What is up with people thinking that 1 + 2 + 3 + = -1/12?

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The discussion centers on the controversial claim that the infinite series 1 + 2 + 3 + ... equals -1/12, a concept often referenced in String Theory. Participants assert that the manipulations leading to this conclusion are mathematically invalid, particularly under standard definitions of convergence taught in Real Analysis. However, they acknowledge that physicists utilize Zeta regularization techniques, which allow for the assignment of finite values to divergent series, in their theoretical work.

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This discussion is beneficial for mathematicians, physicists, and students of theoretical physics who are interested in the intersection of mathematics and physics, particularly in understanding controversial mathematical claims and their implications in advanced theories like String Theory.

Jamin2112
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What is up with people thinking that 1 + 2 + 3 + ... = -1/12?

My friend showed me a Youtube video where a Physicist "proves" that ∑kεNk = -1/12. The guy in the video uses a lot of illegal maneuvers. But apparently this "fact" is used in String Theory. Do Physicists use different definitions of convergence or something? I can easily prove that the sequence {1 + 2 + ... + n} is unbounded using the definitions I learned in Intro to Real Analysis in college.
 
Mathematics news on Phys.org
We had a recent thread on this.

tl;dr The manipulations are indeed invalid. But physicists do use the Zeta regularization in their work.
 

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