Asymptotic Notation 4 - More Using Definitions

[@Deksudo]

1. Formal definitions of the asymptotic sets. Check. 2. Uses "element of" and not the equality sign. Check. 3. Easy to follow reasoning with tight mathematical notation. Check. I hereby declare this to be the best playlist on asymptotic notation. Better than MIT's OCW!

[@sarelaiber2775]

This channel is amazing! Extremely clear and very-well laid out. It is a pleasure learning from you. Some nitpicking - in 4:26 you say you divide by n^2 as it is always positive. If I understand this correctly then that would be true only if you hadn't decided to adopt the definition of 0 as a natural number (making n nonnegative, rather than positive). So I think we might say "Assume n>=1 and then divide both sides by n^2" and later on intersect the solution of n>=7 with the assumption that n>=1, getting to the desired n>=7. The very fact that I picked up on that is a testament that your explanations are crystal clear and verbose, not hiding any thinking from the viewer. Amazing pedagogy. I plan on refreshing and deepening my knowledge of algorithm analysis using your channel. It is an absolute gem, and I am so lucky to have found it.

[@jeremiahayres103]

So is the goal not to get a negative C for big omega? Meaning if we just have used the -7n^3 and have gotten c= sqrt(-1) for big omega?

[@kilahan1411]

in 1:45, is that should be square root of 14 n^3 instead of 15 n^3 because of 6 + 3 + 5 = 14?

[@ProfessorPainter]

Correct! Basic arithmetic is my nemesis. Thanks for the catch :)