Past exam of the year 1 of the computer science course of the University of Oxford / 2023 / Discrete mathematics, probability and continuous mathematics / 1 / d / iii

Table of contents
- Solution iii

Solution

The floor function is constant at

j

on the four consecutive integers

4 j, 4 j + 1, 4 j + 2, 4 j + 3

. Consequently the partition of a set is ${{4 j, 4 j + 1, 4 j + 2, 4 j + 3} : j \in N}$ . Different blocks are disjoint and every nonnegative integer has exactly one quotient and remainder upon division by

4

.

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