The following is written in my mathematical proofs book "Z4 consists of the four classes (sets of integers) [0],[1],[2],[3], where for r ∈ {0, 1, 2, 3}, [r] = {3q + r : q ∈ Z}" Im confused on why it's 3q+r and not 4q+r, I know there is a general rule but i cannot find it, I know why it consists of 4 classes, but somehow i dont get the "{3q + r : q ∈ Z}" part, please explain step by step.
The following is written in my mathematical proofs book "Z4 consists of the four classes (sets of integers) [0],[1],[2],[3], where for r ∈ {0, 1, 2, 3}, [r] = {3q + r : q ∈ Z}" Im confused on why it's 3q+r and not 4q+r, I know there is a general rule but i cannot find it, I know why it consists of 4 classes, but somehow i dont get the "{3q + r : q ∈ Z}" part, please explain step by step.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
The following is written in my mathematical proofs book
"Z4 consists of the four classes (sets of integers)
[0],[1],[2],[3], where for r ∈ {0, 1, 2, 3}, [r] = {3q + r : q ∈ Z}"
Im confused on why it's 3q+r and not 4q+r, I know there is a general rule but i cannot find it, I know why it consists of 4 classes, but somehow i dont get the "{3q + r : q ∈ Z}" part, please explain step by step.
![Z4 of integers modulo 4. Recall that Z4 consists of the four classes (sets of integers)
[0], [1], [2], [3], where for r = {0, 1, 2, 3}, [r] = {3q + r : q € Z}. Furthermore, if a, b = [r]
for some r with 0 ≤ r ≤ 3, then [a] = [b] and a = b (mod 4).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8e237d3f-b8e6-4775-a6f9-5671b153aef2%2F4a6b0ed2-93d7-4401-9867-945d53225358%2Fisd65e8_processed.png&w=3840&q=75)
Transcribed Image Text:Z4 of integers modulo 4. Recall that Z4 consists of the four classes (sets of integers)
[0], [1], [2], [3], where for r = {0, 1, 2, 3}, [r] = {3q + r : q € Z}. Furthermore, if a, b = [r]
for some r with 0 ≤ r ≤ 3, then [a] = [b] and a = b (mod 4).
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 3 steps with 4 images
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
