SLOG 9 November 17th 2014

During last week's CSC165, I learned about what big O and big Omega meant, and how the functions look like graphically, as well as how to prove that some functions are of big O or big Omega of others.  I learned that a big O function of a function f is a function that always produces a y value greater than f(x) when x is greater than a certain value.  This value is denoted as B, the break point.  The value c in the definition of a big O function is essentially the multiplier that makes the big O function greater than f.  Big Omega is basically the same as big O, except big Omega is a function that is always below function f after the break point.  What below means is that every y value that big Omega returns is less than f(x).  Then, knowing the full definition of big O and big Omega, the professor showed us a number of new relationships that about big O and big Omega.  I learned that when attempting to prove these relationship, it is much easier to first picture the relationship in my head.  For example, if the statement is something such as ' if f is O(g) and g is O(h), then f is O(h)'.  Thinking about this scenario graphically, i realise that f is bounded above by g, which is bounded above by h, so f is also bounded above by h.  I think that the difficult part of these proofs is not finding the c value, but locating the correct B, because the value c's relationship to the functions is directly shown through the definitions of big O and big Omega, but B is only found when we start creating boundaries of n through our manipulations.  Therefor, it is sometimes hard for me to keep track of all of the boundaries that i have set for n through my proof.