radx is right.

From:
http://en.wikipedia.org/wiki/Riemann_zeta_function
(Emphasis mine)

because of the series definition for zeta when the real part of s is greater than 1, this fact is sometimes (mis)used to state

zeta(-1) = 1 + 2 + 3 + 4 + ... = -1/12

which is only true in a very informal sense (i.e. this is just an abuse of notation, and the series does not actually converge to this value).

You are correct, the way it is written in the title is wrong. One possible notation as I was taught many years ago would be to add an "R" for Ramanujan above the equals sign to point out that we're talking about the sum of a diverging infinite series.

No idea if it's the correct notation, especially since I've seen different versions of it.

That said, there are multiple proofs that the Riemann zeta function of -1, which is the infinite series mentioned above, does in fact equal -1/12.

As a reminder, the Riemann zeta function is this:

zeta(s) = sum(n=1,inf) 1/n^s

If you restrict it to real numbers, it converges for all s>1, so by evaluating it at s=-1, you are messing around with a diverging series, which is why it looks so funky. It's a holomorphic continuation outside its defined area and it seems to work for theoretical physics. And it gives me a headache.

It's called, " Ella Enchanted (2004)"
http://www.imdb.com/title/tt0327679/


Obviously a gem that slipped-through the cracks and inspired a casting-call for her her to eventually star in another version of Les Miserables, and her inevitable Oscar for her multi-talented skills as the pert, cute, and can sing-her-own-parts-kinna powerhouse (hate all the Les Miserable screen-adaptations, have yet to see this one).

Compare to these classic multi-talented hotties Debbie Reynolds, Rita Hayworth, Marlene Dietrich

The only modern actress' that come close in actual pipes and raw beauty are Scarlet Johansson and Nicole Kidman, who can pretty-much sing her tiny little cute Aussie ass off...

Oh wait, lest we forget the two dames from Chicago (2002), who can hold their own with the rest-Zeta-Jones and Zelweger, but Renée was trumped by Catherine in that film.

This must be an advert targeting the booming Zetas' business-They have strippers as funerary personnel!

Gravediggers are busy, busy en Mexico hoy!

The Canadian Zetas are much less hostile, eh?

I posted about this before, so many of the problems that drugs create are actually created by the War On Drugs.

Governments can't beat drug dealers, but Capitalism can. If Tesco's sold Fair Trade Cannabis, drug dealers would be utterly screwed in no time. Plus, farmers in Columbia/Afghanistan/etc would have a legitimate market, which would erode the illegal market, in turn decimating FARC/Taliban/etc's income and ability to operate. I saw one report that said half of the Afghan Taliban's $3B annual income is from heroin and cannabis sales.

The financial implications would be vast, tax revenue for governments would be a big help while the money, and therefore power, of drug cartels shrinks. There would be even more horrific violence here as cartels look to consolidate on their remaining business, I shudder to think of how the Zetas, the Tijuana Gang and the Juarez Cartel among others in Mexico would respond and it would take considerable political strength to get through.

Is legalising drugs the answer to peace on earth? The war on drugs is subsidising organised crime.

Anonymous advised its members to protect their online identities, and not to wear the traditional Anonymous mask in public, or even purchase them online, as a core group decides if it should take on a Mexican drug cartel that is said to have kidnapped a member of the group.

The hacker group had earlier threatened to expose the identity of members and supporters of a Mexican drug cartel by Nov. 5, in retaliation for the kidnapping of a group member, and hacked the web site of a former state official, alleging that he has associations with the dreaded Zetas cartel.

But there are fissures showing among the leaders as fear of handling the drug cartel builds up, with some expressing concern that new, inexperienced members could get quickly exposed and compromised.

The action has been cancelled, Sm0k34n0n wrote in a Twitter message in Spanish on Monday. High-profile colleague anonymouSabu described sm0k34n0n as one of the campaign's promoters in another Twitter message. But other groups from Latin America are said to be considering a core action group, and warning other members to stay away. AnonymouSabu was all for the action late Sunday.

A video in Spanish posted on YouTube on October 6 by a person calling himself "MrAnonymousguyfawkes", threatened that Anonymous will publish the names, photos, and addresses of police officials, journalists, and taxi drivers that collaborate with the drug cartel, hoping the government will arrest them.

"You made a huge mistake by taking one of us. Release him. And if anything happens to him, you (expletive) will always remember this upcoming November 5th," said a masked person in the video, according to a translation provided by another user of YouTube.

November 5 is known in the U.K. as Guy Fawkes day after his November 5, 1605, conspiracy to attempt to blow up the British Parliament. The Guy Fawkes mask, popularized by the movie V for Vendetta, has been adopted by Anonymous.

Anonymous claimed on Sunday to have defaced the website of a former official in the Mexican state of Tabasco. On Monday, the website bore a message in Spanish by Anonymous Mexico stating that he was a part of Zetas.

"We all know who they are and where they are," said the speaker in the video. Anonymous did not however claim that its hacking skills gave it special access to information on the cartel. Nor are its traditional tactics such as DDoS (distributed denial-of-service) attacks on websites likely to be of use against armed gangs, according to various analysts.

The drug cartel has killed people who have criticized them on blogs and other social media, according to reports. The Committee to Protect Journalists in New York reported in September the murder of a journalist in direct retaliation for information posted on social media.

As newspapers are censored by fear, Mexican citizens, and many journalists, are turning to social media and online forums to share news and inform each other, said Sara Rafsky, a research associate in CPJ's Americas program. "So it should be no shock that drug cartels are turning their attention to the Internet."
http://www.pcworld.com/businesscenter/article/242845/anonymous_threatens_to_expose_mexican_drug_cartel.html

>> ^gwiz665:

♪Call Mr. Plow, that's my name
that name again is Mr Plow.♫


I was surprised you didn't sift this one :B

>> ^Fusionaut:

Also:
A longer version of the scene.


Not a bad way for a pensioner to spend his day.

Gratuitous?

http://videosift.com/video/Catherine-Zeta-Jones-and-Lasers-and-um

Tags for this video have been changed from 'Elizabeth Arden, Provocative Woman, puddle, hotness, melt, water' to 'Elizabeth Arden, Provocative Woman, puddle, hotness, melt, water, catherine zeta jones' - edited by Issykitty

In order - Mary Pickford, Lillian Gish, Gloria Swanson, Marlene Dietrich, Norma Shearer, Ruth Chatterton, Jean Harlow, Katharine Hepburn, Carole Lombard, Bette Davis, Greta Garbo, Barbara Stanwyck, Vivien Leigh, Greer Garson, Hedy Lamarr, Rita Hayworth, Gene Tierney, Olivia de Havilland, Ingrid Bergman, Joan Crawford, Ginger Rogers, Loretta Young, Deborah Kerr, Judy Garland, Anne Baxter, Lauren Bacall, Susan Hayward, Ava Gardner, Marilyn Monroe, Grace Kelly, Lana Turner, Elizabeth Taylor, Kim Novak, Audrey Hepburn, Joanne Woodward, Shirley MacLaine, Natalie Wood, Angie Dickinson, Janet Leigh, Brigitte Bardot, Sophia Loren, Ann-Margret, Julie Andrews, Raquel Welch, Tuesday Weld, Jane Fonda, Julie Christie, Faye Dunaway, Catherine Deneuve, Jacqueline Bisset, Candice Bergen, Isabella Rossellini, Diane Keaton, Goldie Hawn, Meryl Streep, Susan Sarandon, Jessica Lange, Michelle Pfeiffer, Sigourney Weaver, Kathleen Turner, Holly Hunter, Jodie Foster, Melanie Griffith, Sharon Stone, Meg Ryan, Demi Moore, Julia Roberts, Uma Thurman, Sandra Bullock, Julianne Moore, Diane Lane, Nicole Kidman, Catherine Zeta-Jones, Angelina Jolie, Charlize Theron, Reese Witherspoon, Gwyneth Paltrow