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Let I be the set of all integers and let m be a fixed positive integer. Two integers a and b are said to be congruent modulo m-symbolized by a is congruent to b (mod m) - if a - b is exactly divisible by m, i.e., if a - b is an integral multiple of m. Show that this is an equivalence relation , describe the equivalence set, and state the number of distinct equivalence sets.

Topology
Sets and Functions (XLVII)
Functions

Let I be the set of all integers and let m be a fixed positive integer. Two integers a and b are said to be congruent modulo m-symbolized by
a is congruent to b (mod m) - if a - b is exactly divisible by m, i.e., if a - b is an integral multiple of m.
Show that this is an equivalence relation , describe the equivalence set, and state the number of distinct equivalence sets.

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Topology
Sets and Functions (XLVII)
Functions

Let I be the set of ...

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This solution is comprised of a detailed explanation of the properties of the equivalence relation.
It contains step-by-step explanation of the following problem:

Let I be the set of all integers and let m be a fixed positive integer. Two integers a and b are said to be congruent modulo m-symbolized by
a is congruent to b (mod m) - if a - b is exactly divisible by m, i.e., if a - b is an integral multiple of m.
Show that this is an equivalence relation , describe the equivalence set, and state the number of distinct equivalence sets.

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