You are correct, the point being made was that a lot of people aren't aware of that and just take it as gospel that O(1) algorithms must be faster than O(n) one

You are correct, the point being made was that a lot of people aren't aware of that and just take it as gospel that O(1) algorithms must be faster than O(n) ones -- but, as you said, big-O notation only says that is true after n goes above some threshold n0 which may be (and usually is) very large. After all, the most efficient (in terms of big-O) known algorithm for multiplying two numbers uses a 1729-dimensional Fourier transform and only becomes more efficient once the numbers involved are significantly larger than the number of atoms in the universe[1]. [1]: https://en.wikipedia.org/wiki/Galactic_algorithm https://en.wikipedia.org/wiki/Galactic_algorithm