CMPSCI 251: Mathematics of Computation

David Mix Barrington

Spring, 2007

Discussion Notes #3

from Wednesday 14 February 2007

Proofs with Big-O Notation

In lecture this week we gave formal definitions of the big-O and big-Omega notation. Here f and g are functions from N to the reals, ε is a positive real, and n and n0 are naturals.

Questions are in black, answers in blue.

In this discussion we will use these definitions, and the proof rules for quantified statements from CMPSCI 250, to prove some of the properties of big-O and big-Omega. (Anyone who took 250 from me should remember the rules of Existence, Instantiation, Specification, and Generalization -- I'll go over these on the board as needed.)

Last modified 14 March 2007