As a self-taught, I always get nervous when I see articles explaining Big O because they are almost always wrong. While this one is mostly correct, it is a bit simplistic and misleading, and it could use considerable annotations. The "scary" Wikipedia article has examples that are more nuanced than what is written here; the first example shows a constant time algorithm with nested for loops.

I take issue with the math fearing throughout the article. Time complexity is math, period. There is no getting around this fact, and the sooner you accept it, the sooner you learn that the math isn't that difficult, and the sooner you realize that, without some intuition on what the math is saying, you'll never really have a firm grasp of Big O or any of the other variations.

And also, why no mention of log time?