Thanks for the detail - self taught so I'll defer and try to take on board (also written quickly - I'm sure doing no help to my annoyance that sparked the response - the single minded and to me complex approach of most of these explanations - which I'm sure you'll agree many of which make the same mistakes I have)

one question though - do you have a source for this 'irregularities' bit? I've never seen that mentioned before at all and a Google hasn't helped. doesn't seem to fit with 'upper bound' and 'worst case'.

[edit: also still not sure how you say im confusing for theta. that's what 'the largest number of times it might' was for.]