The general rule for big-O is that you take the portion of the term that grows quickest and that becomes the big-O value. n^2 will grow FAR quicker than 6n, so whatever you're analyzing will have On^2 performance. e.g. if n = 1,000,000, n^2 = 1,000,000,000,000 and 6n = 6,000,000 or basically nothing in the bigger picture. I know that the relation n = Big-O1 is false. But if we use induction involving Big-O it can be proved. But the fallacy is we cannot induct Big-O. But my question is how we can disprove the relation by using the constants. The false proof is here. Big O notation is a mathematical notation that describes the limiting behavior of a function when the argument tends towards a particular value or infinity. It is a member of a family of notations invented by Paul Bachmann, Edmund Landau.

Big O tries to ignore these complicated details and look at how algorithms change when the size of the inputs change. So in big O notation, we drop the multiplication of constants. You might be tempted to say algorithm 1 is while algorithm 2 is, but we drop the constants and say they are both. Big O also prefers dominant terms to non-dominant.