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3 Pages
HW s 3-3
School: George Mason University
Course: MATH 290
MATH 290 WRITING ASSIGNMENT 3 SOLUTIONS 1. Define the Fibonacci sequence {f1, f2, f3, ...} by f1 = f2 = 1 and for n > 2, fn = fn−1 + fn−2. Use induction to prove that for all natural numbers n, fn = αn − βn α − β , where α = ...
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3 Pages
hw4sol
School: Carnegie Mellon University
Course: MATH 21127
... Page 1 of 3 1. 1. Note that 1 is not in the image of f(x, y) = x+y. There are no two natural numbers x and y such that x + y = 1. Thus f is not surjective. ...
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2 Pages
quiz 1 solutions
School: University Of California, Riverside
Course: MATH CS11
Math 11 Name: Spring 2012 SID: Quiz 1 1. (6 points) Let X and Y be sets and |X|,|Y | denote the number of elements in X and Y respectively (which we will assume are natural numbers). Suppose |X| = n, |Y | = m, and |X n Y | = k. What is (a) |XUY | ...
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2 Pages
222a1s
School: University Of Victoria
Course: MATH 222
MATH 222 FALL 2011, Assignment One (Answer key) 1. Let f : N → N be defined by f = {(x, 3x) : x ∈ N}. Let S be the set of all even natural numbers. Find the following sets. (a) f(S). f(S) = {6k : k ∈ N}. (b) f−1(S). f−1(S) = S. (c) f−1...
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Natural Numbers Homework Help View All Natural Numbers Study Resources Homework Help
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3 Pages
hw4sol
School: Carnegie Mellon University
Course: MATH 21127
... Page 1 of 3 1. 1. Note that 1 is not in the image of f(x, y) = x+y. There are no two natural numbers x and y such that x + y = 1. Thus f is not surjective. ...
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1 Page
hw5
School: Binghamton University
Course: MATH 330
... b) Prove that n < 2n for every natural number nc) Let a, b be natural numbers. Prove that if a. ... b) Prove that n < 2n for every natural number n c) Let a, b be natural numbers. Prove that if a|b then a ≤ b. Make sure you justify ...
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2 Pages
01
School: University Of British Columbia
Course: MATH 320
Math 320 Assignment 1, out of ? send corrections to db5dmath.ubc.ca The natural numbers N = cfw_1, 2, . . . have properties that we will use without proof because I think you learned them in Math 220. ...
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7 Pages
HW4 Solutions
School: Carnegie Mellon University
Course: MATH 21-127
... 3.43 - From the solutions manual: 3.44 - In this problem we must determine which natural numbers can be expressed as the some of a nonnegative number of 3's and a nonnegative number of 10's. ...
Natural Numbers Lab Reports View All Natural Numbers Study Resources Lab Reports
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43 Pages
lecture1
School: Cairo University
Course: MATHEMATIC Mathematic
... University of Oslo August 26, 2010 Notation ▶ The set of natural numbers, integers, rational numbers, real numbers, and complex numbers are denoted by N,Z,Q,R,C, respectively. ▶ R n(Cn ...
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3 Pages
Natural Numbers Notes View All Natural Numbers Study Resources Notes
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3 Pages
HW s 3-3
School: George Mason University
Course: MATH 290
MATH 290 WRITING ASSIGNMENT 3 SOLUTIONS 1. Define the Fibonacci sequence {f1, f2, f3, ...} by f1 = f2 = 1 and for n > 2, fn = fn−1 + fn−2. Use induction to prove that for all natural numbers n, fn = αn − βn α − β , where α = ...
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2 Pages
quiz 1 solutions
School: University Of California, Riverside
Course: MATH CS11
Math 11 Name: Spring 2012 SID: Quiz 1 1. (6 points) Let X and Y be sets and |X|,|Y | denote the number of elements in X and Y respectively (which we will assume are natural numbers). Suppose |X| = n, |Y | = m, and |X n Y | = k. What is (a) |XUY | ...
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2 Pages
222a1s
School: University Of Victoria
Course: MATH 222
MATH 222 FALL 2011, Assignment One (Answer key) 1. Let f : N → N be defined by f = {(x, 3x) : x ∈ N}. Let S be the set of all even natural numbers. Find the following sets. (a) f(S). f(S) = {6k : k ∈ N}. (b) f−1(S). f−1(S) = S. (c) f−1...
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117 Pages
MAT371
School: Arizona State University
Course: MAT 371
... 2 Chapter 1 The real numbers 1.1 Ordered Fields [1, Sec.11] We use the following symbols: N set of natural numbers (without 0), N = {1, 2,...} Z set of integers, Z = {...2,−1,0, 1,2,...} Q set of rational numbers R set of real numbers C ...
Natural Numbers Test Prep View All Natural Numbers Study Resources Test Prep
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1 Page
325S16Q5sols
School: University Of Nebraska, Lincoln
Course: MATH 325
... 1. (10 points) Use induction to prove that 3+11+19+···+8n-5) = 4n2 -n for all natural numbers n. If at any point, you use circular logic (assume the statement you are trying to prove), you will receive no credit. ...
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1 Page
Camp Problem 6B Final
School: Duquesne University
Course: MATHEMATIC 250
Brianna Camp Theorem 6B. For all natural numbers n, n ∑ i=1 1 4i2 - 1 = n 2n + 1 . Proof. ... Therefore, by the Principle of Mathematical Induction, n ∑ i=1 1 4i2 - 1 = n 2n + 1 for all natural numbers n. 1
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10 Pages
Lesson 1a - Sets, Tuples, Fields, and Inverses
School: Carleton University
Course: MATH 1107
... B = {n2 : n = 1, 2, 3, } Some common sets you should know: ∅ - Empty set N Natural Numbers {1,2,3, } Z Integers { , -2, -1, 0, 1, 2, } ...
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2 Pages
Concept Questions and Review Guide Section 1 - Sets of Numbers
School: Lewis University
Course: MATH 13-325
... Page 1 of 2 Concepts Questions 1. What is the set of natural numbers? 2. What symbol is used to denote the set of natural numbers? ...
