6. Define the floor [x] of a real number x to be "a rounded down", in other words, the greatest integer less than or equal to : [x] = max{m | m = Z, m ≤ x} For instance, [-2] = -2, [1.74] = 1, and [] = 3. Define the relation S on the set R of all real numbers: = {(x, y) | [x] = [y]}. For instance, (π, 3.7) = S, because the floor of both is 3. Describe the equivalence classes of R under S. You will not be able to list them out, but you should be able to name a few and tell that there is one equivalence class for each...
6. Define the floor [x] of a real number x to be "a rounded down", in other words, the greatest integer less than or equal to : [x] = max{m | m = Z, m ≤ x} For instance, [-2] = -2, [1.74] = 1, and [] = 3. Define the relation S on the set R of all real numbers: = {(x, y) | [x] = [y]}. For instance, (π, 3.7) = S, because the floor of both is 3. Describe the equivalence classes of R under S. You will not be able to list them out, but you should be able to name a few and tell that there is one equivalence class for each...
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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discrete math
![6. Define the floor [x] of a real number a to be "a rounded down", in other
words, the greatest integer less than or equal to x:
[x] = max{m | m = Z, m ≤ x}
For instance, [-2] = −2, [1.74] = 1, and [π] = 3.
Define the relation S on the set R of all real numbers:
S = {(x, y) | [x] = [y]}.
For instance, (π, 3.7) = S, because the floor of both is 3.
Describe the equivalence classes of R under S. You will not be able to list them
out, but you should be able to name a few and tell that there is one equivalence
class for each...](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7cef3050-b0aa-40af-9112-57cab04a18ba%2F0e557a19-bee4-4bde-b208-67edc25f3910%2Fiwqzqo9_processed.jpeg&w=3840&q=75)
Transcribed Image Text:6. Define the floor [x] of a real number a to be "a rounded down", in other
words, the greatest integer less than or equal to x:
[x] = max{m | m = Z, m ≤ x}
For instance, [-2] = −2, [1.74] = 1, and [π] = 3.
Define the relation S on the set R of all real numbers:
S = {(x, y) | [x] = [y]}.
For instance, (π, 3.7) = S, because the floor of both is 3.
Describe the equivalence classes of R under S. You will not be able to list them
out, but you should be able to name a few and tell that there is one equivalence
class for each...
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