Math 302 Exam 2 (with 100% correct answers)

What is a one-to-one correspondence? Explain how the sizes of two finite sets can be compared without counting. Give an example. correct answers A one-to-one correspondence when there is the same number of two objects. This can be used to compare the size of two finite sets by pairing each object with another object from the other set. Is there a one-to-one correspondence between UT students and UT EID's? Explain why or why not. correct answers There is a one-to-one correspondence because each student has a UT EID. Unless faculty have a UT EID then there would be more UT EIDs than there are students. Suppose a UT alum tells you their license plate is H00K3M. If you had a listing of all the registered vehicles in the United States, would you be able to identify the vehicle belonging to that person? Explain why or why not, using the idea of a one-to-one correspondence. correct answers You would be able to identify the vehicle because there is a one-to-one correspondence between licence plates and cars. A professor wishes to distribute one exam paper to each student in the class. What is the more efficient method: count students, or pass out exams? How does this relate to one-to-one correspondence? correct answers The most efficient method is to pass out exams. Each student present will receive one exam. This is the one-to-one crrespondence Are there an infinite number of grains of sand on the Earth? Explain. correct answers There is a finite number of grains of sand on Earth. It would be tedious but one could count or estimate the number of grains of sand. Define the term cardinality. When do two sets have the same cardinality? correct answers Cardinality is the term used to describe two infinite sets of objects that have the same "number" of objects. Two sets have the same cardinality when there is a one-to-one correspondence. Define or describe the following sets of numbers: natural numbers, integers, rational numbers, real numbers. correct answers Natural: the positive intergers 1, 2, 3, 4, ... Inegers: a whole number (not a fraction), can be either positive or negative. Rational: any number that can be expressed as a fraction. Real: any number that exists on the number line. Do the natural numbers and the even numbers have the same cardinality? Explain. correct answers Natural numbers and even numbers have the same cardinality because for every natural number you can multiply it by two. Do the natural numbers and the integers have the same cardinality? Explain. correct answers Natural numbers and integers have the same cardinality. 0, -1, 1, -2, 2, -3, 3 (imagine the snaking around)