Question: Show that the open interval a, b and the closed interval a, b are both convex sets of R with the natural order (example 1.20).

Show that the open interval a, b and the closed interval a, b are both convex sets of R with the natural order (example 1.20). The hybrid intervals a, b and a, b are also convex. Show that intervals are the only convex sets in R.

Step by Step Solution

★★★★★

3.29 Rating (178 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

Assume that This means that and Fo r every 0 1 1 1 and 1 1 Th... View full answer

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Document Format (1 attachment)

914-M-N-A-O (140).docx

120 KBs Word File

Students Have Also Explored These Related Numerical Analysis Questions!

Let a R and let f and g be real functions defined at all points x in some open interval containing a except possibly at x = a. Decide which of the following statements are true and which are false....

Let f C[a, b], and let p be in the open interval (a, b). a. Suppose f (p) 0. Show that a > 0 exists with f (x) 0, for all x in [p , p + ], with [p , p + ] a subset of [a, b]. b. Suppose f (p) =...

Assume that f and g continuous functionals on [a, b] that are differentiable on the open interval (a, b). Then there exists some x (a, b) such that Provided g(a) g(b) and g²(x) 0, this can be...

Recall that N is the set of positive integers and Q is the set of rational numbers. NOTE: "Limit point\Sequences - Part 2 (Week 4) Infinite Limits Definition. A sequence (sn) is said to diverge to +...

Lesson 12 Quiz (Show/Explain all Work) IST 230 Relations on Sets, Databases 1. Let A = {0, 1, 2, 3, 4, 5, 6, 7, 8} and B = {1, 2, 3, 4, 5, 6, 7, 8}. Now let R be a binary relation R from A to B such...

Show work/explanation where indicated. Answers without any work may earn little, if any, credit. You may type or write your work in your copy of the exam, or if you prefer, create a document...

. Answer the following questions. 1. (3 points) In Metropolis only taxicabs and privately owned automobiles are allowed to use the highway betwem the airport and downtown. The market for taxi cab...

Set Week Three During this week, we will look at ways of testing multiple (more than two) data samples at the same time. We will continue to use the data and assignment file that we opened in Week 2,...

Set Student Name: 1. Describe the relationship between two variables that have a correlation coefficient value: a. Near -1 b. Near 0 c. Near 1 2. Data was collected where a weightlifter was asked to...

Consider the trigonometric series a0 2 + X r=1 (ar cos rx + br sin rx) where a0, a1, a2, . . . and b1, b2, . . . are constants and suppose that f(x) is a periodic function of x with period 2. (a)...

Read chapter one of Ruppel New Developments and select one GASB statement from the list of statements available and do the following. Write a brief description of your selection and the impact the...

A nylon guitar string has a density of 7.20g/m and is a tension of 150 N. The fixed supports are distance D = 90.0 cm apart. The string is oscillating in the standing wave pattern shown in Figure....

QUESTION 2 8 A study has been conducted to determine if Product A should be dropped. Sales of the product total $ 4 0 0 , 0 0 0 per year; variable expenses total $ 2 7 0 , year. Fixed expenses...

The most common communication problem that occurs during negotiation is that a. Each side may misinterpret what the other side has said b. Each side may give up on the other side c. One side may try...

Three masses are suspended vertically by a series of identical springs where mass 1 is at the top and mass 3 is at the bottom. If g = 9.81 m/s2, m1 = 2 kg, m2 = 3 kg, m3 = 2.5 kg, and the k's = 10...

Recall from Sec. 8.2 that determining the chemistry of water exposed to atmospheric CO2 can be determined by solving five nonlinear equations (Eqs. 8.6 through 8.10) for five unknowns: cT, [HCO-3],...

Use Gauss elimination to solve: 8x 1 + 2x 2 2x 3 = 22 10x 1 + 2x 2 + 4x 3 = 4 12x 1 + 2x 2 + 2x 3 = 6 Employ partial pivoting and check your answers by substituting them into the original equations.

A stock has a price of $35 and an annual return volatility of 48 percent. The risk-free rate is 3.03 percent. Perform calculations in Excel. a. Calculate the European call and European put option...

Give product examples for each of the four types of competition Pure competition Monopolistic competition Oligopolistic competition Pure monopoly

A stock is currently priced at 19.25 when options are about to expire. What is the net profit of a PUT option with a strike price of 22.5 for the BUYER of the option if the premium paid was 2.75 ?...