Note that only the highest exponent is relevant. With some work we could prove that for example O(n^3 + n^2 + n) is equivalent to O(n^3).
just adding on for others that “some work” can be simply explained as figuring out the answer to “as n grows, which of n3, n2 or n affects the result the most?”
Yes, it’s pretty intuitive. A formal proof is still a bit more work than what I can fit in an ELI5 but at the same time simple enough that it can be given to a 2nd semester computer science student as an exercise.
just adding on for others that “some work” can be simply explained as figuring out the answer to “as
ngrows, which of n3, n2 or n affects the result the most?”Yes, it’s pretty intuitive. A formal proof is still a bit more work than what I can fit in an ELI5 but at the same time simple enough that it can be given to a 2nd semester computer science student as an exercise.