Math 319 Solutions to Homework 8
... Problem 1. (a) Give an example of a sequence that is bounded above but not bounded below and that has a convergent subsequence. There are many examples. eg xn = 1 if n is even and xn = −n if n is odd. (b) Explain how √ to construct a monotonic increasing sequence of rational numbers that converges t ...
... Problem 1. (a) Give an example of a sequence that is bounded above but not bounded below and that has a convergent subsequence. There are many examples. eg xn = 1 if n is even and xn = −n if n is odd. (b) Explain how √ to construct a monotonic increasing sequence of rational numbers that converges t ...
The Real Number Line 0.1 THE REAL NUMBER LINE AND ORDER
... production varied from a high of $1325 to a low of $1200 per day. Find the high and low production levels during the month. SOLUTION Because it costs $2.50 to produce one unit, it costs 2.5x to produce x units. Furthermore, because the fixed cost per day is $500, the total daily cost of producing x ...
... production varied from a high of $1325 to a low of $1200 per day. Find the high and low production levels during the month. SOLUTION Because it costs $2.50 to produce one unit, it costs 2.5x to produce x units. Furthermore, because the fixed cost per day is $500, the total daily cost of producing x ...
Math is Beautiful
... Knowing our square roots, tells us when to stop looking for factors. 27’s square root is between 5 and 6 so I only need to count to 5 to find all of the numbers up FPM 27: 1, 3 – and we’re ready to climb down! ...
... Knowing our square roots, tells us when to stop looking for factors. 27’s square root is between 5 and 6 so I only need to count to 5 to find all of the numbers up FPM 27: 1, 3 – and we’re ready to climb down! ...
Formal Power Series and Algebraic Combinatorics S´ eries Formelles et Combinatoire Alg´ ebrique
... finite set of data. Specifically the number of points over Fq , Fq2 , . . . , and Fqg will be sufficient data to determine the number of points on a genus g algebraic curve over any other algebraic field extension. This observation begs the question of how the points over higher field extensions cor ...
... finite set of data. Specifically the number of points over Fq , Fq2 , . . . , and Fqg will be sufficient data to determine the number of points on a genus g algebraic curve over any other algebraic field extension. This observation begs the question of how the points over higher field extensions cor ...
XR3a
... Prove: The sum of an irrational number and a rational number is irrational. Proof: Let q be an irrational number and r be a rational number. Assume that their sum is rational, i.e., q+r=s where s is a rational number. Then q = s-r. But by our previous proof the sum of two rational numbers must be ra ...
... Prove: The sum of an irrational number and a rational number is irrational. Proof: Let q be an irrational number and r be a rational number. Assume that their sum is rational, i.e., q+r=s where s is a rational number. Then q = s-r. But by our previous proof the sum of two rational numbers must be ra ...
Lecture 1: Introduction to complex algebra
... either tends to +∞ or converges to a bounded real limit. Similarly, every monotonic decreasing sequence of real numbers must either tend to −∞ or to a finite real number. The set of all rational numbers form an ordered field, but is not complete. This means that the limit of a sequence of rational n ...
... either tends to +∞ or converges to a bounded real limit. Similarly, every monotonic decreasing sequence of real numbers must either tend to −∞ or to a finite real number. The set of all rational numbers form an ordered field, but is not complete. This means that the limit of a sequence of rational n ...
Chapter 8 Number Theory 8-1 Prime Numbers and Composite N
... n=d’q> n ． n =n, which is a contradiction. Thus q< n . Therefore, n has a divisor d= q satisfying 2 d n . ( ): If n has a divisor d which satisfies 2 d n , according to the definition of composite number, n is composite. Algorithm Testing whether an integer is prime ...
... n=d’q> n ． n =n, which is a contradiction. Thus q< n . Therefore, n has a divisor d= q satisfying 2 d n . ( ): If n has a divisor d which satisfies 2 d n , according to the definition of composite number, n is composite. Algorithm Testing whether an integer is prime ...
Sequences 9.1
... The primary focus of this chapter concerns sequences whose terms approach limiting values. These ...
... The primary focus of this chapter concerns sequences whose terms approach limiting values. These ...
CSNB143 – Discrete Structure
... being born in the same day (Monday to Sunday). Show that by using pigeonhole principle. Sol: Because there are 8 people and only 7 days per week, so Pigeonhole Principle says that, at least two or more people were being born in the same day. Note that Pigeonhole Principle provides an existence p ...
... being born in the same day (Monday to Sunday). Show that by using pigeonhole principle. Sol: Because there are 8 people and only 7 days per week, so Pigeonhole Principle says that, at least two or more people were being born in the same day. Note that Pigeonhole Principle provides an existence p ...