In this case, we use s in deference to Riemann, who defined the zeta function in an paper [pdf]. For a very good, in-depth explanation of a way that doesn't require complex analysis—complete with homework exercises—check out Terry Tao's post on the subject.
The Numberphile video bothered me because they had the opportunity to talk about what it means to assign a value to an infinite series and explain different ways of doing this.
If you already know a little bit about the subject, you can watch the video and a longer related video about the topic and catch tidbits of what's really going on. But the video's "wow" factor comes from the fact that it makes no sense for a bunch of positive numbers to sum up to a negative number if the audience assumes that "sum" means what they think it means. If the Numberphiles were more explicit about alternate ways of associating numbers to series, they could have done more than just make people think mathematicians are always changing the rules.
Padilla cheekily says, "You have to go to infinity, Brady! Other people have written good stuff about the math in this video. After an overly credulous Slate blog post about it, Phil Plait wrote a much more levelheaded explanation of the different ways to assign a value to a series.
If you'd like to work through the details of the "proof" on your own, John Baez has you covered. Blake Stacey and Dr. Richard Elwes posts an infinite series " health and safety warning " involving my old favorite, the harmonic series. I think that the proliferation of discussion about what this infinite series means is good, even though I wish more of that discussion could have been in the video, which has more than a million views on YouTube so far! The views expressed are those of the author s and are not necessarily those of Scientific American.
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We'll talk about two reasons today. The first has to do with how division is related to multiplication. Let's imagine for a second that division by zero is fine and dandy. We don't know what it is, but we'll just assume that x is some number.
We can also look at this division problem as a multiplication problem asking what number, x , do we have to multiply by 0 to get 10? Of course, there's no answer to this question since every number multiplied by zero is zero. Which means the operation of dividing by zero is what's dubbed "undefined.
In other words, as we divide 1 by increasingly small numbers—which are closer and closer to zero—we get a larger and larger result. In the limit where the denominator of this fraction actually becomes zero, the result would be infinitely large. Which is yet another very good reason that we can't divide by zero. Wrap Up OK, that's all the math we have time for today. Thanks for reading, math fans!
Apple addition and infinity lightbulb images from Shutterstock. He provides clear explanations of math terms and principles, and his simple tricks for solving basic algebra problems will have even the most math-phobic person looking forward to working out whatever math problem comes their way. Jump to Navigation. May 16, We are currently experiencing playback issues on Safari.
If you would like to listen to the audio, please use Google Chrome or Firefox. About the Author. Follow Facebook Linkedin. That said, unless you're into Wheel Algebra i. I'd rather stick to those assumptions, and to simple stuff like Minkovsky spacetime and Schrodinger equations oh, and don't ask me to touch Strings with a meter, 4-dimensional pole. I'm not crazy enough for that yet So what's the value of x?
We can't decide. But we can still make calculations with this formula. They use this formula in quantum mechanics. That's even more crazy!
But then, I'm studying physics, not mathematics. Sure, there are mathematical lectures, but I'm not that good at understanding the theory being this all though I do manage to apply those mathematics when I need them. Binary was originally designed for computers I think.
An electrical circuit can be one of two things: on or off. Either the circuit is complete, or it isn't. In binary, it looks like I'm going to skit the work for the first six zeros as it would be a headache to type all of them. Now it is a matter of conversion. The figure "2" is not a valid figure in binary. However, we can use binary to arrive at this solution. Y'know, dyscalculiacs like me want to kill such threads with fire I have enough problems memorising my own phone number.
When someone drops a bombshell like this i want to bite him. Well, changing between number radices can be fun. To be clear, I'm fine with binary. That is the sort of thing I'm confused about. More precisely, 0. But this is obvious at high school level if you've got a good teacher. Basically, you can express any number like 0. Simple enough. That's a so called group which only consists of the numbers 0 and 1.
Whatever you do with these numbers, on the result you must calculate the remainder and use that as the result. And that will always be 0 or 1. You can't break out of it.
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