
Big Oh and Relations - ColinWright
https://www.solipsys.co.uk/new/BigOhAndRelations.html
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empath75
I realize that the traditional algorithm for multiplication is O(n^2) with the
number of digits, but it’s kind of a questionable choice to use in a CS
context where it’s almost always considered O(1)

Good article, though, I hadn’t considered it as an equivalence class before.

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oddity
The “CS context” is very broad and diverse. In the context of teaching (which
is, I think closest to what you mean), arithmetic being O(1) is primarily
because it simplifies the analysis of most common algorithms. In this context,
the most important thing is to identify some set of operations of interest and
show how they scale to infinity. Instructors are primarily interested in
ensuring students know how to do this analysis. The exact set of operations is
unimportant. However, the side effect of this approach is that students walk
away with weird, incorrect assumptions of how the hardware works.

In non-academic contexts where performance matters, one should almost never
assume anything is O(1).

