 Solution

ID: past-exam-of-the-year-1-of-the-computer-science-course-of-the-university-of-oxford/2022/discrete-mathematics-continuous-mathematics-and-probability-resit/2/c/i/solution

True. For every integer

n \geq 1

n^{2} \leq n^{3}

and

1 \leq n^{3}

. Therefore

0 \leq n^{3} + 1000 n^{2} + 96 \leq 1097 n^{3} .

C = 1097

and

N = 1

satisfy the definition of Big O notation. Whether the chosen convention for natural numbers includes zero is immaterial to this eventual assertion.

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