Think of these slices as buckets, which hold a set of numbers. For example, 26 would go in the slice labelled 1, because .
Above is a figure that shows some integers that we would find in each of the slices.
The way we express this mathematically for mod C is:
- is the symbol for congruence, which means the values and are in the same equivalence class.
- tells us what operation we applied to and .
- when we have both of these, we call “” congruence modulo .
so it is in the equivalence class for 1, as well.
Insights into Congruence Modulo
First, we would label slices .
Then, for each of the integers, we would put it into a slice that matched the value of the integer .
Below is a figure that shows some representative values that we would find in each of the slices.
The values in each of the slices are equal to the label on the slice plus or minus some multiple of .
This means the difference between any two values in a slice is some multiple of .
This observation can help us understand equivalent statements and equivalence classes next.