Question: 9. A real number x is defined to be a rational number providedthere exist integers m and n with n does not equal 0 such

9. A real number x is defined to be a rational number providedthere exist integers m and n with n does not equal 0 such that x=m/n.

A real number that is not a rational number is called anirrational number. It is known that if x is a positive rationalnumber, then there exist positive integers m and n with n does notequal 0 such that x= m/ n . Is the following proposition true orfalse? Explain. For each positive real number x, if x isirrational, then sqrt(x) is irrational.

Step by Step Solution

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

The proposition states For each positive real number x if x is irrational then sqrtx is irrational T... View full answer

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Students Have Also Explored These Related Statistics Questions!

CANMNMM January of this year. (a) Each item will be held in a record. Describe all the data structures that must refer to these records to implement the required functionality. Describe all the...

Here are definitions of sequences and trees with integer elements: type iseq = Nil | Cons of int * (unit -> iseq) type itree = Leaf of int | Branch of itree * itree (a) In an ascending sequence such...

Define the contextual-equivalence relation ` M =ctx M0 : for pairs of PCF terms M, M0 , PCF types , and PCF type environments . [3 marks] (ii) For PCF terms M and N with respective typings ` M : and...

# 7 (chapter 5)(40 points, Due on Friday November 11) Question 1. [3 points each] Use the definition of Limit of functions to prove that x2 2 . 5 5 2 lim x 3 x 1 1 (B) x 1 (A) lim x 0 if x 2 2x (C)...

1) Find all real solutions of: 4 2 2 x + x =3 2 x 4 + x23=0 4 2 2 2 x 2 x +3 x 3=0 x ( 21)=0 2 x 2 ( x 21)+ 3 ( 2 x2 +3 ) ( x 21 ) =0 ( 2 x2 +3 ) =0 2 2 x =3 3 x 2= 2 3 x= 2 3 x= i 2 2) Given the...

In a Hopfield neural network configured as an associative memory, with all of its weights trained and fixed, what three possible behaviours may occur over time in configuration space as the net...

Let i and j be positive integers. (i) Prove that there exist natural numbers a and b such that ai = bj+gcd(i, j). You may use standard results provided that you state them clearly. [4 marks] (ii) Let...

Consider the trigonometric series a0 2 + X r=1 (ar cos rx + br sin rx) where a0, a1, a2, . . . and b1, b2, . . . are constants and suppose that f(x) is a periodic function of x with period 2. (a)...

In this question you will be asked to reflect on a project you have been involved in or observed, in which a design evolved, or could have evolved, through applying a theory of user behaviour. You...

6. Let A = {x E Z |x 2 5a + 2 for some integer a}, B = {y E Z | y = 10!) 3 for some integer b}, and C = {z E Z | z = 106 + 7 for some integer C}. Prove or disprove each of the following statements....

(a) What linear speed must an Earth satellite have to be in a circular orbit at an altitude of 160 km above Earth's surface? (b) What is the period of revolution?

Purpose: To help familiarize you with the financial reporting of a real company in order to further your understanding of the chapter material you are learning. This case will help you to better...

What are Lakeside's largest two categories of property and equipment as of September 3 0 , 2 0 2 4 ? Describe in general terms the types of expenditures inclused in these categories. Lakeside's...

How many moles of a gas will occupy a volume of 0.64 L at a temperature of 333 K and a pressure of 22 atm ?

A friend of yours wants to become a client and start a new company Cyberdyne Systems, specializing in AI research. In order to get seed money, she wants to sell a rental property she has owned for...

Tulia Industries Inc. issued $10,000,000 face value of convertible ten year, 8% bonds on January 1, 2018 for $9,850,000. If the bonds had not been convertible, they would have sold at 96. Interest on...

5) Consider a product with constant annual demand of 900 units, fixed ordering cost of $80 per order, and inventory cost of 10% per unit per year. The product's cost price is $100 per unit. It is...

John Adams, Thomas Jefferson, and the Barbary Pirates: An Illustration of Relevant Costs for Decision Making Dennis Caplan, Assistant Professor Iowa State University. The concepts of incremental...

Can we put that she will be making weekly payroll deductions inthe amount of $52.75 to the housing equalling $211.00 monthly

Evaluate the following improper integrals. a) (b) (c) d) 14 dx I r n2 cosx sinsd log x dx

Suppose that (a, b) is an open interval, that f: (a, b) R is differentiable on (a, b), and that x0 (a, b) is a proper local maximum of f (see Exercise 4.1.8). a) Prove that given > 0, there exist...

Let V be open in Rn and V = {Vj}jN, W = {Wk}kN be coverings of V. If {j}jN is a Cp partition of unity on V subordinate to V and {k}kN is a Cp partition of unity on V subordinate to W, prove that {j...

Suppose that a company would like to purchase a fairly complicated machine to use in its manufacturing operation. Several different machines are available, and their prices are more or less...

Explain in your own words why swing weights produce meaningful weights for evaluating alternatives.

Explain in your own words the difference between preferential independence and utility independence.