I know that the relation n = Big-O(1) 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, please give me the proof of it being false using the constants. I'm getting confused with the constants, I don't know whether each relation used in the proof is having different constant or the same. Please enlighten on the topic.
TO prove: n= O(1) for n=1 , 1= O(1) proved
induction hypothesis : let it is true : n-1 = O(1) now we prove that n = O(1)
LHS : n = (n-1) + 1 = O(1) + 1 = O(1) + O(1) = O(1)
Falsely proved.. I want the clarification of the fallacy in terms of <= and constants, that is in the basic definition of Big-O.