As the test approached, I was seriously worried about well-ordering and structural induction. We had only just covered these topics, and hadn't gotten to practice them in a tutorial. They felt exactly like the other flavours of induction to me, and I was confused as to why we needed to call them something different.
However, after rewriting the lecture problems with extra explanations on the side, everything just sort of...clicked. It suddenly made sense, when it didn't before.
Structural induction wasn't clear to me at the beginning because I didn't realize that having a recursive definition of a set was important to writing a structural induction proof. Or rather, structural induction is used to prove a claim about a set that can be recursively defined.
I noticed on the day of the test that many students were still confused about structural induction. To those still confused, I hope my illustrated explanation is somewhat helpful.
Today: Nanjing, China
We had cake; now we'll have pie! Zu Chongzhi 祖沖之 (429-500) was a Chinese mathematician whose approximation of pi was held as the most accurate for over 900 years. His approximation was 355/113 (3.1415929203...), whereas the Greeks' approximation was 22/7 (3.1428571428...). This is pretty impressive, because the only tools Zu used to approximate pi were sticks arranged in certain patterns.
No comments:
Post a Comment