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EXAMPLE 0.8 Consider the function f: {0, 1, 2, 3, 4} {0, 1, 2,3,4}. f(n) 1 2 3 4 0 n 0 1 2 - 3 4 This function adds 1 to its input and then outputs the result modulo 5. A number modulo m is the remainder after division by m. For example, the minute hand on a clock face counts modulo 60. When we do modular arithmetic, we define Zm = {0, 1, 2,...,m 1}. With this notation, the aforementioned function f has the form f: 25-25.

EXAMPLE 0.8 Consider the function f: {0, 1, 2, 3, 4} {0, 1, 2,3,4}. f(n) 1 2 3 4 0 n 0 1 2 - 3 4 This function adds 1 to its input and then outputs the result modulo 5. A number modulo m is the remainder after division by m. For example, the minute hand on a clock face counts modulo 60. When we do modular arithmetic, we define Zm = {0, 1, 2,...,m 1}. With this notation, the aforementioned function f has the form f: 25-25.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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EXAMPLE 0.8 Consider the function f: {0, 1, 2, 3, 4} {0, 1, 2, 3, 4}. f(n) 1 2 3 4 0 N 0 1 2 3 4 This function adds 1 to its input and then outputs the result modulo 5. A number modulo m is the remainder after division by m. For example, the minute hand on a clock face counts modulo 60. When we do modular arithmetic, we define Zm = {0, 1, 2,...,m 1}. With this notation, the aforementioned function f has the form f: 25 25.
Transcribed Image Text:EXAMPLE 0.8 Consider the function f: {0, 1, 2, 3, 4} {0, 1, 2, 3, 4}. f(n) 1 2 3 4 0 N 0 1 2 3 4 This function adds 1 to its input and then outputs the result modulo 5. A number modulo m is the remainder after division by m. For example, the minute hand on a clock face counts modulo 60. When we do modular arithmetic, we define Zm = {0, 1, 2,...,m 1}. With this notation, the aforementioned function f has the form f: 25 25.
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