A dyadic rational is a number of the form k/2n for some k, n Z. Prove

Question:

A dyadic rational is a number of the form k/2n for some k, n ∈ Z. Prove that if a and b are real numbers and a < b, then there exists a dyadic rational q such that a < q < b.

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

Step by Step Answer:

Related Book For book-img-for-question

An Introduction to Analysis

ISBN: 978-0132296380

4th edition

Authors: William R. Wade

See More Books

Question Posted: Mar 29, 2016 03:53 AM

See More Questions

Decide which of the following statements are true and which are false. Prove the true ones and give counterexamples to the false ones. a) Suppose that E is a set. If there exists a function f from E...
Prove that if a < b are real numbers, then there is an irrational such that EER
If ∫∞ f(x) dx- is convergent and a and b are real numbers, show that f) dx + r) dx = f) dx + fx) dx
Zebra Corporation has always been an S corporation and is 100% owned by Paul. Paul has a basis of $40,000 in his Zebra stock at the beginning of the year. During the year, Zebra has an ordinary loss...
What is the difference between an internal reorganization and an external reorganization under formal bankruptcy procedures?
The probability that a car will enter an intersection within a period of x minutes is given by P(x) = 1 -e -0.5x Determine symbolically the elapsed time x when there is a 50-50 chance that a car has...
Dudley Ltd produces two products, X and Y, at a joint cost of $$480$ 000. The company can sell 620 000 units of product X for $$30$ per unit, or the units can be processed further at a cost of...
The College of Business and Public Administration at Kenton University has a copy machine on each floor for faculty use. Heavy use of the five copy machines causes frequent failures. Maintenance...
related theoretical construct - consciousness. The understanding of consciousness (what it is and how it occurs) has changed over time as neuroscience has advanced. define consciousness? How might...
All reliable analysts agree that a share of ABC Corp., selling today for $50, will be priced at either $65 or $45 1 year from now. They further agree that the probabilities of these events are 0.6...
Suppose that E, A, B R and E = A U B. Prove that if E has a supremum and both A and B are nonempty, then sup A and sup B both exist, and sup E is one of the numbers sup A or sup B.
Decide which of the following statements are true and which are false. Prove the true ones and give counterexamples to the false ones. a) If a > 0 and b 0, then (a + b) n > b n for all n N. b) If a...
What has been the impact of deregulation on the relative wages and employment of unionized workers in the airline and trucking industries? What factors help explain the difference in outcomes between...
A square bar carries a series of loads as shown in Figure P1-37. Compute the stress in each segment of the bar. All loads act along the central axis of the bar. -250 mm Rigid support A 80 kN B 30 mm...
Consider the truss below. Determine the force in members BC, CF, and FE using the method of sections and state if the members are in tension or compression. -2 m B 30 kN -2 m- E 30 kN -2 m 2 m 40 kN...
Black Bear Bakery ( BBB ) has 4 0 % debt and 6 0 % common equity. The YTM on their bonds is 8 % and their tax rate is 3 0 % . The required return on equity is 1 2 % . What is their Weighted Average...
What is the sensing mechanism behind vibration sensors? Thermo-resistive/capacitive Galvanomagnetic effect Photoelectric effect Piezoelectric/piezoresistive effect
Q.6. (a). Alternative method A and B using different tooling setups may be employed to manufacture a component on a particular machine tool whose operating cost (including wages of operator) is Rs....
Do you think students can benefit from training focused on challenging unethical behavior? Why or why not? Share your teams assessment with the rest of the class.
How do network effects help Facebook fend off smaller social-networking rivals? Could an online retailer doing half as much business compete on an equal footing with Amazon in terms of costs? Explain.
Integration provides a means to compute how much mass enters or leaves a reactor over a specified time period, as in where t1 and t2 = the initial and final times, respectively. This formula makes...
The outflow chemical concentration from a completely mixed reactor is measured as For an outflow of Q = 0.3 m3/s, estimate the mass of chemical in grams that exits the reactor from t = 0 to 20min. 16...
Ficks first diffusion law states that Where mass flux = the quantity of mass that passes across a unit area per unit time (g/cm2/s), D = a diffusion coefficient (cm2/s), c = concentration, and x =...
What is Fibonacci heap? Explain CONSOLIDATE operation with suitable example for Fibonacci heap ?
Discuss the impact of global supply chain disruptions, exacerbated by events like the COVID-19 pandemic, on inventory management strategies and market resilience across various industries?
A pharmaceutical retailer decided to host a website for home delivery of medicines according to user orders. The web application is deployed on a single Amazon EC2 instances. within a few months, the...

A dyadic rational is a number of the form k/2n for some k, n Z. Prove

Question:

Step by Step Answer:

By induction 2 n n Hence by the Archimedean Principle there is an n N such th...View the full answer

An Introduction to Analysis

Students also viewed these Numerical Analysis questions