How to find sin of any fraction-angles, and how do you find them in fraction forms and not in decimal forms? What is the rationale behind making it illegal to hand out water to voters in line in Georgia? Prove that $f$ is Riemann integrable if and only of $I(f)=\lim_{||P||\to 0}\sum_{i=1}^nf(t_i)\Delta x_i$. Please be sure to answer the question. where R is real numbers. What do angle have to do with waves? The best answers are voted up and rise to the top, Mathematics Stack Exchange works best with JavaScript enabled, Start here for a quick overview of the site, Detailed answers to any questions you might have, Discuss the workings and policies of this site, Learn more about Stack Overflow the company, Learn more about hiring developers or posting ads with us. If $\tan(a) $ is rational then $\sqrt{\sin(4a)}$ is irrational. \DeclareMathOperator is designed to create commands that should typeset operator names such as sin and lim.Some of these are already defined in base TeX or LaTeX so one writes 2\sin\theta. It only takes a minute to sign up. Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. New Archive Conversion Utility in Version 12. What's motivic about correspondences? How to show that the following product is bounded? Picturing $2$-sphere with antipodes identified. Is a neural network essential for deep learning? Making statements based on opinion; back them up with references or personal experience. Proper advection equation for non-conservative values in polar cylidrical coords. Soon there will be 100,000 questions on MathOverflow.net, a question-and-answer site for professional mathematicians!To celebrate this event, I have been working on a Wolfram Language utility package to convert archives of Stack Exchange network websites into Wolfram Language entity stores.. To subscribe to this RSS feed, copy and paste this URL into your RSS reader. Can the derivative difference be arbitrarily larger than the function difference? What to do if filament spool won't fit in 3D printer. How do you calculate CAGR when the value of the end term is negative? Probably an equivalent for StackOverflow policy would be answering questions about problems with solutions of homework problem (something like "I did such-and-such but resulting answer is clearly wrong even for n=1. What were the motives of the chief priests and elders in persuading the multitudes for the execution of Jesus, Matthew 27:20. But avoid … Asking for help, clarification, or responding to other answers. Use MathJax to format equations. Is $L^p(\mu)$ isometrically embedded into $L^q(\mu)$ when $p=\infty$ or $q=\infty$? How do Christians who reject pre-fall death reconcile their views with the Cretaceous–Paleogene extinction event (66 million years ago)? Provide details and share your research! Note that while Math.Pow(Math.E, d) produces the same result as Math.Exp(d), a quick benchmark comparison shows that Math.Exp actually executes about twice as fast as Math.Pow: Trial Operations Pow Exp 1 1000 0.0002037 0.0001344 (seconds) 2 100000 0.0106623 0.0046347 3 10000000 1.0892492 0.4677785 By clicking “Accept all cookies”, you agree Stack Exchange can store cookies on your device and disclose information in accordance with our Cookie Policy. What are some interesting and unusual theorems, identities, notations in Trigonometry? A sufficient condition for the singularity of two measures, Converse of a result about the analyticity of an integral $\int_0^\infty e^{-zt} f(t) dt$, Exponential growth of principal sum with constant growth rate, Incomparable Cardinal Invariants of the Continuum, Find matrix representation of following linear transformation, Sphere falling in viscous fluid boundary condition. The archives are hosted on the Internet … Embedding of $C(X)$ into $B(H)$ where $H$ is separable. Connect and share knowledge within a single location that is structured and easy to search. Asymptotic expansion of q-Pochhammer symbol near q = 1. Not a question; more of a notification. rev 2021.4.1.38970. For those who are unaware, MathOverflow is upgrading to the "new" StackExchange platform. Map of complexes induce a map of de Rham cohomology, Dynamics of probability of hitting a barrier. Thanks for contributing an answer to Mathematics Stack Exchange! Stack Exchange network consists of 176 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share … site design / logo © 2021 Stack Exchange Inc; user contributions licensed under cc by-sa. Example of an invertible, measure-preserving map without measurable inverse. Stack Exchange is a network of question-and-answer (Q&A) websites on topics in diverse fields, each site covering a specific topic, where questions, answers, and users are subject to a reputation award process. How to prove the following set dense in $C_0(\mathbb{R})$? Is it special for a Lagrangian to equal its first integral? 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