The classic equivalence classes are the ones that deal with modular arithmetic. As you look at these examples, remember that numbers that are equivalent mod 4 for example, are related based on the remainder we get when we divide by 4. So 1, 5, 9, 13, … are all equivalent mod 4. What is common about all of these? Can you develop a general expression for any number that is equivalent to 1 mod 4? How do you know your expression is correct? What if you did the same for the values that are congruent to 2 mod 4? What about 3? What do you notice?
The classic equivalence classes are the ones that deal with modular arithmetic. As you look at these examples, remember that numbers that are equivalent mod 4 for example, are related based on the remainder we get when we divide by 4. So 1, 5, 9, 13, … are all equivalent mod 4. What is common about all of these? Can you develop a general expression for any number that is equivalent to 1 mod 4? How do you know your expression is correct? What if you did the same for the values that are congruent to 2 mod 4? What about 3? What do you notice?
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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The classic equivalence classes are the ones that deal with modular arithmetic. As you look at these examples, remember that numbers that are equivalent mod 4 for example, are related based on the remainder we get when we divide by 4. So 1, 5, 9, 13, … are all equivalent mod 4. What is common about all of these? Can you develop a general expression for any number that is equivalent to 1 mod 4? How do you know your expression is correct?
What if you did the same for the values that are congruent to 2 mod 4? What about 3? What do you notice?
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