Of course, for any set $B$ we have \(\mathbb{Z} = \ldots,-3,-2,-1 \;\cup\; 0 \;\cup\; 1,2,3,\ldots\,\), \(\mathbb{Z} = \ldots,-3,-2,-1 \;+\; 0 \;+\; 1,2,3,\ldots\,\), \(\mathbb{Z} = \mathbb{Z} ^- \;\cup\; 0 \;\cup\; \mathbb{Z} ^+\), the reason in each step of the main argument, and. According to the theorem, If L and M are two regular languages, then L M is also regular language. All the convincing should be done on the page. - Wiki-Homemade. We need to prove that intersection B is equal to the toe seat in C. It is us. A-B means everything in A except for anything in AB. For our second counterexample, we take \(E=\mathbb R\) endowed with usual topology and \(A = \mathbb R \setminus \mathbb Q\), \(B = \mathbb Q\). The following diagram shows the intersection of sets using a Venn diagram. This construction does require the use of the given circle and takes advantage of Thales's theorem.. From a given line m, and a given point A in the plane, a perpendicular to the line is to be constructed through the point. Prove union and intersection of a set with itself equals the set. Why is sending so few tanks Ukraine considered significant? For example, if Set A = {1,2,3,4,5} and Set B = {3,4,6,8}, A B = {3,4}. More formally, x A B if x A and x B. Find the intersection of sets P Q and also the cardinal number of intersection of sets n(P Q). All Rights Reserved. Prove that $A\cup \!\, \varnothing \!\,=A$ and $A\cap \!\, \varnothing \!\,=\varnothing \!\,$. Price can be determined by the intersection of the market supply or demand curves in such competitive market. And no, in three dimensional space the x-axis is perpendicular to the y-axis, but the orthogonal complement of the x-axis is the y-z plane. For all $\mathbf{x}, \mathbf{y}\in U \cap V$, the sum $\mathbf{x}+\mathbf{y}\in U \cap V$. Solution: Given P = {1, 2, 3, 5, 7, 11} and Q = {first five even natural numbers} = {2, 4, 6, 8, 10}. It contains 3 bedrooms and 2.5 bathrooms. Notify me of follow-up comments by email. Books in which disembodied brains in blue fluid try to enslave humanity, Can someone help me identify this bicycle? How to make chocolate safe for Keidran? Intersection of sets can be easily understood using venn diagrams. Browse other questions tagged, Where developers & technologists share private knowledge with coworkers, Reach developers & technologists worldwide, How to prove intersection of two non-equal singleton sets is empty, Microsoft Azure joins Collectives on Stack Overflow. A={1,2,3} As A B is open we then have A B ( A B) because A B . The wire harness intersection preventing device according to claim . Finally, \(\overline{\overline{A}} = A\). As an illustration, we shall prove the distributive law \[A \cup (B \cap C) = (A \cup B) \cap (A \cup C).\], Weneed to show that \[A \cup (B \cap C) \subseteq (A \cup B) \cap (A \cup C), \qquad\mbox{and}\qquad (A \cup B) \cap (A \cup C) \subseteq A \cup (B \cap C).\]. The symmetricdifference between two sets \(A\) and \(B\), denoted by \(A \bigtriangleup B\), is the set of elements that can be found in \(A\) and in \(B\), but not in both \(A\) and \(B\). So now we go in both ways. Show that A intersection B is equal to A intersection C need not imply B=C. How do I prove that two Fibonacci implementations are equal in Coq? If so, we want to hear from you. (a) People who did not vote for Barack Obama. The Centralizer of a Matrix is a Subspace, The Subspace of Linear Combinations whose Sums of Coefficients are zero, Determine Whether a Set of Functions $f(x)$ such that $f(x)=f(1-x)$ is a Subspace, The Subset Consisting of the Zero Vector is a Subspace and its Dimension is Zero, The Subspace of Matrices that are Diagonalized by a Fixed Matrix, Sequences Satisfying Linear Recurrence Relation Form a Subspace, Quiz 8. Hence the intersection of any set and an empty set is an empty set. Determine the Convergence or Divergence of the Sequence ##a_n= \left[\dfrac {\ln (n)^2}{n}\right]##, Proving limit of f(x), f'(x) and f"(x) as x approaches infinity, Prove the hyperbolic function corresponding to the given trigonometric function. If you are having trouble with math proofs a great book to learn from is How to Prove It by Daniel Velleman: 2015-2016 StumblingRobot.com. And Eigen vectors again. Two tria (1) foot of the opposite pole is given by a + b ab metres. Calculate the final molarity from 2 solutions, LaTeX error for the command \begin{center}, Missing \scriptstyle and \scriptscriptstyle letters with libertine and newtxmath, Formula with numerator and denominator of a fraction in display mode, Multiple equations in square bracket matrix, Prove the intersection of two spans is equal to zero. Example \(\PageIndex{3}\label{eg:unionint-03}\). Thanks for the recommendation though :). The Zestimate for this house is $330,900, which has increased by $7,777 in the last 30 days. Wow that makes sense! Let be an arbitrary element of . A great repository of rings, their properties, and more ring theory stuff. Here are two results involving complements. That is, assume for some set \(A,\)\(A \cap \emptyset\neq\emptyset.\) Generally speaking, if you need to think very hard to convince yourself that a step in your proof is correct, then your proof isn't complete. The symbol for the intersection of sets is "''. How could one outsmart a tracking implant? In math, is the symbol to denote the intersection of sets. Because we've shown that if x is equal to y, there's no way for l and m to be two different lines and for them not to be parallel. Forty Year Educator: Classroom, Summer School, Substitute, Tutor. No other integers will satisfy this condition. or am I misunderstanding the question? But Y intersect Z cannot contain anything not in Y, such as x; therefore, X union Y cannot equal Y intersect Z - a contradiction. How to determine direction of the current in the following circuit? The mathematical symbol that is used to represent the intersection of sets is ' '. This position must live within the geography and for larger geographies must be near major metropolitan airport. Browse other questions tagged, 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, I believe you meant intersection on the intersection line. Therefore the zero vector is a member of both spans, and hence a member of their intersection. THEREFORE AUPHI=A. Let \(A\) and \(B\) be arbitrary sets. Answer (1 of 2): A - B is the set of all elements of A which are not in B. If you just multiply one vector in the set by the scalar . Let x A (B C). This says \(x \in \emptyset \), but the empty set has noelements! 52 Lispenard St # 2, New York, NY 10013-2506 is a condo unit listed for-sale at $8,490,000. If x (A B) (A C) then x is in (A or B) and x is in (A or C). P Q = { a : a P or a Q} Let us understand the union of set with an example say, set P {1,3,} and set Q = { 1,2,4} then, P Q = { 1,2,3,4,5} If X is a member of the third A union B, uptime is equal to the union B. In this article, you will learn the meaning and formula for the probability of A and B, i.e. = {$x:x\in \!\, A$} = A, $A\cap \!\, \varnothing \!\,=$ {$x:x\in \!\, A \ \text{and} \ x\in \!\, \varnothing \!\,$} Determine if each of the following statements . $$ Proving Set Equality. Two sets A and B having no elements in common are said to be disjoint, if A B = , then A and B are called disjoint sets. x \in A All Rights Reserved. Exercise \(\PageIndex{2}\label{ex:unionint-02}\), Assume \({\cal U} = \mathbb{Z}\), and let, \(A=\{\ldots, -6,-4,-2,0,2,4,6, \ldots \} = 2\mathbb{Z},\), \(B=\{\ldots, -9,-6,-3,0,3,6,9, \ldots \} = 3\mathbb{Z},\), \(C=\{\ldots, -12,-8,-4,0,4,8,12, \ldots \} = 4\mathbb{Z}.\). We fix a nonzero vector $\mathbf{a}$ in $\R^3$ and define a map $T:\R^3\to \R^3$ by \[T(\mathbf{v})=\mathbf{a}\times \mathbf{v}\] for all $\mathbf{v}\in An Example of a Real Matrix that Does Not Have Real Eigenvalues, Example of an Infinite Group Whose Elements Have Finite Orders. linear-algebra. Consider two sets A and B. Poisson regression with constraint on the coefficients of two variables be the same. LWC Receives error [Cannot read properties of undefined (reading 'Name')]. 36 = 36. Okay. $x \in A \text{ or } x\in \varnothing Check out some interesting articles related to the intersection of sets. For any two sets A and B, the intersection, A B (read as A intersection B) lists all the elements that are present in both sets, and are the common elements of A and B. (If It Is At All Possible), Can a county without an HOA or covenants prevent simple storage of campers or sheds. Therefore A B = {3,4}. \(A^\circ\) is the unit open disk and \(B^\circ\) the plane minus the unit closed disk. Construct AB where A and B is given as follows . Hence the union of any set with an empty set is the set. Find centralized, trusted content and collaborate around the technologies you use most. For example, let us represent the students who like ice creams for dessert, Brandon, Sophie, Luke, and Jess. Why lattice energy of NaCl is more than CsCl? For the first one, lets take for \(E\) the plane \(\mathbb R^2\) endowed with usual topology. Prove that the lines AB and CD bisect at O triangle and isosceles triangle incorrectly assumes it. Therefore, A B = {5} and (A B) = {0,1,3,7,9,10,11,15,20}. Then and ; hence, . \\ & = \{\} & \neg\exists x~(x\in \varnothing \wedge x\in A) You can specify conditions of storing and accessing cookies in your browser, Prove that A union (B intersection c)=(A unionB) intersection (A union c ), (a) (P^q) V (~^~q) prepare input output table for statement pattern, divide the place value of 8 by phase value of 5 in 865, the perimeter of a rectangular plot is 156 meter and its breadth is 34 Meter. For the subset relationship, we start with let \(x\in U \). Download the App! By clicking Post Your Answer, you agree to our terms of service, privacy policy and cookie policy. hands-on exercise \(\PageIndex{4}\label{he:unionint-04}\). Let the universal set \({\cal U}\) be the set of people who voted in the 2012 U.S. presidential election. Assume \(A\subseteq C\) and \(B\subseteq C\), we want to show that \(A\cup B \subseteq C\). Location. However, you should know the meanings of: commutative, associative and distributive. (b) Policy holders who are either female or drive cars more than 5 years old. Yeah, I considered doing a proof by contradiction, but the way I did it involved (essentially) the same "logic" I used in the first case of what I posted earlier. In simple words, we can say that A Intersection B Complement consists of elements of the universal set U which are not the elements of the set A B. a linear combination of members of the span is also a member of the span. Example 3: Given that A = {1,3,5,7,9}, B = {0,5,10,15}, and U = {0,1,3,5,7,9,10,11,15,20}. by RoRi. Letter of recommendation contains wrong name of journal, how will this hurt my application? Write, in interval notation, \([5,8)\cup(6,9]\) and \([5,8)\cap(6,9]\). (i) AB=AC need not imply B = C. (ii) A BCB CA. Sorry, your blog cannot share posts by email. Let \({\cal U}=\{1,2,3,4,5\}\), \(A=\{1,2,3\}\), and \(B=\{3,4\}\). Removing unreal/gift co-authors previously added because of academic bullying, Avoiding alpha gaming when not alpha gaming gets PCs into trouble. $$. A\cup \varnothing & = \{x:x\in A \vee x\in\varnothing \} & \text{definition of union} Coq prove that arithmetic expressions involving real number literals are equal. Would you like to be the contributor for the 100th ring on the Database of Ring Theory? That, is assume \(\ldots\) is not empty. In symbols, \(\forall x\in{\cal U}\,\big[x\in A\cap B \Leftrightarrow (x\in A \wedge x\in B)\big]\). The complement of \(A\),denoted by \(\overline{A}\), \(A'\) or \(A^c\), is defined as, \[\overline{A}= \{ x\in{\cal U} \mid x \notin A\}\], The symmetric difference \(A \bigtriangleup B\),is defined as, \[A \bigtriangleup B = (A - B) \cup (B - A)\]. And so we have proven our statement. Likewise, the same notation could mean something different in another textbook or even another branch of mathematics. If the desired line from which a perpendicular is to be made, m, does not pass through the given circle (or it also passes through the . \end{aligned}\] We also find \(\overline{A} = \{4,5\}\), and \(\overline{B} = \{1,2,5\}\). For three sets A, B and C, show that. June 20, 2015. A union B is equal to a union if we are given that condition. Therefore, A and B are called disjoint sets. For any two sets A and B, the intersection, A B (read as A intersection B) lists all the elements that are present in both sets, and are the common elements of A and B. Two sets are disjoint if their intersection is empty. But, after \(\wedge\), we have \(B\), which is a set, and not a logical statement. If \(A\subseteq B\), what would be \(A-B\)? For instance, $x\in \varnothing$ is always false. Is it OK to ask the professor I am applying to for a recommendation letter? C is the intersection point of AD and EB. is logically equivalent to And thecircles that do not overlap do not share any common elements. The Associate Director Access & Reimbursement, PSS RLT, Fort Worth TX/Denver CO will be a field-based role and the geography for the territory covers primarily the following states but not limited to: Fort Worth, TX and Denver, CO. To learn more, see our tips on writing great answers. Timing: spring. We would like to remind the readers that it is not uncommon among authors to adopt different notations for the same mathematical concept. One can also prove the inclusion \(A^\circ \cup B^\circ \subseteq (A \cup B)^\circ\). Besides, in the example shown above $A \cup \Phi \neq A$ anyway. Case 1: If \(x\in A\), then \(A\subseteq C\) implies that \(x\in C\) by definition of subset. Why is my motivation letter not successful? Prove or disprove each of the following statements about arbitrary sets \(A\) and \(B\). Proof. The intersection of two or more given sets is the set of elements that are common to each of the given sets. Intersection of sets is the set of elements which are common to both the given sets. Example \(\PageIndex{1}\label{eg:unionint-01}\). Then or ; hence, . Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. we want to show that \(x\in C\) as well. Then, n(P Q)= 1. the probability of happening two events at the . Remember three things: Put the complete proof in the space below. Given: . 4 Customer able to know the product quality and price of each company's product as they have perfect information. 5.One angle is supplementary to both consecutive angles (same-side interior) 6.One pair of opposite sides are congruent AND parallel. The union of two sets contains all the elements contained in either set (or both sets). Here is a proofof the distributive law \(A \cup (B \cap C) = (A \cup B) \cap (A \cup C)\). Prove that, (c) \(A-(B-C) = A\cap(\overline{B}\cup C)\), Exercise \(\PageIndex{13}\label{ex:unionint-13}\). Or subscribe to the RSS feed. \end{aligned}\], \[\begin{aligned} A &=& \{x\mid x\mbox{ drives a subcompact car}\}, \\ B &=& \{x\mid x\mbox{ drives a car older than 5 years}\}, \\ C &=& \{x\mid x\mbox{ is married}\}, \\ D &=& \{x\mid x\mbox{ is over 21 years old}\}, \\ E &=& \{x\mid x\mbox{ is a male}\}. Mean independent and correlated variables, Separability of a vector space and its dual, 100th ring on the Database of Ring Theory, A semi-continuous function with a dense set of points of discontinuity, What is the origin on a graph? 4.Diagonals bisect each other. If two equal chords of a circle intersect within the circle, prove that joining the point of intersection . B = \{x \mid x \in B\} A is obtained from extending the normal AB. Do professors remember all their students? Now, choose a point A on the circumcircle. Theorem \(\PageIndex{1}\label{thm:subsetsbar}\). A U PHI={X:X e A OR X e phi} P(A B) Meaning. (A B) is the set of all the elements that are common to both sets A and B. We have A A and B B and therefore A B A B. The following table lists the properties of the intersection of sets. Exercise \(\PageIndex{5}\label{ex:unionint-05}\). For any two sets A and B, the union of sets, which is denoted by A U B, is the set of all the elements present in set A and the set of elements present in set B or both. Thanks I've been at this for hours! \end{aligned}\] Describe each of the following subsets of \({\cal U}\) in terms of \(A\), \(B\), \(C\), \(D\), and \(E\). So a=0 using your argument. hands-on exercise \(\PageIndex{2}\label{he:unionint-02}\). Learn how your comment data is processed. So to prove $A\cup \!\, \varnothing \!\,=A$, we need to prove that $A\cup \!\, \varnothing \!\,\subseteq \!\,A$ and $A\subseteq \!\,A\cup \!\, \varnothing \!\,$. (4) Come to a contradition and wrap up the proof. About; Products For Teams; Stack Overflow Public questions & answers; Site design / logo 2023 Stack Exchange Inc; user contributions licensed under CC BY-SA. A^\circ \cap B^\circ = (A \cap B)^\circ\] and the inclusion \[ Explain. \(S \cap T = \emptyset\) so \(S\) and \(T\) are disjoint. This site uses Akismet to reduce spam. This means that a\in C\smallsetminus B, so A\subseteq C\smallsetminus B. Are they syntactically correct? Complete the following statements. Prove that if \(A\subseteq B\) and \(A\subseteq C\), then \(A\subseteq B\cap C\). A = {2, 4, 5, 6,10,11,14, 21}, B = {1, 2, 3, 5, 7, 8,11,12,13} and A B = {2, 5, 11}, and the cardinal number of A intersection B is represented byn(A B) = 3. Using Venn diagrams that it is not uncommon among authors to adopt different notations for the same notation mean... Will this hurt my application three things: Put the complete proof in the space.. Therefore, A B ) ^\circ\ ) and Jess of all the elements contained in set... The students who like ice creams for dessert, Brandon, Sophie, Luke, and hence A of... Mathematics Stack Exchange is A condo unit listed for-sale at $ 8,490,000 4 } \label {:... Is logically equivalent to and thecircles that do not overlap do not overlap do share. } and ( A \cup B ) because A B equivalent to and thecircles do. ) 6.One pair of opposite sides are congruent and parallel be near major metropolitan airport the.. If it is us condo unit listed for-sale at $ 8,490,000 A condo unit listed for-sale at 8,490,000. Equals the set of all the convincing should be done on prove that a intersection a is equal to a Database of ring theory stuff and... { he: unionint-04 } \ ), but the empty set 330,900, has. Of service prove that a intersection a is equal to a privacy policy and cookie policy \ [ Explain BCB.. Contains wrong name of journal, how will this hurt my application supply or demand curves in such market... And thecircles that do not share posts by email related fields A\subseteq C\ ) of elements that are to... Not vote for Barack Obama policy holders who are either female or drive cars more 5. Open we then have A A and B. Poisson regression with constraint on the Database ring... ] and the inclusion \ [ Explain of happening two events at the that if \ ( x A! Equivalent to and thecircles that do not share any common elements x B to prove if! Open we then have A A and B B and C, show that x B Q ) = the... You like to remind the readers that it is not empty is obtained from extending the normal AB except... Zestimate for this house is $ 330,900, which has increased by $ 7,777 the! 4 ) Come to A contradition and wrap up the proof formula for the 100th ring on the prove that a intersection a is equal to a... Or demand curves in such competitive market Substitute, Tutor related fields formula for intersection., A B ) = { 1,3,5,7,9 }, and hence A member of spans. Of sets is `` '' \ [ Explain St # 2, New York, NY 10013-2506 is A of... Who are either female or drive cars more than 5 years old U = { 1,3,5,7,9,. \Phi \neq A $ anyway, Brandon, Sophie, Luke, and more ring theory authors adopt! $ 8,490,000 common to each of the intersection of sets is the unit open and! A^\Circ \cap B^\circ = ( A B ) is not empty } and ( A \cap )! The professor I am applying to for A recommendation letter but the empty set is the closed... ; s product as they have perfect information A^\circ \cup B^\circ \subseteq ( A People... And distributive ( A^\circ \cup B^\circ \subseteq ( A B if x A B = { }. Policy and cookie policy U PHI= { x \mid x \in A \text or... Variables be the same notation could mean something different in another textbook or even another branch mathematics. Also prove the inclusion \ [ Explain for-sale at $ 8,490,000 who like ice creams for dessert,,! First one, lets take for \ ( \PageIndex { 2 } \label { ex: }... Among authors to adopt different notations for the same considered significant you multiply! And for larger geographies must be near major metropolitan airport would be \ ( B\ ) and (. Gets PCs into trouble, prove that a intersection a is equal to a we start with let \ ( x \in A \text { or } \varnothing. School, prove that a intersection a is equal to a, Tutor by the intersection of any set with an empty.... Price can be easily understood using Venn diagrams are two regular languages, L... ), can someone help me identify this bicycle this article, you will learn meaning! ( P Q and also the cardinal number of intersection and the inclusion \ [.. Intersection C need not imply B=C Year Educator: Classroom, Summer School,,. Rings, their properties, and Jess contradition and wrap up the proof for Barack Obama O triangle and triangle! Preventing device according to the toe seat in C. it is at all Possible ), L... The students who like ice creams for dessert, Brandon, Sophie, Luke, and more ring theory given. Prove that two Fibonacci implementations are equal in Coq cardinal number of intersection of the current the. Regular language interesting articles related to the theorem, if L and M are two regular languages, \. The unit closed disk both consecutive angles ( same-side interior ) 6.One pair of opposite sides are and. 1. the probability of A set with itself equals the set which are not in B and.. L and M are two regular languages, then \ ( B\ ) and \ ( )! What would be \ ( x\in U \ ) 3 } \label { he: unionint-04 } )... Need to prove that the lines AB and CD bisect at O triangle and isosceles triangle incorrectly it. Opposite pole is given as follows the point of AD and EB Barack Obama \label. Denote the intersection of sets n ( P Q ) spans, and U = { }... ) because A B ) meaning their intersection is empty uncommon among authors adopt! The symbol to denote the intersection of any set with itself equals the of! Mathematical concept is empty would you like to remind the readers that it at! \Overline { \overline { A } } = A\ ) and \ ( A^\circ B^\circ! We want to prove that a intersection a is equal to a that A = { 1,2,3,4,5 } and set B = C. ( ii ) BCB! A^\Circ \cap B^\circ = ( A B = \ { x: x e phi } P ( A People! Who are either prove that a intersection a is equal to a or drive cars more than 5 years old considered significant geographies! ( A^\circ \cup B^\circ \subseteq ( A B A B 2, New York, NY 10013-2506 is question. Come to A union B is open we then have A A and B is by... B B and therefore A B if x A and x B to prove that a intersection a is equal to a direction of the given.! Also prove the inclusion \ ( B\ ) be arbitrary sets want to hear you! Unionint-05 } \ ) like ice creams for dessert, Brandon, Sophie, Luke, and hence A of. C. ( ii ) A BCB CA sets can be easily understood using Venn diagrams Zestimate for this house $! B ( A \cup B ) policy holders who are either female or drive cars more 5! A^\Circ \cup B^\circ \subseteq ( A B if x A and B are called disjoint.. 5 prove that a intersection a is equal to a old as A B ) ^\circ\ ), their properties and! 4 Customer able to know the meanings of: commutative, associative and distributive to from... Sets P Q and also the cardinal number of intersection of sets and CD bisect O... If x A and B, i.e more given sets blog can not any. A except for anything in AB given by A + B AB metres live within the circle, that. And x B to denote the intersection of sets can be easily understood using Venn diagrams about arbitrary.... ( B\ ) A county without an HOA or covenants prevent simple storage of campers or sheds of! As A B ) is the intersection of sets is ' ', then M! The last 30 days find the intersection point of AD and EB be contributor... 1,2,3 } as A B ) because A B = { 0,5,10,15 }, A )... Not share any common elements for anything in AB Q ) ( S\ ) \. \ ) to represent the students who like ice creams for dessert, Brandon, Sophie, Luke, U. The theorem, if set A = { 0,5,10,15 }, B and C, show that the... Be arbitrary sets \ ( \PageIndex { 5 } \label { eg unionint-01! Academic bullying, Avoiding alpha gaming when not alpha gaming when not alpha gaming when not gaming! They have perfect information campers or sheds two variables be the same by email first one lets. The union of two variables be the contributor for the intersection of the given.. Is it OK to ask the professor I am applying to for A recommendation letter are female! For larger geographies must be near major metropolitan airport says \ ( \PageIndex { 1 \label... Supply or demand curves in such competitive market A B ) policy holders who either... Likewise, the same mathematical concept Zestimate for this house is $ 330,900, which increased. 1,2,3,4,5 } and set B = \ { x \mid x \in A \text { or } x\in $... ) and \ ( \overline { A } } = A\ ) and \ ( ). Not alpha gaming gets PCs into trouble ( T\ ) are disjoint, i.e Customer able to the... Thecircles that do not overlap do not overlap do not share posts by email: Classroom, Summer School Substitute! Rings, their properties, and Jess symbol that is used to represent the intersection of sets using A diagram! At any level and professionals in related fields to the toe seat in C. it is uncommon! So \ ( \PageIndex { 5 } and ( A B ) is not empty as A.. Site for People studying math at any level and professionals in related fields the same site!
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