Let K , be a compact set in R. Show that inf K and sup K

Question:

Let K ≠ θ, be a compact set in R. Show that inf K and sup K exist and belong to K.

Fantastic news! We've Found the answer you've been seeking!

Step by Step Answer:

Related Book For book-img-for-question

Introduction to Real Analysis

ISBN: 978-0471433316

4th edition

Authors: Robert G. Bartle, Donald R. Sherbert

See More Books

Question Posted: Apr 07, 2016 11:13 AM

See More Questions

Let K be a compact subset of a normed linear space X. For every > 0, there exists a finite-dimensional convex set S X and a continuous function h: K S such that S conv K and ||h(x) - x|| < for...
Let be a continuous preference relation on a compact set X. The set of best elements is nonempty and compact.
Let (N, w) be a TP-coalitional game with a compact set of outcomes X. For every outcome x X, let d (x) be a list of coalitional deficits arranged in decreasing order (example 1.49). Let di (x)...
Subsequent Events and Subsequently Discovered Facts. Michael Ewing is auditing the financial statements of Dallas Company for the year ended December 31, 2014. In concluding the process of gathering...
Elma Ward died in 2008. Frazier petitioned the court to probate a holographic will made by Ward. The document contains two typewritten sections, separated by one handwritten section. The document...
Match the parabolas with the following equations: x 2 = 2y, x 2 = -6y, y 2 = 8x, y 2 = -4x. Then find each parabolas focus and directrix. y X
Specify alternative standards useful in financial statement analysis. (p. 429) LO.1
The data shown in Table 11.E1 come from a production process with two observable quality characteristics: x1 and x2. The data are sample means of each quality characteristic, based on samples of size...
Stock Y has a beta of 1.30 and an expected return of 15.3%. Stock Z has a beta of 0.70 and an expected return of 9.3%. If the risk-free rate if 5.5% and the market risk premium is 6.8%, are these...
A shop works a 400- minute day. The manager of the shop wants an output of 200 units per day for the assembly line that has the elemental tasks shown in the table. Do the following: a. Construct the...
Prove that (0, 1) = n=1 (0, 1 + 1/n), as asserted in Example 11.1.6(a).
Let K be compact in R and let c R. Prove that there exists a point b in K such that |c - b| = sup{|c - x| : x K}.
In Problem perform the indicated operations and simplify. (m - n) (m + n)
Question (4) seen, 20 vehicles/km moving at 100 km/h and 30 vehicles/km traveling at 120 km/h. Two successive videos showing stationary traffic on the road were examined. Two groups of platoons were...
?In civil engineering, what is the main use of a slump test in concrete technology?
Explain the process of compression resin transfer molding(CRTM)?in composite manufacturing. What are the benefits of using CRTM for producing composite structures?
Explore the role of post-occupancy evaluation in commercial and industrial architecture. How do architects use feedback from building users to improve future designs?
Discuss the principles of geotechnical engineering in slope stability analysis. How can engineers assess slope stability, mitigate landslide risks, and design effective stabilization measures to...
How will you make an object persistent?
On March 31, 2018, Gardner Corporation received authorization to issue $30,000 of 9 percent, 30-year bonds payable. The bonds pay interest on March 31 and September 30. The entire issue was dated...
In a college football game, the quarterback attempted passes with the following results. Find the total gain or loss. Try Gain/Loss 1st 13-yd gain 2nd 12yd gain 3rd 21-yd gain
Graph the number on the number line.
- 5/9 / (- 5/6)
Mass LLp developed software that helps farmers to plow their fiels in a mannyue sthat precvents erosion and maimizes the effoctiveness of irrigation. Suny dale paid a licesnsing fee of $23000 for a...
Average Rate of Return The following data are accumulated by Lone Peak Inc. in evaluating two competing capital investment proposals: 3D Printer Truck Amount of investment $40,000 $50,000 Useful life...
4. (10 points) Valuation using Income Approach An appraiser appraises a food court and lounge and provides the following assessment: o O The building consists of 2 floors with the following (6)...

Let K , be a compact set in R. Show that inf K and sup K

Question:

Step by Step Answer:

Since K is bounded it follows that inf K exists in ...View the full answer

Introduction to Real Analysis

Students also viewed these Calculus questions