Entry #4

This week we did more proofs. It is very challenging but interesting. However, I did have hard time understanding the proof of prime number, because there are many underlying math knowledge.

If I came across this problem for the first time, I could  think of using proof by contradiction. The general structure and first few steps were easy to come up. However, I would definitely get stuck on the fourth line of the proof. I had to know that prime number starts from 2. I felt this comment was not understandable, because I did not know why we could use this fact without proving it. There were more lines that I was confused with. The comment in the line 6 was not a fact that I could come up by myself. 

The question that bothered me was that I did not know what math knowledge that we could use for granted, because I felt like other than some basic algebra knowledge, I had to prove anything in 165. 

I tried to figure out a another way to prove it without using those facts

Plan: prove by contradiction, and get some result that is contradict to a fact

Carry out plan:
Assume there is finite prime number
           then p1,p2,......pk are prime numbers
           then  (where I get stuck)

Result
I could not come up with another to prove it. Therefore, I chose to understand the way that Danny gave us (sad!)