Practice question · Numerical answer
The relation 'has the same remainder when divided by 3' partitions the integers into equivalence classes. How many classes are there?
Hints
- List the possible remainders on division by 3.
- Each distinct remainder collects one class.
Show the answer
3
Why
The possible remainders are 0, 1 and 2, giving exactly three classes. Every integer lands in precisely one of them, the defining feature of a partition, and the reason equivalence relations and partitions are two views of the same idea.
Practise Relations and Equivalence
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