Mathematical induction is concept for proving that if a procedure, or equation, P(n) is true for all positive integers n, you can prove that P(1) is true, and also that P(n+1) is true. The P(n+1) part if the induction. It is something that you believe to be true. It is something that you worked out long hand and found to be reasonable true.
Knuth writes a very large proof for the previously presented Algorithm E (Extended Euclid's algorithm). This one is nuts and I followed none of it. This goes on for 2 pages.
There was so much math. Knuth offers a way out for the sake of motivation allowing the reader to skim this chapter. After studying for 2 hours, and re-reading many times, I still could not understand the math. I get the induction part, which is what I think the purpose of the section truly is.
I took the out and accepted the skim.
Exercises
I remember being in college and taking a final exam where I could not even understand the questions. Oddly enough this was for a course in my field of study.
There were 15 exercises in this section. The most difficult being a level HM28. I felt like I was sitting in that lecture hall again reading and rereading that test. I was looking for an out and did not have one. Thankfully Knuth gave me one. No exercises were completed.