Give an example of infinitely many sets of real numbers, called such that all four conditions...
Give an example of infinitely many sets of real numbers, called
such that all four conditions are satisfied at once. They are: i)
each set 
is bounded above. ii)
for all m and all n. iii) the intersection of 
and is empty whenever
m and n are not equal. iiii) for all n, 
is not an
element of .
Not sure what to do here, but I believe it can be done using the fact that there is infinitely many prime numbers and that every rational number has a unique representation in lowest terms.
Homework Answers
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Give an example of infinitely many sets of real numbers, called
such that all four conditions...
(c) (5 marks) Give an example of i. a sequence of real numbers that is strictly...
(c) (5 marks) Give an example of i. a sequence of real numbers that is strictly increasing and converges to zero; ii. a sequence of real numbers that is not monotonic and converges to 2 iii. a sequence of real numbers that is bounded and divergent. (d) (5 marks) Calculate the first four terms in the Laurent series representation of e*.
How many of the following sets of quantum numbers n,l,m I are allowed for the hydrogen...
How many of the following sets of quantum numbers n,l,m I are allowed for the hydrogen atom? (0) 1,0,0 (ii) 1,0,1 (iii) 1,1,0 (iv) 1,1,1 Select one: a. 4 b. none C. 3 d. 2 e. 1
10. Use 9 above to prove that the equation x^2 − 2y^2 = 1 has infinitely many solutions over Q. W...
10. Use 9 above to prove that the equation x^2 − 2y^2 = 1 has infinitely many solutions over Q. What can you conclude about the number of solutions over Z? (question9: For F as in 8, define N : F → Q by N(a + b√2) = a^2 − 2b^2. (i) Prove that N(αβ) = N(α)N(β), for all α,β ∈ F. (ii) Find an element u ∈ F such that N(u) = 1 and such that all of the...
An m×n array A of real numbers is a Monge array if for all i,j,k, and l such that 1≤i<k≤m and ...
An m×n
array A
of real numbers is a Monge array if for all i,j,k,
and l
such that 1≤i<k≤m
and 1≤j<l≤n
, we have
>A[i,j]+a[k,l]≤A[i,l]+A[k,j]>
In other words, whenever we pick two rows and two columns of a
Monge array and consider the four elements at the intersections of
the rows and columns, the sum of the upper-left and lower-right
elements is less than or equal to the sum of the lower-left and
upper-right elements. For example, the following...
Please help me solve 3,4,5 3- For all n € N, let an = 1. Let...
Please help me solve 3,4,5
3- For all n € N, let an = 1. Let S = {an in€ N}. 3-1) Use the fact that lim - = 0 and the result of Exercise 1 to show that 0 ES'. Ron 3-2) Use the result of Exercise 2 to show that S = {0}. 4- Prove that 4-1) N' = 0. 4-2) Q =R. 5- Recall that a set KCR is said to be compact if every open cover...
Problem 3. Prove Theorem 1 as tollows [Assume all conditions of the Theorem are met. In many part...
Problem 3. Prove Theorem 1 as tollows [Assume all conditions of the Theorem are met. In many parts, it will be useful to consider the sign of the right side of the formula-positive or negative- ad to write the appropriate inequality] (a) Since f"(x) exists on [a, brx) is continuous on [a, b) and differentiable on (a,b), soMean Value Thorem applies to f,on this interval. Apply MVTtof"m[x,y], wherc α zcysb. to show that ry)2 f,(x), İ.e. that f, is increasing...
I can't get my code to work on xcode and give me an output. #include <conio.h> #include <cstdlib> #incl...
I can't get my code to work on xcode and give me an output.
#include <conio.h>
#include <cstdlib>
#include <fstream>
#include <iomanip>
#include <iostream>
#include <string>
#include <vector>
using namespace std; // So
"std::cout" may be abbreviated to "cout"
//Declare global arrays
int dummy1[10];
int dummy2[10];
int dummy3[10];
int universalSet[] = { 1, 2, 3, 4, 5, 6, 7, 8,
9, 10 };
//Function to return statement "Empty thread" when the
resultant set is
empty
string isEmpty(int arr[])
{
string...
III. ASSIGNMENT 2.1 As discussed in class, the example program enumerates all possible strings (or if...
III. ASSIGNMENT 2.1 As discussed in class, the example program enumerates all possible strings (or if we interpret as numbers, numbers) of base-b and a given length, say l. The number of strings enumerated is b l . Now if we interpret the outputs as strings, or lists, rather than base-b numbers and decide that we only want to enumerate those strings that have unique members, the number of possible strings reduces from b l to b!. Furthermore, consider a...
please answer all prelab questions, 1-4. This is the prelab manual, just in case you need...
please answer all prelab questions, 1-4.
This is the prelab manual, just in case you need background
information to answer the questions. The prelab questions are in
the 3rd photo.
this where we put in the answers, just to give you an
idea.
Lab Manual Lab 9: Simple Harmonic Oscillation Before the lab, read the theory in Sections 1-3 and answer questions on Pre-lab Submit your Pre-lab at the beginning of the lab. During the lab, read Section 4 and...
CMPS 12B Introduction to Data Structures Programming Assignment 2 In this project, you will write...
can i get some help with this program
CMPS 12B Introduction to Data Structures Programming Assignment 2 In this project, you will write a Java program that uses recursion to find all solutions to the n-Queens problem, for 1 Sns 15. (Students who took CMPS 12A from me worked on an iterative, non-recursive approach to this same problem. You can see it at https://classes.soe.ucsc.edu/cmps012a/Spring l8/pa5.pdf.) Begin by reading the Wikipcdia article on the Eight Queens puzzle at: http://en.wikipedia.org/wiki/Eight queens_puzzle In...
(c) (5 marks) Give an example of i. a sequence of real numbers that is strictly increasing and converges to zero; ii. a sequence of real numbers that is not monotonic and converges to 2 iii. a sequence of real numbers that is bounded and divergent. (d) (5 marks) Calculate the first four terms in the Laurent series representation of e*.
How many of the following sets of quantum numbers n,l,m I are allowed for the hydrogen atom? (0) 1,0,0 (ii) 1,0,1 (iii) 1,1,0 (iv) 1,1,1 Select one: a. 4 b. none C. 3 d. 2 e. 1
An m×n
array A
of real numbers is a Monge array if for all i,j,k,
and l
such that 1≤i<k≤m
and 1≤j<l≤n
, we have
>A[i,j]+a[k,l]≤A[i,l]+A[k,j]>
In other words, whenever we pick two rows and two columns of a
Monge array and consider the four elements at the intersections of
the rows and columns, the sum of the upper-left and lower-right
elements is less than or equal to the sum of the lower-left and
upper-right elements. For example, the following...
Please help me solve 3,4,5
3- For all n € N, let an = 1. Let S = {an in€ N}. 3-1) Use the fact that lim - = 0 and the result of Exercise 1 to show that 0 ES'. Ron 3-2) Use the result of Exercise 2 to show that S = {0}. 4- Prove that 4-1) N' = 0. 4-2) Q =R. 5- Recall that a set KCR is said to be compact if every open cover...
Problem 3. Prove Theorem 1 as tollows [Assume all conditions of the Theorem are met. In many parts, it will be useful to consider the sign of the right side of the formula-positive or negative- ad to write the appropriate inequality] (a) Since f"(x) exists on [a, brx) is continuous on [a, b) and differentiable on (a,b), soMean Value Thorem applies to f,on this interval. Apply MVTtof"m[x,y], wherc α zcysb. to show that ry)2 f,(x), İ.e. that f, is increasing...
I can't get my code to work on xcode and give me an output.
#include <conio.h>
#include <cstdlib>
#include <fstream>
#include <iomanip>
#include <iostream>
#include <string>
#include <vector>
using namespace std; // So
"std::cout" may be abbreviated to "cout"
//Declare global arrays
int dummy1[10];
int dummy2[10];
int dummy3[10];
int universalSet[] = { 1, 2, 3, 4, 5, 6, 7, 8,
9, 10 };
//Function to return statement "Empty thread" when the
resultant set is
empty
string isEmpty(int arr[])
{
string...
please answer all prelab questions, 1-4.
This is the prelab manual, just in case you need background
information to answer the questions. The prelab questions are in
the 3rd photo.
this where we put in the answers, just to give you an
idea.
Lab Manual Lab 9: Simple Harmonic Oscillation Before the lab, read the theory in Sections 1-3 and answer questions on Pre-lab Submit your Pre-lab at the beginning of the lab. During the lab, read Section 4 and...
can i get some help with this program
CMPS 12B Introduction to Data Structures Programming Assignment 2 In this project, you will write a Java program that uses recursion to find all solutions to the n-Queens problem, for 1 Sns 15. (Students who took CMPS 12A from me worked on an iterative, non-recursive approach to this same problem. You can see it at https://classes.soe.ucsc.edu/cmps012a/Spring l8/pa5.pdf.) Begin by reading the Wikipcdia article on the Eight Queens puzzle at: http://en.wikipedia.org/wiki/Eight queens_puzzle In...
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