Iff was intentional. Although it seems not to be my reputation here, I am perfectly capable of doing math related to physics, and without making the usual mistakes. I had no tutoring resources to help me with that. Neither of my parents finished high school. This is one reason, I don't always take all of the given explanations or the math for granted. I can work it out for myself. Many techniques I developed over many years actually work better. You seem to be quite astute yourself, Schneibster. Nice conversing with you.