>>12606237The phrase "without loss of generality we may assume P", where P is a stated proposition is correctly used in a situation when it does not matter for the argument whether P is true, or some other relevant condition different from P is assumed true. For instance, if your model of computation is a RAM in which addition of two integers can be performed in time O(1), you may assume for convenience that every addition of two integers can be performed in exactly one step. It makes computation of complexity bounds more easy.
