Definition of multiplication

Assignment Help Mathematics
Reference no: EM131084793

Assignment 1-

1. Prove that the set of rational numbers

{x ∈ Q : x3 < 2}

is a real number. (This is what we would identify as 3√2.)

2. Using our definition of multiplication in class, show that if x and y are real numbers, then so is x · y.

3. Let s be an arbitrary real number.

(a) Based on s, what should the definition of -s be? Give an appropriate definition of -s, and prove that your definition of -s indeed makes it a real number.

(b) Prove that for any real number s we have that s + (-s) = 0.

4. Find, with full justification, the sup and inf of each of the following sets, or prove they don't exist.

(a) {21/2, 21/4, 21/8, . . .}

(b) {1 + (-2)n: n ∈ Z}

(c) {1 + ((-1)n/3n): n ∈ Z}

5. Suppose A and B are sets of real numbers. Prove that if A is a subset of B, then sup B ≥ sup A ≥ inf A ≥ inf B.

Reference no: EM131084793

Questions Cloud

Convert the image to gray scale : Convert the image to gray scale.
What the production on function and marginal output curve : Define and explain what the production on function and the marginal output curve are. Graph the production function and the marginal output curve. How are the two related? Indicate where the ranges of
Which of the following would be considered a status offense : Jim and his mom are in an argument because his mom found out that Jim has smoked marijuana. Jim's defense is, "Half the senior class is doing it!" How accurate is Jim's statement?
Difference between octopuses and mussels : What is the difference between octopuses and mussels regarding their circulatory systems? How does that difference have an effect on the mobility of these animals?
Definition of multiplication : Assignment 1. Using our definition of multiplication in class, show that if x and y are real numbers, then so is x · y. Based on s, what should the definition of -s be? Give an appropriate definition of -s, and prove that your definition of -s indee..
How government policies can influence economic growth : Discuss how government policies can influence economic growth. Analyze how monetary policy could influence the long-run behavior of price levels, inflation rates, costs, and other real or nominal variables.
Exchange of gases and other substances : What part of the vascular system carries out the exchange of gases and other substances between tissues?
Write the matlab program for the decoding process : Write the MATLAB program for the decoding process.
Determine the reaction curve for each of firm : Suppose a second firm enters the market, producing the same product. The total quantity supplied in the market is now the sum of the two producers, a Cournot Duopoly. Determine the equations for each firm’s Total Revenue, TR and for each firm’s Margi..

Reviews

Write a Review

 

Mathematics Questions & Answers

  Determine the number of colorings of the grid

Math 171: Abstract Algebra, Fall 2014- Assignment 6. A coloring of the grid below is an assignment of colors to its triangular cells, where any given triangular cell is colored red or green. Determine the number of colorings of the grid

  The fuel consumption c of micheal''s car

The fuel consumption c of Micheal's car ( measured in gallons per hour ) is a function of speed ( or velocity ) v of the car ( measured in miles per hour). Since he has owned the car for several years now, Micheal has determined through experimentati..

  Find the dimensions of the can which minimize the amount

A soda can is to hold 12 fluid ounces. Suppose that the bottom and the top are twice as thick as the sides. Find the dimensions of the can which minimize the amount of material used.

  In row of six houses each house is different color the

in a row of six houses each house is a different color. the house colors are blue purple red white green and yellow.

  Fifty-one sophomore 42 junior and 55 senior students are

the manager of a company wants to investigate job satisfaction among its employees. one morning after a meeting she

  Linear momentum to be conserved in closed system

Problem 1: What does it mean for linear momentum to be conserved in a closed system?

  Identification of the slope

Identification of the Slope, y-intercept, and x-intercept of the given equation.

  Model that will fit in the display case

A building is 180 feet tall. For a class project, Kari is to make a scale model of the building to place in the front hall display case. The display case is 23 inches tall. Which scale will allow her to make the tallest model that will fit in ..

  What is the probability that your first and second choices

Suppose that each time that you buy a car, you choose between Ford and General Motors. Suppose that each time after the first, you stay with the same company with probability 2/3 and switch with probability 1/3

  How fast is each train going

train A is 20 mph slower than train B, If train A travels 190 miles and it takes train B to travel 290 miles in the same distance, How fast is each train going?

  Find significant difference in automobile insurance rates

is there a significant difference in automobile insurance rates in different cities of comparable size in the u.s.? to

  Generalizing the findings to the target population

What are some of the limitations of this study that decrease the potential for generalizing the findings to the target population - distribution of Mental Health scores for men is normal, where are 99% of the men's mental health scores around the m..

Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd