Question 7 Classify each of the following sets as finite, countable infinite, or uncountable (no proof...
please explain it step by step( not use the example with number) thanks 1. Determine whether each of these sets is countable or uncountable. For those that are countably infinite, prove that the set is countably infinite. (a) integers not divisible by 3. (b) integers divisible by 5 but not 7 c: i.he mal ilullilbers with1 € lex"Juual reprtrainiatious" Du:"INǐ lli!", of all is. d) the real numbers with decimal representations of all 1s or 9s. 1. Determine whether each...
What is the cardinality of each of the following sets '? (i.e., finite, countably infinite, or uncountably infinite) a. The set of all possible Java programs b.The set of all finite strings over the alphabet 10,1,2) c.iO, N, Q. R) d. R-Q
2. Determine whether the given sets are countable or uncountable. Justify each answer with a bijection (or table like we did with Q+) or using results from class/textbook. (a) {0, 1, 2} * N (b) A = {(x, y) : x2 + y2 = 1} (c) {0, 1} R Che set of all 2-element subsets of N (e) Real numbers with decimal representations consists of all 1s. (f) The set of all functions from {0,1} to N
all parts A-E please. Problem 8.43. For sake of a contradiction, assume the interval (0,1) is countable. Then there exists a bijection f : N-> (0,1). For each n є N, its image under f is some number in (0, 1). Let f(n) :-0.aina2na3n , where ain 1s the first digit in the decimal form for the image of n, a2 is the second digit, and so on. If f (n) terminates after k digits, then our convention will be...
Problem 22: Which of the following sets are countable? 1. N × Z 2. Q x Q x Q 3. R x R 4.(pe N p prime 7. Set of all infinite sequences of zeroes and ones. Problem 22: Which of the following sets are countable? 1. N × Z 2. Q x Q x Q 3. R x R 4.(pe N p prime 7. Set of all infinite sequences of zeroes and ones.
please solve the following, and explain what each means please. Problem 1) Classify the following sets as either tabular or rule-based defined, countable or uncountable, and finite or infinite. a) A= {20, 21, 22, ...} b) B= (5, 8, 9, 15} c) C= {0.1 <cs2.1} d) D= (3, 5, 7, 9, 11, 13} e) E-{3<e < 102} (only integers) %3D Problem 2) How many possible subsets can you create using the following universal set S? S= {2, 3, 4, 5,...
cept of a randon PROBLEMS 1.1-1. Specify the following sets by the rule method. A= (1,2,3), B = (8, 10, 12. 14), C (1, 3, 5, 7,... 1.1-2. Use the tabular method to specify a class of sets for the sets of Problem 1.1-1. uncountable, or finite or infinite. A (1), B= (x= 1}, C ={0 < integers), D = (children in public school No. 5), E={girls in public school No. 5), F = {girls in class in public 1.1-3....
The Finite Square Wel A more realistic version of the infinite square well potential has a finite well depth: -a V(x)--V for -a<x <a for x <-a,'r > a =0 This assignment will consider the bound states of a particle (of mass m) in this potential (i.e. total energy E <0). (1) Determine the general solutions to the time-independent Schrödinger equation for the three regions x <-a, -a<x <a, and > a. Write these solutions in terms of k and...
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...
Exercise 2: Finite element method We are interested in computing numerically the solution to a 2D Laplace equation u 0, The triangulated domain is given in the file mesh.mat on Blackboard. which contains the V × 2 nnatrix vertices storing the two coordinates of the vertices and a F × 3 matrix triangles in which each ro w J contains the indices in {1,····V) of the three vertices of the j-th triangle. a) Using for example MATLAB's triplot or trimesh...