With the O() notation the units are some arbitrary computation step or arbitrary unit of memory, which could even mean matrix multiplication of two 1024x1024 ma

With the O() notation the units are some arbitrary computation step or arbitrary unit of memory, which could even mean matrix multiplication of two 1024x1024 matrices of doubles. The whole point of big-O notation is that you don’t care about how fast/expensive it is, but how it scales.