The text states: if the decimal expansions of numbers a and b agree to k places, then

Question:

The text states: if the decimal expansions of numbers a and b agree to k places, then | a - b | ≤ 10−k. Show that the converse is false: For all k there are numbers a and b whose decimal expansions do not agree at all but |a − b| ≤ 10−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 graph theory

ISBN: 978-0131437371

2nd edition

Authors: Douglas B. West

See More Books

Question Posted: May 03, 2016 02:27 AM

See More Questions

Use Dirichlet's theorem, which states there are infinitely many primes in every arithmetic progression ak + b where gcd(a, b) = 1, to show that there are infinitely many primes that have a decimal...
Give an example of numbers a and b such that |a + b| < |a| + |b|.
A random sample of 10 stock market mutual funds was taken. Suppose that rates of returns on the population of all stock market mutual funds follow a normal distribution. a. The probability is 0.10...
Fill the blanks of the following table (last column) and find out the value of SDR in terms of U.S. dollars ($/SDR) and the value of U.S. dollars in terms of SDR (SDR/$) The exchange rate is...
San Falesco Company has a tax rate of 25 percent on taxable income. It is considering a capital project that will make the following annual contribution to operating income: Cash revenues...
Ed is undergoing surgery for an old football injury and must be anesthetized. The anesthesiologist knows Ed will be "under" when the concentration of sodium pentathol in his blood is at least 50...
Correlation and $t$-Statistics. Use the following steps to establish a relationship between the correlation coefficient and the $t$-statistic for the slope. a. Use algebra to check that...
The December 31, 2011, Balance Sheet and the 2012 Statement of Cash Flows for Snow, Inc., follow: Requirement 1. Prepare the December 31, 2012, balance sheet for Snow,Inc. Snow, Inc. Balance Sheet...
Acorn bLtd. has earnings per share of $3. It has 10 million shares outstanding and is trading at $35 per share. Acorn is considering buying a target company named Tofu Inc.. Tofu has earnings per...
John Hall tried to unclog a floor drain in the kitchen of the restaurant where he worked. He used a drain cleaner called Zaps Blue Lye that contained crystalline sodium hydroxide (the chemical name...
Express r1 = 0.27 as fraction. 100r1 - r1 is an integer. Then express r2 = 0.2666 . . . as a fraction.
Find the equation of the circle with center (2, 4): (a) With radius r = 3. (b) That passes through (1,1).
Enterprise coverage under the FLSA applies to employees who work for businesses with at least 20 employees and that do at least $1,500,000 a year in business. True or False
List five consumer goods that you have purchased recently. For each, note the source of a raw material that went into that good. For example, a computer mouse is made from plastic by the...
SLYMN Enterprises has a P/E ratio of 12.5 and a dividend payout ratio of 35%. If its equity cost of capital is 12.5%, what growth rate is its P/E ratio consistent with?
GHL, Inc., has a dividend payout ratio of 55%. Its cost of equity is 10.7% and its dividend growth rate is 4.9%. If its forward EPS is $5.68, what is your estimate of its stock price?
Next year, BHH Co. is expected to pay a dividend of $2.77 per share from earnings of $4.75 per share. The equity cost of capital for BHH is 12.1%. What should BHHs forward P/E ratio be if its...
CSH has EBITDA of $4 million. You feel that an appropriate EV/EBITDA ratio for CSH is 8. CSH has $9 million in debt, $3 million in cash, and 750,000 shares outstanding. What is your estimate of CSHs...
On January 1, 2024, White Water issues $600,000 of 7% bonds, due in 10 years, with interest payable semiannually on June 30 and December 31 each year. Required: Assuming the market interest rate on...
A 6-lb shell moving with a velocity ?? v0k explodes at point D into three fragments which hit the vertical wall at the points indicated. Fragments A, B, and C hit the wall 0.010 s, 0.018 s, and 0.012...
Show by means of an example that limxa [f(x) g(x)] may exist even though neither limxa f(x) nor limxa g(x) exists.
Is there a number a such that exists? If so, find the value of a and the value of the limit. 3x2 ax a 3 lim x-2 x 2
Use the given graph of to find a number such that if |x - 1| 1.2 0.8 0 0.7 1 1.1
Company name is Walmart, Inc. here is the link https://www.sec.gov/ix?doc=/Archives/edgar/data/104169/000010416923000020/wmt-20230131.htm Overview 1. The financial statements for your company are...
Congress would like to increase tax revenues by 19 percent. Assume that the average taxpayer in the United States earns $54,000 and pays an average tax rate of 15 percent. Required: a. If the income...
Best Solutions is a retail merchandiser selling computer equipment. Best uses the gross method of accounting for inventory purchases and sales, a perpetual inventory system with LIFO inventory...

The text states: if the decimal expansions of numbers a and b agree to k places, then

Question:

Step by Step Answer:

Let a 1 and b 09 T...View the full answer

Introduction to graph theory

Students also viewed these Calculus questions