I get the gist of what you are saying and agree with some of it. I still think the article isn't sufficient, at all, for even an elementary introduction to anything. It's incredibly incomplete. An introductory cs course is going to present asymptotic complexity analysis (written using Landau notation) as one of the TOOLS for thinking about the efficiency of code. It will hopefully not just hop to big O without setting up the context. The author can fix this by just reworking the preface. It needs to answer the question: "why are we doing this and how will this accomplish anything?"

If you fail to frame the context and the semantics well enough, you'll end up with people running around saying that an algorithm is "big O of blah." AGH

The introduction to the concept is articulated by the following comparison:

'We want to measure code efficiency. Big O notation describes this. Here are some examples.'

vs.

'We want to measure code efficiency. We can do this by thinking about its usage of resources (complexity). for example, total run time and memory usage. One of the ways to compare the efficiencies of algorithms is to compare their asymptotic behaviors. We can express this using big O notation. Here are some examples.'

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The author talks about how big O notation is awesome because you can drop the constants. It is not explained why this is awesome or useful. Interestingly, it later says that sometimes it isn't good because the constants sometimes matter. What is the reader supposed to understand here?

There's no followup as to what to think about after you determine the "big O" of an algorithm. Either he forgot to write this or figured that it was obvious at that point. Considering that he didn't sufficiently explain the concept's motivation either, I don't see how an uneducated reader will get a clear picture.