I you're right. In fact in the optimizer part I say (in a simple way) that big O (i.e. asymptotic complexity) is not the same as CPU cost but it's easier for me because the real cost of an operation depends on the CPU architecture.

Someone told me the same on the article comments and here is the answer I gave him:

You’re right and I agree with you. When I wrote this part, I REALLY hesitated to give the real asymptotic definition and what it means for the number of operations but I chose a simpler explanation since the aim of this post is not to become an expert but to have a good idea. I hope that this won’t mislead people but I thought the real definition was too hard for a “newcomer” and not important to understand a database. This is also why I added in this part “The time complexity doesn’t give the exact number of operations but a good idea.” and said at the end of the part “I didn’t give you the real definition of the big O notation but just the idea” with a link to the real definition.