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 TOPICS This page:   sets    Search   Dr. Math See also the Internet Library:   sequences/sets and   set theory HIGH SCHOOL About Math Analysis Algebra    basic algebra    equations/graphs/      translations    linear algebra    linear equations    polynomials Calculus Complex Numbers Calculators/    Computers Definitions Discrete Math    permutations/    combinations Exponents    Logarithms Fibonacci Sequence/   Golden Ratio Fractals Functions Geometry    Euclidean/plane      conic sections/        circles      constructions      coordinate plane      triangles/polygons    higher-dimensional      polyhedra    non-Euclidean    practical geometry    symmetry/tessellations History/Biography Interest Logic Negative Numbers Number Theory Physics/Chemistry Probability Projects Puzzles Sequences/Series Sets Square/Cube Roots Statistics Transcendental   Numbers Trigonometry Browse High School Sets Stars indicate particularly interesting answers or good places to begin browsing. Selected answers to common questions:     Venn diagrams. Sets Containing an Infinite Number of Members [02/03/1998] Which of these two sets is larger - the set of all rational numbers, or the set of all irrational numbers? Sets, Injection, and Surjections [12/04/1998] If S is a set, such that every injection A from S to S is also a surjection, does S have the property that every surjection A from S to S is also an injection? Sets N, R, C, Z, and Q [01/22/2001] What are the exact and extensive definitions of the sets N, R, C, Z and Q? What relation do these sets bear to one another? Stirling Numbers [05/26/1999] Can you show how to evaluate Stirling Numbers of the first and second kinds? Subsets and Greatest Common Divisor [03/26/1999] A question on subsets and another on greatest common divisor (GCD). Subsets and Proper Subsets [07/10/1998] What is the difference between a subset and a proper subset? Subsets of Real Numbers and Infinity [08/22/2001] Am I correct in saying that both the whole number set and the integer set have an infinite number of numbers within them, and therefore are of the same size? Sum of Integers in a Set [06/19/2001] Consider the set of all four-digit integers, each of which is formed using the digits 1,2,3,5, or 7 at most once. Find the sum of the integers in this set. Sum of Set Numbers [07/02/2001] a_1, a_2, a_3,....a_15 are positive real numbers... what is the smallest possible value of the largest of a_1, a_2, a_3...a_15? Total Membership [08/20/1999] At a country club 35 people play golf, 28 swim, and 24 play tennis. Of these, 6 play golf and tennis only, 9 play golf and swim only, and 7 play tennis and swim only. 8 people do all three. How many members are there altogether? Transfinite Arithmetic [10/28/1997] What is transfinite arithmetic? I pretty much know what it means, but I am having trouble applying it to aleph-null. Transfinite Numbers [11/07/1997] I know that Georg Cantor discovered transfinite numbers, but what are they? Truth Table [04/14/1999] Prove that the complement of X intersects Y = X' union Y' without using a Venn diagram. Types of Numbers [10/30/1998] How are the different types of numbers related? For example, what about counting, whole, rational, irrational, integers, prime, ... ? Union and Intersection of Empty Family of Sets [03/20/2003] In what sensible way can we define the union and intersection of an empty family of sets? Unions and Intersections [05/10/1999] How are the union and intersection of sets related? Unions and Intersections: Proving Sets [10/17/1999] How can I verify a proof of the statement A - (B union C) = (A - B) intersect (A - C)? Universal Sets [08/19/2002] If I had to place the President of the U.S. in three universal sets, what are some possibilities? Unknown Numbers and a Venn Diagram [11/26/2001] The GCF of two numbers is 20 and the LCM is 840. One of the numbers is 120. Explain how to find the other number and use the Venn diagram method to illustrate. Venn Complications Set In [01/04/2013] A student struggles to draw a Venn diagram that represents the union and intersection of three sets or their complements. Before walking through an illustrated example, Doctor Peterson shows how to take apart such problems, then concludes with how to check your work. Venn Diagram - Choose One of Three Options [01/24/1999] Members of a computer class choose at least one of three options. How many are taking just one? ... Use a Venn diagram. Venn Diagram: Goops, Gorps, Gorgs [09/19/2002] Every Goop is a Gorp. Half of all Gorgs are Gorps. Half of all Gorps are Goops. There are 40 Gorgs and 30 Goops. No Gorg is a Goop. How many Gorps are neither Goops nor Gorgs? Venn Diagram of Natural Numbers [09/22/1999] How can I construct a Venn diagram comparing the numbers 1 through 100 in these 4 areas: odd, even, composite and prime? Venn Diagram of Our Number System [12/13/2002] I don't know how to include complex numbers that consist of a real part and an imaginary part. Can you please diagram this for me? Venn Diagram to Classify Quadrilaterals [01/02/2003] I am looking for a Venn diagram that will accurately display the relation among trapezoids, parallelograms, kites, rhombi, rectangles, and squares. What is a Loop? [10/06/1997] Further, exactly what is _an_ algebra? Thirdly, what is a Lie group? What is a Subset? [10/13/2001] I would like to know what a subset is. What is a Venn Diagram? [02/26/1998] What is a Venn Diagram? What is its use, definition, and what does it look like? Z Values in the Mandelbrot Set [04/27/2006] Could you please explain why for the Mandelbrot set the modulus for the resulting z value must remain less than 2? Page: [

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