The difficulty I had with this section is that there were no examples of application of relatively prime integers. It was stated in the text that we would see that they are very useful. However, I only read about theorems and lemmas and proofs thereof. Perhaps we will see their usefulness later on. I suppose, actually, that there was one reference to its usefulness. At the end of the section it stated:
"By Theorem 11.16 then, if we wish to show that 12, say, divides some integer c, we need only show that 3|c and 4|c since 12 = 3 · 4 and 3 and 4 are relatively prime."
It didn't actually show how to do this, but it did mention it. I typically retain the knowledge better if I see some examples.
Looking back on previously learned mathematics, I don't recall ever hearing about relatively prime numbers. I am grateful for the opportunity in this class to learn about a lot of new topics, definitions, and mathematical ideas. When I come across something new in this class, I always think - I should have learned this, or at least heard about this, before during one of my mathematics classes or textbooks. It is surprising to me that I haven't. It leads me to believe that there is more to learn than I could even imagine. After all, many mathematicians let scholastic discovery be their life's pursuit and I'm sure there is no way to ever know it all.
No comments:
Post a Comment