1.3 Defining O-notation

Question 1

Formal definition of:

Answer 1

Question 2

Formal definition of:

Answer 2

Question 3

Formal definition of:

Answer 3

Question 4

Formal definition of:

Answer 4

Question 5

Formal definition of:

Answer 5

Question 6

Intuitive meaning and comparison analogue of:

Answer 6

Question 7

Intuitive meaning and comparison analogue of:

Answer 7

Question 8

Intuitive meaning and comparison analogue of:

Answer 8

Question 9

Intuitive meaning and comparison analogue of:

Answer 9

Question 10

Intuitive meaning and comparison analogue of:

Answer 10

Question 11

How to prove something f(n) is in _ notation?

Answer 11

• Prove that there exists C, n_0 for all n >= n_0
• It is essential to prove that something is true for all n >= n_0, not just a specific value
• Can often be reasoned and simplified using equalities

Question 12

How does multi-variable O-notation work for f(m,n)

Answer 12

Question 13

What is the requirement for negative functions?

Answer 13

Functions must eventually become non-negative as n becomes larger.