Either way is correct. "Have defined" sounds a little more conventional, but it depends on context. If the simple past makes more sense to you, then you shoul

Either way is correct. "Have defined" sounds a little more conventional, but it depends on context. If the simple past makes more sense to you, then you should use it. > Simple past is used when there is a specific time involved. For instance "although we defined the Riemann Sum in chapter eight..." is correct while "although we have defined the Riemann sum in chapter eight" is probably wrong.