4. Let A be a set of real numbers such thatinf{|a1 – a2| : a1, a2 E A a1 # a2} > 0.Prove that every Cauchy sequence of elements in A converges to a point of A.

Answered: 4. Let A be a set of real numbers such…

4. Let A be a set of real numbers such that inf{a1a2a1, a2 € A a1 # a2} > 0. Prove that every Cauchy sequence of elements in A converges to a point of A.

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter10: Sequences, Series, And Probability

Section10.1: Infinite Sequences And Summation Notation

Problem 32E

See similar textbooks

Related questions

Q: Two numbers when multiplied equals 104. one number is x and the other number is greater than x by 5…

Q: Use the Laplace transform to solve the given initial-value problem. dy dt y(t) = 1 - exp(-t) sinh(t)…

Q: 4.9. Show that if f has a bounded derivative on [a, b], then f is of bounded variation.

Q: Which of the following subsets of R³×3 are subspaces of R³×³? A. The non-invertible 3 x 3 matrices…

Q: 39. y (0, 3) C.4 D. 7 R What is the length of RL? A. 6 B. 5 L (4,0) X

A: In the given problem Length of the line is RL=5 Hence option (C) is correct.

Q: 4.3. Show that the function f(x) = Ja² sin, if x 0, 0, if x = 0 is not of a bounded variation over…

Q: 42 -(-48)x; X(0)-(1) is -30 The solution of the system X'= Select the correct answer. O a. * x =((…

A: Introduction: In solving a system of first order differential equation, eigenvalues and eigenvectors…

Q: DUSES 4+ + + x + 8 = 4 X=4 Би мојо! Әч Јәр

A: We have to find the area between y=x2 & y=8+x using graphing utility

Q: For each A, B, C below, determine whether {A, B, C) is is linearly independent or linearly…

Q: What is the area of the parallelogram formed by the two vectors = (1,5) and 7 = (-3,-2)?

A: We need to find the area of a parallelogram formed by the given two vectors u→=(1, 5), v→=(-3, -2)

Q: A brine solution of salt flows at a constant rate of 7 L/min into a large tank that initially held…

A: Let x(t) be the mass of salt in the tank at the time t.xi(t) be the amount of solution coming in to…

Q: Determine a suitable form for Y(t) if the method of undetermined coefficients is to be used. y (4) +…

A: Introduction: The method of undetermined coefficient is a method to determine the particular…

Q: 4. Find the complete general solution, putting in explicit form of the ODE x"-4x'+4x=2 to find the…

A: Introduction: A second-order differential equation is a particular kind of differential equation…

Q: Write the interpretation of independent vectors, span, basis and dimension. Take the example of…

A: We have to give the interpretation of independent vectors, span, basis and dimension by taking the…

Q: Given that F(x, y, z) = (e", xe" + e², ye) is a conservative vector field. a. Find a potential…

Q: Prove the following statement by proving the contrapositive. Prove: If 3n +7 is an odd integer, then…

Q: G= G(2:3,:) G= ? 1 4 7 2 5 8 3 6 9

A: It is provided that: G=123456789. We need to evaluate the expression: G2:3,: using a computer…

Q: A continuous distribution is described as follows: The distribution effectively forms a line…

Q: Sketch the region that corresponds to the given inequalities. 10x + 5y ≥ 50 5x + 10y ≥ 50 5x +…

Q: 1. When the function x is of a single variable e.g x= x(t) then the differential is termed (a) First…

A: The answer is ordinary differential equation. Option C is correct.

Q: The population of a certain inner-city area is estimated to be declining according to the model P(1)…

Q: Prove that coo cannot be a Banach space under any norm.

A: To prove: c00 cannot be a Banach space under any norm.

Q: 2. Given that F(x, y, z) = (e", xe" + e*, ye*) is a conservative vector field. a. Find a potential…

Q: c-[and D-191 = C = a) Compute: 3C-5D @ @ (iv) C and D. DC det (C) C-¹ b) Find the eigenvalues and…

Q: @ Determine if the following series is convergent on divergent ntl ² حل Σ (-1) n=t ²³+4

Q: Solve for x. 4.25x = 21.

Q: Find the particular solution of the differential equation (x+1)+ xy = (x + 1)²e-³x, y(0) = 4

A: *By Bartleby policy I have to solve only first one as these are all unrelated problems.These are all…

Q: Evaluate the iterated integral below. π 1 S. *S'y cos (x) dy 0 0 dx

A: Here in above question we have to find iterated integral.

Q: II. Solves problems involving linear equation in two variables Write an equation in the…

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: DERIVATIONS PROVE THAT THESE ARGUMENTS ARE VALID no truth tables ((PVT)-(SR)) + (-S-P) 1.…

Q: A manufacturing company makes two types of water skis, a trick ski and a slalom ski. The relevant…

Q: 2. State why the function f(z) = 2z²-3-ze²+e-² is entire.

A: Introduction: Every complex valued function corresponds to a power series. The convergence of power…

Q: Compute the volume of the solid bounded by the hemisphere z = √4c²-x² - y² and the horizontal plane…

A: Given the solid bounded by the hemisphere z=4c2-x2-y2 and the horizontal plane z=c.

Q: Let B := (b₁,b2, b3) be an orthonormal basis of R³ such that b3 = √/2 * Let V = 0 and let C₁, C2, C3…

A: Given B:=(b1, b2, b3) be an orthonormal basis of ℝ3 such that b3=121-10. Also given v=0-1-1, and…

Q: (a) cos(iz) = cos(iz) (b) sin(iz) = sin (iz) for all z; if and only if z = nлi (n = 0, +1, +2, ...).

Q: What is the area of the parallelogram formed by the two vectors = (1,5) and = (-3,-2)?

Q: c) x²y" + 5xy + 4y = 0, x > 0, y(1) = 5, y(1) = -9

A: To solve the following problem, we use the couchy homogeneous linear differential equations method.

Q: Suppose U = {1, 2, 3, 4, 5, a, b, c) is a universal set with the subset A = {a, b, c, 1, 2, 3, 4).…

Q: 4.4. Show that the function f(x) = Sx² cos 1, if x = 0, ૨૦. if x = 0 is a BV-function over the…

Q: A tailor has the following materials available: 16 square yards of cotton, 11 square yards of silk,…

Q: JA ITI system is described by the D.E. y +6 Y+8y=2X(+) find h(t), then find y(t) if X(t) = te²t tro-

Q: The Euler path of the graph K₁ is h O a O b O c Od g C e К1 d (h, a, b, f, g, e, d, j, c, a) (g. f,…

A: The only way to identify Euler path ~ Use every edge EXACTLY once + start & end at different…

Q: you didnt answer the rest of the questions on the page

Q: the if f₁ (t) properties of Fourier transform ē at ult) JF.T ماز =ff(t) ējwt dt 0 How did he get the…

Q: The half-life of Palladium-100 is 4 days. After 20 days a sample of Palladium- 100 has been reduced…

Q: For the curve x³ + y² + 2xy = 4x Find all the x-intercepts of the curve. Then for each x-intercept…

Q: Find the simple interest and future value of a loan of $20,000 for 4 years at an interest rate of 5%…

Q: R = 8 Σ n = 1 I = xn 1.3.5. (2n-1) Find the interval, I, of convergence of the series. (Enter your…

A: Follow the steps.

Q: Maximize Z=150x1+125x2+95x3 Subject to Assembly Inspection Packaging D 3.5x1 +2.75x2 +1.25x3 <= 150…

Q: e -t.6t rule

Question

4. Let A be a set of real numbers such that
inf{|a1 – a2| : a1, a2 E A a1 # a2} > 0.
Prove that every Cauchy sequence of elements in A converges to a point of A.

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Step by step

Solved in 2 steps

SEE SOLUTION Check out a sample Q&A here