Write the irrationals

Assignment Help Mathematics
Reference no: EM131034752

1. Indicate the least upper bound of the following sets. If a set does not have a least upper bound, just write "none."

a. (2,3)

b. (2,3]

c. Q

d. Q∩ (1, π]

2. Prove each of the following using induction:

1. Let a∈R and a ≥ 1. Prove an ≥ a for all n∈N.

2. Prove that 1/2 + 1/4 + 1/8 + ? + 1/2n = 1 - 1/2n for all n∈N.

3. Using basic set notation, do the following:

a. Write Z in terms of N and 0

b. Write Q in terms of Z

c. Write the irrationals in terms of R and Q

4. There exists real numbers a, b, c such that a ≤ b, 0 < c and ac ≤ bc. (T/F)

5. Let a, b∈R with a ≠ 0, b ≠ 0. Prove that (ab)-1 = a-1b-1

6. Let q∈Q and x∈R - Q. Prove that q + x∈R - Q.

7. Let a∈R and let A∈ (0, ∞) with x ∈ (a - A, a + A). Then there exists some P∈ (0, A) such that x ∈ (a - P, a + P). (T/F)

Reference no: EM131034752

Questions Cloud

What is the probability of a favorable seismic survey : The Mobile Oil company has recently acquired oil rights to a new potential source of natural oil in Alaska. The current market value of these rights is $90,000. If there is natural oil at the site, it is estimated to be worth $800,000; however, the c..
What is the optimal production quantity for the card : Wholemark is an Internet order business that sells one popular New Year greeting card once a year. The cost of the paper on which the card is printed is $0.40 per card, and the cost of printing is $0.10 per card. What is the optimal production quanti..
Most important element in the external environment : Contemporary best-selling management books often argue that customers are the most important element in the external environment. Do you agree? In what company situations might this statement be untrue?
Security problems resulting from software defects : Realistically, users have no control over software at the code level, but there are steps a user can take to avoid the security problems resulting from software defects. What are the steps consumers can take to mitigate security vulnerabilities that ..
Write the irrationals : Write the irrationals in terms of R and Q. There exists real numbers a, b, c such that a ≤ b, 0
Describe and analyze the architecture of a selected system : Describe and analyze the architecture of a selected system in terms of class concepts presented in lectures. Your analysis should discuss how the architecting process led to the architectur
Reliability and validity important in selection measurement : Why are reliability and validity important in selection measurement? In what ways do they impact selection? What do you think is the main purpose of selection? How does it fit into HR's strategy?
What is the problem with power : What is the problem with power, according to Hoyk & Hersey: The more the power holder has at his or her disposal the means to punish and reward, the greater the temptation to use this power. The more the power holder uses his or her power, the more h..
An employer has the burden of showing-among other things : According to the court’s decision in Wexler v. Greenberg, an employer has the burden of showing, among other things: ___________

Reviews

Write a Review

 

Mathematics Questions & Answers

  Computing complex numbers

Write the expression in the standard form a + b i. First convert to rectangular form--- calculate the magnitude-- find reference angle--then the argument of z---

  Find the validity of following argument form

Find the validity of following argument form.

  What is the value for ssbetween treatments

A two factor analysis of variance produces SSA = 20, SSB = 40 and SSAxB = 90. For this analysis, what is the value for SSbetween treatments?

  Find the dimensions of the aquarium

The base of an aquarium with volume V = 220 is made of slate and the sides are made of glass. If slate costs five times as much (per unit area) as glass, find the dimensions of the aquarium that minimize the cost of the materials.

  What is its worth in 2006

Asaro was given $1,000 worth of stock in 2001. By 2004, the stock was worth $1,750. If the value of the stock increases at a constant rate, what is its worth in 2006?

  Question about equilibrium point

At a price of $1.90 per bushel, the annual U.S. supply and demand for barley are 410 million bushels and 455 million bushels, respectively. When the price rises to $2.70 per bushel

  Graphs of rational functions and in particular asymptotes

In photography fixed focal length means that the focal length is not adjustable. Photographers are unable to zoom in and out on a particular subject when using such a lens. Not being able to easily zoom in on a subject might seem like a huge disad..

  What is the mean and standard deviation of the number

What is the mean and standard deviation of the number of individuals with conditions caused by outside factors?

  What are the dimensions of the garden

The width of a rectangular garden is 2 feet shorter than one-half its length. If the perimeter of the garden is 32 ft., what are the dimensions of the garden?

  Use the p-value method

At a=0.05 does it appear that the average is lower than what was stated by the Tennis Industry Association? Use the P-Value method, and assume that the variable is approximately normally distributed.

  What is the approximate length

The area of an isosceles right triangle is 121 feet squared. what is the approximate length of each of the two equal sides?

  At what time has the amplitude of oscillation

At what time has the amplitude of oscillation of a spring-mass system with negligible friction decayed to 1/e of its original value? Does this time depend in a reasonable way on k, m, and c?

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