It might be a good idea to say something about the connection between the axiom of choice and the Banach-Tarski paradox. The reason the Banach-Tarski paradox is counterintuitive is that we expect that if you split up a sphere into finitely many pieces, the total "mass" of all the pieces is still the same - so you shouldn't be able to put those …Here's your chance to earn bonus Amex points for spending with Four Seasons. Update: Some offers mentioned below are no longer available. View the current offers here. It's new Ame...I have coordinates of 3d triangle and I need to calculate its area. I know how to do it in 2D, but don't know how to calculate area in 3d. I have developed data as follows. (119.91227722167969, 122.$\begingroup$ FYI, you can do something similar to "explain" the Chain Rule: Define a space curve by < f(t), h(t), t > where h(t) = g(f(t)), and (assuming it makes sense) let its tangent vector be < a, b, 1 > (with a != 0). The zx-graph is x = f(z), with slope-of-tangent-line dx/dz = a/1 = a; the zy-graph is y = h(z), with tangent slope dy/dz = b/1 = b; the bridging …I think a great book for doing calculus problems that may prepare you for the Putnam is Titu Andreescu's book- "Problems in Real Analysis: Advanced Calculus on the Real Line". Andreescu's texts are known to be useful in preparing students for mathematics competitions. In this textbook, Andreescu exposes you to a lot of techniques (especially …10. The Lebesgue integral is a generalization of the usual Riemann integral taught in basic calculus. If the Riemann integral of a function over a set exists then it equals the Lebesgue integral. So the Lebesgue integral of x2 x 2 over [0, 1] is just the old (1/3)13 − (1/3)03. Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers. An inner product space is a vector space for which the inner product is defined. The inner product is also known as the 'dot product' for 2D or 3D Euclidean space. An arbitrary number of inner products can be defined according to three rules, though most are a lot less intuitive/practical than the Euclidean (dot) product.Whether you’re a teacher in a school district, a parent of preschool or homeschooled children or just someone who loves to learn, you know the secret to learning anything — particu...Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.. Visit Stack ExchangeApply Stokes theorem on a curve which is intersection of a sphere and plane. Apply Stokes theorem to prove that ∫cydx + zdy + xdz = − 2√2πa2 Where C is the curve given by x2 + y2 + z2 − 2ax − 2ay = 0, x + y = 2a ; and begins at the point (2a,0,0) and it goes first below ... vector-analysis. surface-integrals.Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.. Visit Stack Exchange$\begingroup$ Note that to use this we must have a basis already chosen (to write down matrices) and that our inner product must match the standard dot product in terms of this basis (so that matrix multiplication corresponds to taking inner product of rows of the left matrix with columns of the right matrix). Also, to apply the first comment, the number of …Okay, so everyone knows the usual methods of solving integrals, namely u-substitution, integration by parts, partial fractions, trig substitutions, and reduction formulas. But what else is there? E...Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.. Visit Stack ExchangeMathematics Stack Exchange. Help center. Our model. How can I format mathematics here? Many posts at Mathematics Stack Exchange include …Advertisement While in prison, cons are subject to the rules set by prison officials. If a con commits an infraction, he gets a hearing before the warden or some lower ranking offi...The algebraic degree of a particular sum of algebraic numbers. Let p p be a prime number and let m m be a positive integer. We know that β:=p−1/m β := p − 1 / m is an m m -degree algebraic number (in fact, its minimal polynomial is pXm − 1 p X m − 1 ). I would like to prove that ... number-theory.$\begingroup$ @Om3ga Incidentally, there are at least three different Discord servers of significant size "called 'Mathematics' where people can ask for help to certain questions.", in addition to others not named "Mathematics" (e.g. general STEM help servers - advanced math servers - subject-area-specific servers - servers for math people at a ...Closed form of ∑ m=0∞ (a)mBp(b+m,c−b)zm m! ∑ m = 0 ∞ ( a) m B p ( b + m, c − b) z m m! with the Incomplete Beta function. This question comes from related “sum of incomplete gamma function” problems. Also,there are many research papers trying to make the Hypergeometric Incomplete. Here is one confluent example from ...2 Answers. To be separable means to have a countable dense subset. Suppose that (M, d) is a metric space and that U ⊆ M be an uncountable subset and r > 0. Suppose that for all x ≠ y ∈ U, d(x, y) ≥ r. Let C be any countable subset of M. Then C can only meet a countable number of the balls Br / 2(x) for x ∈ U.Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.. Visit Stack Exchange Stack Exchange Q&A communities are different. Here's how: Expert communities. Each of our 182 communities is built by people passionate about a focused topic. The right answer. Right on top. Experts like you can vote on posts, so the most helpful answers are easy to find. Share knowledge. Earn trust. Does watching Outer Banks on Netflix make you want to book a trip to the place the popular show was inspired by? If you're looking to live out your "Pogue Life" dreams, here are th...The vertices of a triangle are three random points on a unit circle. The side lengths are a, b, c. Show that P(ab > c) = 12. The vertices of a triangle are three unifomly random points on a unit circle. The side lengths are, in random order, a, b, c . Show that P(ab > c) = 1 2 . The result is strongly suggested by ...Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.. Visit Stack Exchange Understanding predicates and quantifiers ∀ , ∃ (my reasoning) So lets say we are trying to figure out if: P (x, y) is the predicate of x2 < y as defined for x, y ∈ Z. This means using quantifiers: ∀ and ∃, I can logically say: 1. ∀x∃y of P (x,y) is ... discrete-mathematics. logic. first-order-logic. quantifiers. coolcat. Welcome to Mathematics Stack Exchange. Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals …Add a comment. 6. There are ways to calculate it, modulo is remainder counting basically. 7 = 2 mod 5 because 7 = 5 ∗ 1 + 2 12 = 2 mod5 because 12 = 5 ∗ 2 + 2 and so on, so if you want to calculate for example 73 = a mod 7 you can do this, that is want to get a, take 73 and continue subtracting 7 until you no longer can. 73 − 7 = 66, 66 ... The vertices of a triangle are three random points on a unit circle. The side lengths are a, b, c. Show that P(ab > c) = 12. The vertices of a triangle are three unifomly random points on a unit circle. The side lengths are, in random order, a, b, c . Show that P(ab > c) = 1 2 . The result is strongly suggested by ... Good morning, Quartz readers! Good morning, Quartz readers! South Korea commemorates comfort women. Japan issued a travel advisory warning visitors about anti-Japanese sentiment in...Mathematics Stack Exchange is moderated by you. Review queues contain posts (also known as review tasks) that might need community attention, as determined by the system or other community users. You see posts one at a time so that you can evaluate what, if any, action is needed.Apply Stokes theorem on a curve which is intersection of a sphere and plane. Apply Stokes theorem to prove that ∫cydx + zdy + xdz = − 2√2πa2 Where C is the curve given by x2 + y2 + z2 − 2ax − 2ay = 0, x + y = 2a ; and begins at the point (2a,0,0) and it goes first below ... vector-analysis. surface-integrals.Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.. Visit Stack ExchangeThe second part, containing problems from the British Mathematical Olympiad, is much more challenging.) _ [Beginner-Intermediate] E. Lozansky and C. Rousseau, Winning solutions, A good introduction to some useful background material from number theory, algebra, and combinatorics, and to problem-solving techniques.Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.. Visit Stack ExchangeStack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.. Visit Stack Exchange1. This might be useful to notice both on main and on meta: You can use several tabs: such as Newest, Active, Bountied, Unanswered, Frequent. Depending on the choice of tab, you're shown different question. If you choose newest, the name of the user which is displayed is the poster of the question.Mathematics Stack Exchange. Help center. Our model. How can I format mathematics here? Many posts at Mathematics Stack Exchange include …Find the center of all circles that touch the x -axis and a circle centered at the origin. Given a circle C of radius 1 centered at the origin, I want to determine the locus of the centers of all circles that touch C and the x -axis. This is the red curve in the following Desmos ... geometry. inverse-function. locus.Are you looking for a fun and interactive way to improve your mathematical skills? Look no further than free online math games. These games not only make learning math enjoyable, b...How do you know when to replace a furnace? Check out this guide to learn how to see the writing on the wall that your furnace might be failing. Expert Advice On Improving Your Home...Definition 1: Let f(x) f ( x) be defined on an interval that contains x = a x = a. Then we say that, limx→a f(x) = L lim x → a f ( x) = L. if for every number ϵ ϵ there is some number λ λ such that. |f(x) − L| < ϵ whenever 0 <|x − a| < λ. | f ( x) − L | < ϵ whenever 0 < | x − a | < λ. I understand what this theorem is trying ...Aside from the mathematical answers provided by others, the computational verification of the Collatz problem is a good exercise for programmers. There are many optimization opportunities (e.g., time-space trade-off using lookup tables, parallelism), many pitfalls (e.g., integer type overflow), possibilities of exploiting various implementation ...$\approx$ is used mostly for the approximate (read: calculated) value of a mathematical expression like $\pi \approx 3.14$ In LaTeX it is coded as \approx. $\cong$ is used to show a congruency between two mathematical expressions, which could be geometrical, topological, and when using modulo arithmetic you can get different numbers that are …How do you know when to replace a furnace? Check out this guide to learn how to see the writing on the wall that your furnace might be failing. Expert Advice On Improving Your Home...Mathematics Educators Stack Exchange. Explore our questions. Ask Question. undergraduate-education secondary-education mathematical-pedagogy calculus …Approach0 is a math-aware search engine. “Math-aware” means you can add math expression (s) as some of your keywords to have search engine help you find similar expressions. Check out here: https://approach0.xyz. To restrict matches to this site paste the string "AND site:math.stackexchange.com" into the search window (this …The call from Consumer Reports is a more aggressive one than the CDC is making, as the second E. coli scare linked to lettuce this year spreads across the US. A major US consumer w... Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers. If not, you should post your attempted solutions online on, say, math.stackexchange or r/learnmath for feedback. In general, effective learning cannot occur when the only thing you do is absorb information. You must practice using that information--memorization becomes the side effect.An addition to Martin Scharrer's answer. \textcolor has a side effect in math, that the contents is put in curly braces (see definition of \@textcolor).The color implementation of package color is based on groups (the color is restored at the end of the group automatically), but curly braces also make a subformula in math. This affects the …Aside from the mathematical answers provided by others, the computational verification of the Collatz problem is a good exercise for programmers. There are many optimization opportunities (e.g., time-space trade-off using lookup tables, parallelism), many pitfalls (e.g., integer type overflow), possibilities of exploiting various implementation ...President Trump bans travel to Europe for 30 days to combat coronavirus spread. Americans will be allowed to return home. President Donald Trump has ordered a ban on travel from Eu...5. Please help me understand swapping the bounds of an integral better. I learned that. ∫b a f(x)dx = −∫a b f(x)dx ∫ a b f ( x) d x = − ∫ b a f ( x) d x. Now when I try to visualize this, take sin(x) sin ( x) for example, ∫2π π sin(x)dx ∫ π 2 π sin ( x) d x and −∫π 2π sin(x)dx − ∫ 2 π π sin ( x) d x both give ... This tag is for questions that are asking for online resources in mathematics (references, dictionaries, encyclopaedic collections, online tools, videos and lectures, etc), or asking about the mathematics behind tools and technology found on the internet. Make your title interesting for others. Mathematics.SE is designed to be a repository of good mathematical questions and answers. Thus, there is no need to refer to your personal situation in the title. Make your title a question of universal value. For example, the title Help me solve a2 + b2 = c2 for my exam preparation is very specific to ...Ask Question. On standards or conventions specific to mathematics as an academic discipline, and programs that lead to a degree in this field. For regular mathematics questions, visit our sister sites Math Stack Exchange and …The vertices of a triangle are three random points on a unit circle. The side lengths are a, b, c. Show that P(ab > c) = 1 2. probability. integration. definite-integrals. intuition. geometric-probability. Dan. 21.5k.Apr 13, 2017 · MathOverflow is for research level math questions. Math.stackexchange.com is not restricted to any particular level of difficulty (though one expects that it won't get much in the way of research level questions since those are at MO). There was a lot of feeling on SO and MO that it'd be good if there was a site for more elementary math questions. If you just upgraded to macOS Sierra and your Dropbox app is acting up, you’re not alone. Even with the latest version of the app, some users are experiencing strange behavior—erro...In mathematics, inequalities are a set of five symbols used to demonstrate instances where one value is not the same as another value. The five symbols are described as “not equal ...As with many mathematical concepts, there are slight variations in how they are defined. Some authors require that all rings have an identity, and describe what we called a ring a rng (the omission of the letter i signals that it is unnecessary for there to be an identity).Getting credit for something you’ve accomplished can be a struggle in the business world, but with Microsoft PowerPoint, you’ve got multiple options to put your name or your compan...Okay, so everyone knows the usual methods of solving integrals, namely u-substitution, integration by parts, partial fractions, trig substitutions, and reduction formulas. But what else is there? E...Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.. Visit Stack ExchangeStack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.. Visit Stack ExchangeOkay, so everyone knows the usual methods of solving integrals, namely u-substitution, integration by parts, partial fractions, trig substitutions, and reduction formulas. But what else is there? E... Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers. Mathematics Educators Stack Exchange. Explore our questions. Ask Question. undergraduate-education secondary-education mathematical-pedagogy calculus reference-request algebra textbooks geometry proofs primary-education more tags. Active Hot Week Month. 0 votes. 0 answers. 7 views. 3 Answers. First consider the simplest case where a(x) = a a ( x) = a and b(x) = b b ( x) = b for all x x. Then the Leibniz formula becomes. d dx(∫b a f(x, t)dt) =∫b a ∂ ∂xf(x, t)dx d d x ( ∫ a b f ( x, t) d t) = ∫ a b ∂ ∂ x f ( x, t) d x. i.e. it is reduced to moving the derivative inside the integral. In this special case, the ...Three players toss an unfair coin - Give an intuitive explanation of dependent. Three players toss an unfair coin each, independently of each other, with the same probability p = 1/3 that the coin shows heads. Let X = 1 if player #2 gets the same result as player #1 - Call this a ... probability. independence.10. The Lebesgue integral is a generalization of the usual Riemann integral taught in basic calculus. If the Riemann integral of a function over a set exists then it equals the Lebesgue integral. So the Lebesgue integral of x2 x 2 over [0, 1] is just the old (1/3)13 − (1/3)03.Kiwis can now get paid in crypto, the US securities regulator isn't so sure about bitcoin funds, and news from elsewhere. Kiwis can now get paid in crypto. Bitcoin faces legal unce...In the second case, A ′ is not right invertible, since the last row of A ′ D is completely zero for any D. Therefore A cannot be right invertible, since if AB = I, then A ′ (BC − 1) = CABC − 1 = CC − 1 = I. Conclusion: if A has a right inverse B, we must be in the first case, so A is (two-sided) invertible. P.S.The vertices of a triangle are three random points on a unit circle. The side lengths are a, b, c. Show that P(ab > c) = 1 2. probability. integration. definite-integrals. intuition. geometric-probability. Dan. 21.5k. Mathematics Educators Stack Exchange. Explore our questions. Ask Question. undergraduate-education secondary-education mathematical-pedagogy calculus reference-request algebra textbooks geometry proofs primary-education more tags. Active Hot Week Month. 0 votes. 0 answers. 7 views. Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.
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3 Answers. Sorted by: 376. The two sites are meant for very different audiences, and have very different types of questions. From the MathOverflow …Welcome to Mathematics Stack Exchange. Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals …Mathematics Stack Exchange. Explore our questions. Ask Question. Interesting 41 Bountied Hot Week Month. 0 votes. 0 answers. 3 views. Show that the function is … Understanding predicates and quantifiers ∀ , ∃ (my reasoning) So lets say we are trying to figure out if: P (x, y) is the predicate of x2 < y as defined for x, y ∈ Z. This means using quantifiers: ∀ and ∃, I can logically say: 1. ∀x∃y of P (x,y) is ... discrete-mathematics. logic. first-order-logic. quantifiers. coolcat. Proofs for the properties of μ(σ) μ ( σ), the order of ζ(s) ζ ( s) The following is a text from Section 5.1 of Titchmarsh's book The Theory of the Riemann Zeta-Function: For each σ σ we define a number μ(σ) μ ( σ) as the lower bound of numbers ξ ξ such that $... soft-question. proof-explanation. book-recommendation. Newest Questions - Mathematics Meta Stack Exchange. All Questions. Ask Question. 9,522 questions. Newest. Active. Filter. 2 votes. 0 answers. 95 views. Was the style of the up/down-vote arrows changed? I noticed that the style of the up/down-votes button has changed (for me at least). Find the center of all circles that touch the x -axis and a circle centered at the origin. Given a circle C of radius 1 centered at the origin, I want to determine the locus of the centers of all circles that touch C and the x -axis. This is the red curve in the following Desmos ... geometry. inverse-function. locus.I am very interested in mathematics, particularly mathematical physics, but I currently do not have access to an institution or any professors. ... You can also look on Math StackExchange (e.g., questions with the [book-recommendation] tag) for recommendations about books for either your particular interests, problem solving, proof …n) For n = 0 n = 0 there isn't any number greater then 0 and lesser or equal to n n, so the product is empty; the empty product is defined by convention as 1. It has many reasons. For example, we can have a power series: ex = ∑nxn/n! e x = ∑ n x n / n! and we would like the first term to be 1 1. This tag is for questions that are asking for online resources in mathematics (references, dictionaries, encyclopaedic collections, online tools, videos and lectures, etc), or asking about the mathematics behind tools and technology found on the internet. What happens when I comment? The following community members will be automatically notified of your comment: the owner of the post you're commenting on. one additional user when your comment contains a @username 1 reply. 1 You can only @reply to users who have already left a comment, or edited the post. The first three non-whitespace …Okay, so everyone knows the usual methods of solving integrals, namely u-substitution, integration by parts, partial fractions, trig substitutions, and reduction formulas. But what else is there? E...Stack Exchange Q&A communities are different. Here's how: Expert communities. Each of our 182 communities is built by people passionate about a focused topic. …Emily Riehl's recently published book Category theory in context is a fantastic introductory text for those interested in seeing lots of examples of where category theory arises in various mathematical disciplines. Understand the examples from other branches of mathematics requires some mathematical maturity (e.g., a bit of exposure … To search within specific tag (s), enter them in square brackets: [maintenance] seat searches for mentions of "seat" within the [maintenance] tag. To find a specific phrase, enter it in quotes: "flat tire". To limit your search to just the title of a question, use title: followed by the search term. Likewise, search the body only (exclude the ... How do you know when to replace a furnace? Check out this guide to learn how to see the writing on the wall that your furnace might be failing. Expert Advice On Improving Your Home....
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