The definition of a "big" input size is somewhat circular, yes. "The big O performance of an algorithm only matters for a sufficiently large value of n." "Def

The definition of a "big" input size is somewhat circular, yes. "The big O performance of an algorithm only matters for a sufficiently large value of n." "Define a sufficiently large value of n." "Large enough that the big O performance of the algorithm starts to matter more than the coefficients of n and constant time operations." So yes, that could be 10 or 10 million depending on the nature of the problem, the constants and coefficients of the algorithm, the language, the hardware, etc etc. You could have an algorithm that takes factorial time but maybe you're only using it in a problem domain where n is always < 10 so you'll probably never notice or care that it's O(n!)