1/19/2024 0 Comments Calculus jokes limit![]() Some people might say that if it doesn't have a concrete interpretation, then it's "wrong" no matter what its implications in higher math. Of course, this is all a matter of interpretation. When you're studying certain properties of analytic functions, it is no longer "wrong," but useful. ![]() However, there are certain cases where it is useful to assign finite "sums" to things that don't ordinarily sum finitely. In this context, you might call it "wrong." for purposes like simple integrals or the comparison test in elementary analysis, interpreting it as finite won't help you. If you need to know the properties of 1 + 2 + 3 + 4. ![]() You see, this tool of Ramanujan summation isn't useful everywhere, and its bizarre results make it indeed kind of a hindrance out of its proper context. I'm going to give you full marks on the first question but none on the second, you smartass. Let me say, if I'm grading your high school homework, and I ask you to tell me what series diverge and converge. Well, "wrong" is really dependent on context. See 's_law_of_eponymy )Įdited for formatting and more for typos. X (Like so many other things in life, this might not actually be his original result. A mathematical way of thinking is trying to find the right contexts for the right applications when generalizing. This stuff happens all the time in mathematics. The point is that this idea of a Ramanujan sum has, through generalization, pulled so far away from the ordinary as to be ridiculous when taken out of contexts like Analytic Number Theory (eek!) etc. That's bizarre! Our intuition tells us that the sum of all of those numbers is infinity. For example, Rammy's summation tells us that the "sum" of the natural numbers (1, 2, 3.) is -1/12. This can lead to absurd conclusions, or conclusions that SEEM absurd if not placed in the right context. But the more you generalize, the more you pull away from the "real world" - the stuff that non-mathematicians see every day. Math, in its purest impulse, is "Generalize! Generalize!" Generalization is helpful, and like in Ramanujan's case, it can lead to important results. The problem here is a classic one in the history and institutional philosophy of mathematics. So he came up with a method of assigning "sums" even to series that diverge (don't work) in the old way of infinite summation. Ramanujan, x being the crazy, effed-up genius that he was, wanted to generalize further. It only works for certain kinds of series ("convergent" ones). The nitty-gritty details of how they do that (math folks call it "rigor") are based in limits - the stuff of Calculus and its snotty, pretentious half-sister Analysis.īut that generalization, the one you learn in Calc II or whatever, the one the first joke is based on, this generalization isn't complete. So they say, let's come up with a concept of sums that DOES work for an infinite series, instead of just a finite set. Mathematicians like to generalize, though. But if we visualize them like this, infinite sums make absolutely no sense. ![]() Can you imagine a box full of numbers and adding them together? Cool. Nobody really knows what it means to sum an infinite number of things. The standard way of summing an infinite series isn't really a sum. If you find certain comments or submissions here offensive, the best way to address it is with more speech. Accounts with very low or negative karma may need to seek manual approval for their submissions. Users with spam-like activity, spam-enabling behavior, or evidence of karma-farming in their histories may only post their own wholly original content. Repeated or egregious violations will result in bans. Remember to treat your fellow Redditors with politeness and respect. Please keep your comments lighthearted and civil. NSFW or NSFL content in comments must be appropriately tagged. Links of any kind are not allowed in posts. Users may only submit three jokes in a twenty-four-hour period.Īdult-oriented media must be properly tagged. Spam and spam-enabling activity is strictly prohibited, regardless of how or where it takes place. No spam or spam-enabling activity of any kind. Per Reddit's site-wide rules, unwelcome content is not allowed in posts or comments. No bigotry, sexualization of minors, hate-speech, or other unwelcome content. While reposts in /r/Jokes are allowed, they must meet all criteria for acceptance. Jokes should be offered according to our list of best practices.įor explanations and examples, please read our complete rules page. Please read our complete rules page before participating.
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