what you seek!). Is there anyway to disable this behavior? -70.112.97.77 (talk) 21:01, 7 February 2014 (UTC)

You are at the wrong reference desk. Gutworth (talk) 03:51, 8 February 2014 (UTC)

Please, in plain English: the sum of integers to infinity equals -1/12

Suppose a kid were to ask what the above meant - is there even an easy explanation to be had there (the 26 dimensions of string theory and all aside)? As it is, I can barely make heads or tails of it myself! -70.112.97.77 (talk) 21:22, 7 February 2014 (UTC)

Well, there are reasonably easy explanations, but easy and correct, not so much. It's an equation that makes sense in some contexts and not in others, and making the distinction among those contexts is AFAICT murky even for experts. However, take a look at our 1 + 2 + 3 + 4 + ⋯ article and let us know what you still want to know. --Trovatore (talk) 21:33, 7 February 2014 (UTC)

It's not really true that the sum of the positive integers is $-1/12$. That's just a myth that seems to have been started recently. This is a properly divergent series that diverges to $+\infty$. In some contexts, it is useful to pretend as if this series was actually equal to $-1/12$, but if you don't understand the details of this construction via analytic continuation of the Riemann zeta function, then chances are you aren't in one of those contexts. This series really comes up in rather specialized applications to spectral theory, where one would like to assign a finite value to something that turns out to actually be infinite (like a trace of an operator that isn't properly trace class). The motivation for doing this is that sometimes you want to compare two different things, both of which are actually infinite. Nevertheless, in certain circumstances this comparison is meaningful, although the specific value of the series may not be. Sławomir Biały (talk) 22:19, 7 February 2014 (UTC)

As others have said, it is not true that $1+2+3+\dotsb =-{\frac {1}{12}}$ under any normal interpretation of infinite summation. In some very specific mathematical constructions, assigning that sum the value $-{\frac {1}{12}}$ is meaningful. This subtlety has been completely lost in popular media accounts of the series. Gutworth (talk) 03:56, 8 February 2014 (UTC)

Consider first the simpler case 9+90+900+9000+... This series emerges if you evaluate the digits of a = −1 : the first digit is a modulo 10, which is 9. The remaining digits are computed by subtracting the first digit from the original number (giving −10) and dividing by 10 (giving −1). So all digits are = 9 and ....999999 = −1. Computing binary digit you get 1+2+4+8+16+... = −1. So it makes sense to assign a value to a divergent series. Bo Jacoby (talk) 07:21, 10 February 2014 (UTC).

I'm struggling to see how this is relevant. Certainly if all of the terms of the series but the first one are "actually" zero, then it makes sense to add them. But there is nothing remarkable about this. Sławomir Biały (talk) 13:30, 10 February 2014 (UTC)

The series is $S=\sum _{k=0}^{\infty }9*10^{k}$. The terms are not zero. The value of S is not defined by convergence because the series is divergent. But the series satisfies the equation S = 9+10S, and the solution is S = −1. Bo Jacoby (talk) 22:38, 10 February 2014 (UTC).

Does this external link help? RJFJR (talk) 00:04, 11 February 2014 (UTC)