> Ultimately when an algorithm has worse complexity than another it might still be faster up to a certain point.
Sure, but the author didn't argue that the simpler algorithm would be faster for 5 items, which would indeed make sense.
Instead, the author argued that it's OK to use the simpler algorithm for less than 5 items because 5 is a constant and therefore the simpler algorithm runs in constant time, hence my point that you could use the same argument to say that 2^140 (or 2^256) could just as well be used as the cut-off point and similarly argue that the simpler algorithm runs in constant time for all arrays than can be represented on a real-world computer, therefore obviating the need for the more complex algorithm (which obviously makes no sense).
If you set n=2^140, then sure, it’s constant. If instead you only have n<=2^140, then n varies across a large set and is practically indistinguishable from n<=infinity (since we get into the territory of the number of atoms in the universe), therefore you can perform limit calculations on it, in particular big O stuff.
In the article n was set to 5. All of those arrays (except maybe 1) have exactly 5 elements. There is no variance (and even if there was, it would be tiny, there is no point in talking about limits of 5-element sequences).
Sure, but the author didn't argue that the simpler algorithm would be faster for 5 items, which would indeed make sense.
Instead, the author argued that it's OK to use the simpler algorithm for less than 5 items because 5 is a constant and therefore the simpler algorithm runs in constant time, hence my point that you could use the same argument to say that 2^140 (or 2^256) could just as well be used as the cut-off point and similarly argue that the simpler algorithm runs in constant time for all arrays than can be represented on a real-world computer, therefore obviating the need for the more complex algorithm (which obviously makes no sense).
In the article n was set to 5. All of those arrays (except maybe 1) have exactly 5 elements. There is no variance (and even if there was, it would be tiny, there is no point in talking about limits of 5-element sequences).